Broad Street Scientific 2018-2019

BROAD
STREET
SCIENTIFIC
VOLUME 8 | 2018-2019
The North Carolina School of Science and Mathematics Journal of
Student STEM Research

Front Cover
This map segment of Durham features
the North Carolina School of Science and
Mathematics campus (upper-center) as well as
the nearby Duke University campus (lowerleft)
and several historic neighborhoods. Map
data © 2019 Google; Image created by Kathleen
Hablutzel.
Approximate Scale: 6.5 kilometers
Biology Section
This image of the dorsal raphe nucleus labels
dopamine neurons in green, red, and yellow.
This region of the brain is critical in generating
the increased sociability that typically occurs
after a period of social isolation. Image credit
Gillian Matthews, Ungless Lab, Imperial
College London.
Approximate Scale: 450 micrometers
Chemistry Section
This is a transmission electron microscope image
of a graphene lattice. Graphene is a periodic
structure entirely composed of carbon atoms. At
this scale, individual atoms can be observed at
the corners of the hexagons. Image credit Ethan
Minot, Department of Physics, Oregon State
University (Original grayscale image colorized).
Approximate Scale: 4 nanometers

Engineering Section
Visualizing patterns of air traffic over the
contiguous United States reveals major airports
and commonly flown-over regions. The darkest
areas receive little-to-no flyovers. Image credit
Aaron Koblin, Scott Hessels, and Gabriel
Dunne, UCLA.
Approximate Scale: 4500 kilometers
Mathematics and Computer Science Section
The Opte Project aims to visualize the internet
by mapping routing paths from all over the
world. Each color represents computers from a
different region of the world. This visualization
is from 2015. Image credit Barrett Lyon/The
Opte Project.
Approximate Scale: One zettabyte for the
year 2015
Physics Section
The Baryon Oscillation Spectroscopic Survey
(BOSS) Great Wall, a galaxy supercluster, is
one of the largest structures in the observable
universe. This image shows a simulation of how
galaxy clusters form. The filaments are regions
where galaxies are more likely to be found.
Image credit Volker Springel, Max Planck
Institute for Astrophysics.
Approximate Scale: 1 billion light years
Back Cover
Scientific collaborations span the globe.
This map depicts collaboration networks
between researchers in different locations.
Collaborations often - but not always - seem
to follow linguisic and cultural connections.
Image computed by Oliver H. Beauchesne and
SCImago Lab, data by Elsevier Scopus.
Approximate Scale: 39,000 kilometers

TABLE of CONTENTS
4 Letter from the Chancellor
5 Words from the Editors
6 Broad Street Scientific Staff
7 Essay: The AI We Haven't Considered
JACKSON MEADE, 2020
Biology
10 Overexpression of a Heat Shock Protein in Cyanobacteria to Increase Growth Rate
ROBERT LANDRY, 2019
18 Hypoglycemic Effect of Momordica charantia Against Type 2 Diabetes Modeled in Bombyx mori
AARUSHI VENKATAKRISHNAN, 2019
Chemistry
26 Tetraethyl Orthosilicate-Polyacrylonitrile Hybrid Membranes and their Application in Redox
Flow Batteries
ETHAN FREY, 2019
32 Novel Synergistic Antioxidative Interactions Between Soy Lecithin and Cyclodextrin-
Encapsulated Quercetin in a Lipid Matrix
ANIRUDH HARI, 2019
37 Utilization of Atomic Layer Deposition to Create Novel Metal Oxide Photoanodes for Solar-
Driven Water Splitting
ANNIE WANG, 2019

Engineering
44 Using a Hybrid Machine Learning Approach for Test Cost Optimization in Scan Chain Testing
LUKE DUAN, 2019
49 Novel Water Desalination Filter Utilizing Granular Activated Carbon
GEOFFREY FYLAK, 2019
Mathematics and Computer Science
59 Long Prime Juggling Patterns
DANIEL CARTER AND ZACH HUNTER, 2019
67 An Analysis of a Novel Neural Network Architecture
VATSAL VARMA, 2019 ONLINE
Physics
75 Effects of Relativity on Quadrupole Oscillations of Compact Stars
ABHIJIT GUPTA, 2019
84 Effect of Elliptic Flow Fluctuations on the Two- and Four-Particle Azimuthal Cumulant
BRIAN LIN, 2019
Featured Article
89 An Interview with Dr. Valerie Ashby

LETTER from the CHANCELLOR
"Science is a cooperative enterprise, spanning the generations. It's the passing of a torch from teacher, to student, to
teacher. A community of minds reaching back to antiquity and forward to the stars."
~ Dr. Neil deGrasse Tyson
I am proud to introduce the eighth edition of the
North Carolina School of Science and Mathematics’
(NCSSM) scientific journal, Broad Street Scientific. Each
year students at NCSSM conduct significant scientific
research, and Broad Street Scientific is a student-led and
student-produced showcase of some of the impressive
research being done by students.
Excellence in scientific research has a deep and
far-reaching impact on nearly every aspect of daily life,
including (among other areas) health care, food safety,
space travel, national security, and the environment.
When NCSSM students are given opportunities to apply
their learning through research, they are doing more than
increasing their individual knowledge; their valuable
work is increasing our collective body of knowledge
and strengthening our ability to address current global
challenges and prepare for those to come.
Opened in 1980, NCSSM was the nation’s first public
residential high school where students study a specialized
curriculum emphasizing science and mathematics.
Teaching students to do research and providing them with
opportunities to conduct high-level research in biology,
chemistry, physics, computational science, engineering
and computer science, math, humanities, and the social
sciences are critical components of NCSSM’s mission
to educate academically talented students to become
state, national, and global leaders in science, technology,
engineering, and mathematics. I am thrilled that each year
we continue to increase the outstanding opportunities
NCSSM students have to participate in research.
This publication serves to highlight some of the high
quality research students conduct each year at NCSSM
under the direction of our outstanding faculty and in
collaboration with researchers at major universities. For
thirty-four years, NCSSM has showcased student research
through our annual Research Symposium each spring and
at major research competitions such as the Regeneron
Science Talent Search and the International Science and
Engineering Fair. The publication of Broad Street Scientific
provides another opportunity to share with the broader
community the outstanding research being conducted by
NCSSM students each year.
I would like to thank all of the students and faculty
involved in producing Broad Street Scientific, particularly
faculty sponsor Dr. Jonathan Bennett, and senior editors
Emily Wang, Navami Jain, and Kathleen Hablutzel.
Explore and enjoy!
Dr. Todd Roberts, Chancellor
4 | 2018-2019 | Broad Street Scientific

WORDS from the EDITORS
Welcome to the Broad Street Scientific, NCSSM’s journal
of student research in science, technology, engineering
and mathematics. In this eighth edition of Broad Street
Scientific, we hope to inspire readers to get involved in the
scientific community by sharing the innovative research
conducted by our students. We hope you enjoy this year’s
edition!
This year’s theme is networks: the connections we
find within and between groups throughout our world.
Connectivity is an integral component of modern life,
and studying people or objects interacting in networks
allows us to describe collective behavior of groups.
Billions of interconnected neurons comprise the human
brain, yet a brain is more than a bunch of cells. Brains can
think, feel, and act both consciously and unconsciously.
Thus, networks do not simply behave as the sum of their
parts. Networks are powerful in predicting the complex
behavior of a dynamic group without needing complex
information on each individual in a network. For example,
networks can predict the spread of an infectious disease
without needing information on each individual in the
network. Networks are powerful tools in describing our
interconnected world.
In the featured images of this journal, we explore the
scales of networks, from the atomic to astronomical levels.
The featured image for the Chemistry section displays
a network of carbon atoms on the scale of fractions of
a nanometer, while the featured image for the Physics
section displays a network of superclusters of galaxies on
the scale of approximately one billion light years – one of
the largest known structures in the universe. On any scale,
our world is built on interactions, and these interactions
organize our world into networks.
We would like to thank the faculty, staff and
administration of NCSSM for their continued support
towards our student researchers. It is this unmatched
encouragement that prepares us to use our interests and
skills in STEM to address problems in our community,
both locally and beyond. For 39 years, NCSSM has
fostered an environment conducive to learning through
encouraging students to take risks and take ownership of
their academic path. We would especially like to thank our
faculty advisor, Dr. Jonathan Bennett, for his support and
guidance throughout the publication process. We would
also like to thank Chancellor Dr. Todd Roberts, Dean of
Science Dr. Amy Sheck, and Director of Mentorship and
Research Dr. Sarah Shoemaker. Lastly, the Broad Street
Scientific would like to acknowledge Dr. Valerie Ashby,
chemistry professor and Dean of Trinity College of Arts
and Sciences at Duke University, for speaking with us
about her inspiring journey in STEM and offering advice
to young prospective scientists.
Kathleen Hablutzel, Navami Jain, and Emily Wang
Editors-in-Chief
Broad Street Scientific | 2018-2019 | 5

BROAD STREET SCIENTIFIC STAFF
Editors-in-Chief
Kathleen Hablutzel, 2019
Navami Jain, 2019
Emily Wang, 2019
Publication Editors
Rohit Jagga, 2020
Grishma Patel, 2019
Sanjana Pothugunta, 2020
Eleanor Xiao, 2020
Biology Editors
Megan Wu, 2019
Ishaan Maitra, 2020
Joseph Wang, 2020
Chemistry Editors
Melody Wen, 2020
Varun Varanasi, 2020
Engineering Editors
Aakash Kothapally, 2020
Jason Li, 2020
Mathematics and
Computer Science Editors
Hahn Lheem, 2019
Olivia Fugikawa, 2020
Physics Editors
Will Staples, 2020
Ben Wu, 2020
Faculty Advisor
Dr. Jonathan Bennett
6 | 2018-2019 | Broad Street Scientific

THE AI WE HAVEN'T CONSIDERED
Jackson Meade
Jackson Meade was selected as the winner of the 2018-2019 Broad Street Scientific Essay Contest. His award included the
opportunity to interview Dr. Valerie Ashby, distinguished chemist and professor and Dean of Trinity College of Arts and
Sciences at Duke University. This interview can be found in the Featured Article section of the journal.
“People worry that computers will get too smart and take over the world, but the real problem is that they’re too stupid and they’ve
already taken over the world.”
~ Pedro Domingos
When we bring up artificial intelligence in
conversation, the rhetoric is relatively future-oriented.
Discussions about the “possibilities” AI possesses – and
the dangers it poses – abound, all in the context of what
our technological future holds. But peel back the layer of
speculation, and you may find something surprising. It
might not be obvious, but artificial intelligence is already
here – in fact, it’s everywhere.
Though that statement sounds concerning, there isn’t
a conspiracy of shadowy Artificial Intelligences operating
behind the backs of the public. We’ve simply grown
accustomed to its cohabitation in our systems. Artificial
Intelligence, through “Machine Learning,” started
accelerating in 1957, when Frank Rosenblatt designed
the first Neural Network, called a perceptron (Lewis &
Denning), to model the structure of the human brain
(Marr). By 1985, Professor Terry Sejnowski had created
NetTalk, which could pronounce 20,000 English words
with just a week of training (New York Times).
When you flip through a stuffed email inbox, machine
learning keeps it from exploding by marking most of the
spam and trashing it, arguably with impressive precision
(Aski & Sourati). Go to your search engine and type your
query, and the “suggested search” bar that appears at the
bottom, as well as the results your query generates, are the
product of a well-trained, personalized machine learning
algorithm (Schachinger). When you purchase something
on Amazon or scroll through your recommended videos
page on YouTube, a machine learning system makes sure
you see the kinds of things you might want to watch or
buy, even if you couldn’t articulate it yourself. If you are
looking at a screen, it is likely that machine learning had
its hands (for lack of a more computerized term) in it.
Since the early days of computing, computers have
required painstaking algorithms – increasing by orders of
magnitude in complexity – to do anything from displaying
text to managing Google’s 40,000 search queries per
second (Alphabet, Inc). This creates a ceiling of capabilities
for our systems that grows infinitely harder to raise. But
computer systems are, after all, human systems, and we
should model them that way. This is exactly what machine
learning algorithms do. Based on inferences from the data
we give them, they teach themselves how to analyze and
manipulate it, and the more data we give them, the better
they get at doing their jobs (Faggella) (Lewis & Denning).
This is significantly “human” – barring willful ignorance,
we get better at analyzing and understanding our world
given new information.
Despite possible concerns, you are kept safe because of
machine learning. In 2014, Kaspersky Lab's Anti-Malware
Research Team processed between 200,000 and 315,000
malicious files per day (Kaspersky Lab). But malicious files
aren’t so different from each other, so machine learning
algorithms can very easily identify the code for files with
malicious intent far faster than any human actors could. In
a country and world growing ever more concerned with
data security, these algorithms provide a necessary wall
between us and the actions of evil people.
In our finances, we’re relinquishing control to the
machines as well. Micromanagement of our funds is a
multibillion-dollar business, and artificial intelligence
completely disrupts it. While humans are good at predicting
what the stock market can do over large spans of time
because of noticeable trends, on smaller and smaller time
scales and in more volatile markets, our grand spending
schemes are fundamentally nothing short of guesswork.
And while machine learning algorithms are admittedly
built on guesswork, they can achieve super-human levels
of accuracy during training on multitudes of data that are
simply unattainable for even the most dedicated human.
Predicting stocks is not the only artificial-intelligenceguided
moneymaker around. Advertising is one of the most
lucrative businesses of the modern world, having generated
about $32.66 billion dollars in revenue for Google’s parent
company, Alphabet, in Quarter 2 of 2018 (D’Onfro). This
comes from thousands of paying customers, all of them
companies hoping their product appeals to the right niche,
and only works because of machine learning.
Broad Street Scientific | 2018-2019 | 7

In this realm, one cannot avoid the topic of driverless
cars. Artificial intelligences are crucial to computer vision
algorithms (Khirodkar, Yoo, & Kitani), though other
hard-coded solutions can aid them. 74% of automotive
company executives expect that these smart cars will be on
the road by 2025, according to a report from IBM (IBM).
The menial tasks of our lives – our driving, our purchases
– will be automated if they can be.
We have been exploring the risks of developing artificial
intelligences prior to the day we could make them. In 1942,
science fiction author Isaac Asimov published his nowfamous
laws of robotics in a short story, “Runaround.”
They stated:
First, “A robot may not injure a human being or,
through inaction, allow a human being to come to harm.”
Second, “A robot must obey the orders given to it by
human beings, except where such orders would conflict
with the First Law.
Third, “A robot must protect its own existence as long
as such protection does not conflict with the First or
Second Law.”
But restricting our concerns about Artificial Intelligence
to this view is too narrow. It comes from an assumption
about the types of intelligences we intend to create. It
assumes that we will “build ourselves” – that we will build
copies of humans, in humanoid robot bodies with human
emotions and human capabilities.
We are a species that changes its environment to fit its
needs instead of adapting to its surroundings. Machine
learning and artificial intelligence are the newest evolution
of this pattern – just another way that the world and the
patterns within it can be adjusted according to our wishes.
The patterns of our world once influenced us to a degree
we could not control, but artificial intelligence will allow
us to take full control and then completely relinquish it. All
this works because machine learning is based in prediction
– on understanding the once-unintelligible patterns that
comprise the fabric of our world. That is a flaw that could
spell the end of our humanity.
It seems unlikely a malicious AI will attempt to literally
end life on Earth. At the least, we have Asimov’s three laws
to thank for that. But in a world where everything can be
predicted, where everything we want to see can be shown
to us, and where things that are “unpopular” or “troubling”
never reach our eyes, it feels like a part of our humanity
is lost. An artificial intelligence could operate in plain
sight, tailoring our world to the patterns that dictate us.
As mentioned, artificial intelligences are human systems,
so they will follow the human model of changing the world
to fit their needs. It is reasonable that if our needs rely on a
series of predictable patterns, then an artificial intelligence
with benevolent intentions could inadvertently neutralize
the world’s ideological diversity and the differences that
give us the human condition.
This isn’t to say that we shouldn’t create artificial
intelligences – in fact, it seems clear that our modern
world couldn’t operate without them. There are proactive
steps we must take to be stewards of our humanity. We
must make an active choice to diversify our interests
and the viewpoints to which we expose ourselves, even
when they aren’t completely satisfying. We should model
another fundamental element of our humanity into our
artificial intelligences: variation. Our machine learning
algorithms cannot rely on optimizing patterns alone – they
must contain anomalies in their paradoxically predictive,
average-based algorithms. If we do this, we can ensure
that our artificial intelligences will enhance us instead of
dictating conformity.
References
A Q & A with Pedro Domingos: Author of ‘The Master
Algorithm’ [Interview by J. Langston]. (2015, September
17). Retrieved January 4, 2019, from https://www.
washington.edu/news/2015/09/17/a-q-a-with-pedrodomingos-author-of-the-master-algorithm/
Aski, A. S., & Sourati, N. K. (2016). Proposed efficient
algorithm to filter spam using machine learning
techniques. Pacific Science Review A: Natural Science
and Engineering, 18(2), 145-149. doi:10.1016/j.
psra.2016.09.017
D’Onfro, J. (2018, July 23). Alphabet jumps after big
earnings beat. Retrieved January 7, 2019, from https://
www.cnbc.com/2018/07/23/alphabet-earnings-q2-2018.
html
Faggella, D. (2018, December 21). What is Machine
Learning? | Emerj - Artificial Intelligence Research and
Insight. Retrieved January 9, 2019, from https://emerj.
com/ai-glossary-terms/what-is-machine-learning/
Google Search Trends, Search Per Second. (n.d.).
Retrieved January 12, 2019, from https://trends.google.
com/trends/?geo=US
IBM (2015). Automotive 2025: Industry without Borders.
IBM Institute for Business Value. Retrieved January
9, 2019, from http://www-935.ibm.com/services/
multimedia/GBE03640USEN.pdf
Kaspersky Lab is Detecting 325,000 New Malicious
Files Every Day. (n.d.). Retrieved January 5, 2019, from
https://www.kaspersky.com/about/press-releases/2014_
kaspersky-lab-is-detecting-325000-new-malicious-filesevery-day
8 | 2018-2019 | Broad Street Scientific

Khirodkar, R., Yoo, D., & Kitani, K. M. (2018).
VADRA: Visual Adversarial Domain Randomization
and Augmentation. Carnegie Mellon University.
Retrieved December 10, 2018, from https://arxiv.org/
pdf/1812.00491.pdf
Learning, Then Talking. (1988, August 16). Retrieved
January 6, 2019, from https://www.nytimes.
com/1988/08/16/science/learning-then-talking.html
Lewis, T. G., & Denning, P. J. (2018). The Profession of
IT: Learning Machine Learning. Communications of the
ACM, 61(12), 24-27. Retrieved December 26, 2018, from
https://calhoun.nps.edu/bitstream/handle/10945/60898/
Denning_Learning_Machine_Learning_ACM_2018-12.
pdf?sequence=1&isAllowed=y.
Levenson, E. (2014, January 31). The TSA is in the
Business of ‘Security Theater,’ Not Security. Retrieved
January 7, 2019, from https://www.theatlantic.com/
national/archive/2014/01/tsa-business-security-theaternot-security/357599/
Marr, B. (2016, March 08). A Short History of Machine
Learning -- Every Manager Should Read. Retrieved
January 5, 2019, from https://www.forbes.com/sites/
bernardmarr/2016/02/19/a-short-history-of-machinelearning-every-manager-should-read/#2493077c15e7
Matney, L. (2017, May 17). Google has 2 billion users on
Android, 500M on Google Photos. Retrieved January 5,
2019, from https://techcrunch.com/2017/05/17/googlehas-2-billion-users-on-android-500m-on-google-photos/
Schachinger, K. (2018, December 06). A Complete Guide
to the Google RankBrain Algorithm. Retrieved January
4, 2019, from https://www.searchenginejournal.com/
google-algorithm-history/rankbrain/
Scott, T. (2018, December 06). Retrieved January 13,
2019, from https://www.youtube.com/watch?v=-
JlxuQ7tPgQ
Wu, J., Zhang, C., Xue, T., Freeman, W. T., &
Tenenbaum, J. B. (2016). Learning a Probabilistic Latent
Space of Object Shapes via 3D Generative-Adversarial
Modeling. Advances In Neural Information Processing
Systems, 29. Retrieved November 11, 2018, from https://
arxiv.org/abs/1610.07584.
Yoganarasimhan, H. (2017). Search Personalization
Using Machine Learning. SSRN Electronic Journal.
doi:10.2139/ssrn.2590020
Broad Street Scientific | 2018-2019 | 9

OVEREXPRESSION OF A HEAT SHOCK PROTEIN IN
CYANOBACTERIA TO INCREASE GROWTH RATE
Robert Landry
Abstract
To increase earth’s capacity to support human population growth, methods of growing food more efficiently, especially
in warmer environments as climate change progresses, must be developed. This project sought to increase the growth
rate of one population of photosynthetic organisms, cyanobacteria, through genetic engineering. Synechococcus elongatus
UTEX 2973 cultures were transformed to overexpress dnaJ, a heat shock protein, in normal and heat-stressed conditions
to determine the gene’s effects on growth rates. The growth rates of the dnaJ overexpressing strain were related to the
control--wild-type Synechococcus elongatus UTEX 2973 transformed with a plasmid without dnaJ--through comparisons
of optical density measurements at 745 nanometers (OD745), which can accurately quantify growth rates. The change
in OD745 in the dnaJ overexpressing strain was significantly greater than the OD745 measurements for the control in
normal conditions. When the temperature was increased to 42˚C, the dnaJ overexpressing strain continued to grow,
while the control strain’s OD745 measurements decreased. From this data, it appeared that the overexpression of a heat
shock protein in the genome of cyanobacteria significantly increased their growth rates and provided heat resistance.
Researching the effects of overexpressing a heat shock protein could be furthered in organisms such as corn, rice, soybeans,
and other photosynthetic species.
1. Introduction
Cyanobacteria, bacteria that conduct photosynthesis,
have the potential to revolutionize both agricultural
practices and the food industry, if higher yields of target
materials are attained (Chow et al., 2015). Cyanobacteria,
capable of utilizing 10% of the sun’s energy, are nearly 10
times more efficient at fixing carbon found in CO2 than
other energy plants such as sugar cane or corn, which
harness only 1% of the sun’s energy (Hunt, 2003). This
efficiency drives cyanobacteria into the energy industry’s
spotlight as a possible, influential source of energy for
humanity. Moreover, their increased photosynthetic rates
decrease the amount of CO2 in the atmosphere, which
benefits the global environment. Five other aspects of
these photosynthetic bacteria that interest scientists are
that they: grow in high densities, use water as an electron
donor, utilize infertile land, require non-food-based
feedstock, and thrive in many different water conditions
(brackish, fresh, or saltwater) (Parmar et al., 2015).
Although all of these benefits already apply to
cyanobacteria, it is still expensive to culture, grow, and
eventually utilize the products of the bacteria in an
efficient way. In order for cyanobacteria to be widely used,
a sharp increase in target yields and decrease in expense
must occur in order to compete with the simplicity and
economic benefits of plants.
Coupled with being more cost-effective when producing
target materials, plants have also been genetically modified
with genes originating from cyanobacteria to increase
efficiency. For example, carbon fixation rates in transgenic
tobacco were increased significantly after transforming
cyanobacterial Rubisco into the tobacco’s genome.
Photosynthetic efficiency was increased as a result of
cyanobacteria’s efficiency, which serves as a precedent for
future research (Occhialini et al., 2015).
This transgenic tobacco demonstrates the viability of
increasing the efficiency of plant growth with cyanobacteria
research. This pursuit is important because scientists of
the Global Harvest Institute estimate that the world could
face a food crisis by 2030 (Martin, 2017). Developing new
methods of growing crops is paramount to mitigating this
impending humanitarian need.
In recent decades, knowledge regarding cyanobacteria
has increased exponentially, stemming first from the
genome-mapping of Synechocystis sp. 6803, one species
of cyanobacteria. Now there are more than 128 different
strains of cyanobacteria fully sequenced, which provides
many opportunities in genetic engineering to study
the properties of the bacteria. This developing field
of genetic engineering allows researchers to utilize
various transformation techniques in order to optimize
photosynthetic rates within cyanobacteria, and ultimately
in other organisms as well (Al-Haj et al., 2016).
The species Synechococcus elongatus PCC7942 is one
species of cyanobacteria that has had its entire genome
sequenced and therefore is a candidate for many genetic
engineering projects that study photosynthetic processes,
regulation of nitrogen-containing compounds, and
acclimation to stressed conditions (Home - Synechococcus
elongatus PCC 7942). Synechococcus elongatus PCC7942,
previously known as Anacystis nidulans R2, is a freshwater
cyanobacteria that was the first cyanobacteria to be
successfully transformed using exogenous DNA (Shestakov
10 | 2018-2019 | Broad Street Scientific BIOLOGY

Table 1. The list of forward and reverse primers used for isolating dnaJ.
Species Gene Direction Melting
Temperature
(°C)
Synechococcus elongatus
UTEX L 2973
Sequence (5’-3’)
dnaJ Forward 69.2 GAGAATTCATGGGTC-
GTCGCTGGA
Purpose
Transformation
Synechococcus elongatus
UTEX L 2973
dnaJ Reverse 68.19 GAGGATCCCTAGCATG-
CAAGCTCTCCTG
Transformation
Synechococcus elongatus
UTEX L 2973
Synechococcus elongatus
UTEX L 2973
dnaJ Forward 68.16 ATGCAAAATTTTCGC-
GACTACTATGCC
dnaJ Reverse 67.47 TCAACGCGATTGTTC-
GAGCGAT
RT-PCR
RT-PCR
& Khyen, 1970). Synechococcus elongatus PCC7942 are
obligate photoautotrophs, which means that they only
rely on their photosynthetic ability to produce nutrients
instead of being able to break down and use nutrients found
in their environment (Minda et al., 2008). Due to this
attribute, Synechococcus elongatus PCC7942’s photosynthetic
efficiency must be optimized for any condition, including
stress, to outlast their natural competition. One such way
that Synechococcus elongatus PCC7942 has been shown
to adapt to extreme heat and high light conditions is the
induction of the dnaK and dnaJ genes (Hihara et al., 2001).
The gene dnaK has three different homologues found
in the genome of Synechococcus elongatus PCC7942,
designated dnaK1, dnaK2, and dnaK3. DnaK1’s function is
unknown in the Synechococcus elongatus PCC7942, although
it is known to be found in the cytosol of the cyanobacteria.
Both dnaK2 and dnaK3 are essential for the growth of
Synechococcus elongatus PCC7942 (Watanabe, 2007). Similar
to dnaK, dnaJ has 4 homologues within the Synechococcus
elongatus PCC7942 genome, referred to as dnaJ1, dnaJ2,
dnaJ3, and dnaJ4. DnaJ3 has been found to be located in
the membrane of the cyanobacteria. DnaJ2 is shown to be
induced in extreme heat and high light conditions. Apart
from these two homologues, dnaJ2 and dnaJ3, most of
dnaJ roles in the cell have not been discovered (Shestakov
& Khyen, 1970). The substitute for Synechococcus elongatus
PCC7492 that will be used in this experiment due to
budget constraints is Synechococcus elongatus UTEX L 2973.
Within Synechococcus elongatus UTEX L 2973, there are
10 homologues of dnaJ (Genome). Their respective roles
within the cell beyond molecular chaperones are largely
unknown, apart from dnaJ3, which is a known heat
shock protein (Genome). The third homologue of dnaJ
was isolated and overexpressed in a transformed strain of
cyanobacteria in this research project.
The goal of this project is to determine the effects of
dnaJ on the photosynthetic rate of Synechococcus elongatus
UTEX L 2973 and explore the correlation between the
genes’ overexpression and growth rates in various heat
conditions. This research could lead to new advancements
in industry and agriculture through the higher production
rates of glucose and target materials.
2. Methods
2.1 – Culturing Synechococcus elongatus UTEX L 2973
Synechococcus elongatus UTEX L 2973 thrive in BG-11
liquid medium at 30°C under 12-hour light cycles from a
Percival Incubator. Once the cyanobacteria showed initial
growth in the medium, the bacteria were aliquoted to more
containers to protect the Synechococcus elongatus UTEX L
2973 from contamination that could ruin the whole strain
(Kufryk et al., 2002).
2.2 – DNA extraction, PCR and RT-PCR
The DNA from Synechococcus elongatus UTEX L 2973
was extracted using the QIAamp DNA Mini Kit and its
corresponding protocol (QIAGEN). Using the primers
listed in Table 1, dnaJ was isolated including the restriction
enzyme cut sites necessary for ligation. The PCR was run
according to the OneTaq Hot Start protocol (Biolabs). The
extension phase lasted for 2 minutes and the annealing
temperature was 61°C.
2.3 – Cloning
Using BamHI and EcoRI restriction enzymes, dnaJ
was ligated into the plasmid pSyn_6 from a GeneArt
Synechococcus Engineering Kit.
2.4 – Transformation of E. Coli
A 5-alpha E. coli strain was transformed using the
heat shock method to replicate the desired plasmid. Two
different plasmids were used to transform the E. coli, one
vector without dnaJ and one plasmid including dnaJ. After
transformation, the E. coli grew in SOC medium, which
was then spread on LB plates with spectinomycin at 50
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μg/mL concentration. After growing overnight, colonies
were labeled and were inoculated into tubes corresponding
to their label to grow overnight.
2.5 – Transformation of Synechococcus Elongatus UTEX L
2973
The plasmid DNA from the E. Coli was extracted using
a Spin Miniprep Kit and its corresponding protocol. This
plasmid DNA was then used to transform Synechococcus
Elongatus UTEX L 2973 following the protocol provided
by GeneArt Synechococcus Engineering Kit. This vector
has not been used to transform pSyn_6 before.
2.6 – Statistical Analysis
To analyze the OD745 data, error bars were calculated
by multiplying the standard error of the mean by two. To
test significance, a t-test calculator for the comparison of
means was used to determine a p-value. One asterisk (*)
represents significance at a p-value of < .05; two asterisks
(**) concludes significance at a p-value of < .01; three
asterisks (***) demonstrates that the data are significant at
a p-value of < .005
show the successful isolation of dnaJ, a gene of length
1.8kb (Fig. 2a).
Figure 2a. Successful PCR amplification of dnaJ. The
band at 1.8kb is dnaJ.
Figure 2b. The cutout portion of the gel isolated the
vector that was used in gel extraction and ligation.
Figure 2c. Cutouts from the gel isolated dnaJ.
These bands were ligated into the plasmid after gel
extraction.
Figure 1. dnaJ will be inserted in between EcoRI and
BAMHI
3. Results
3.1 – Cloning Strategy
A cloning strategy was used (Fig. 1). DnaJ was isolated
including the restriction enzyme cut sites necessary for
ligation using the aforementioned primers (Table 1). The
enzymes cut the target gene at the lines on either side of
dnaJ (Fig. 1). The vector for GeneArt also had the same
two restriction enzyme cut sites, BamHI and EcoRI, as the
isolated gene. Utilizing DNA Ligase, the dnaJ was inserted
into the plasmid in the 5’-3’ direction with a constitutively
active promoter, PpsaA (NEB).
The bands around 1.8kb surrounded by the red boxes
Figure 2d. Gel electrophoresis of restriction enzyme
digested plasmid from transformed E. coli. The bands
at 1.8kb and 4.5 kb in lane 7 demonstrate correct
ligation and transformation of the E. coli colony.
Plasmid from this colony was used to transform
Synechococcus elongatus UTEX L 2973.
12 | 2018-2019 | Broad Street Scientific BIOLOGY

Following the preliminary PCR, another PCR reaction
was run, and its products were cut with restriction enzymes
before being exposed to ultraviolet light. Ultraviolet is a
known DNA mutagen and hence, exposing dnaJ to this
light before transformation in the cyanobacteria could
alter its natural use in the cell. The vector was also cut
with the restriction enzymes, BamHI and EcoRI. These
two cut products were run through gels to purify the
digested DNA (Fig 2b & 2c). Once the products were
cut out, gel extraction was run to purify the DNA from
the gel, so that ligation could be run (QIAquick). After
the ligated plasmid was formed using DNA Ligase and a
ligation buffer, the E. coli strain 5-alpha from New England
Biolabs was transformed using heat-shock method (Fig.
1). 1, 3, and 6 μL of extracted DNA solution were added
into separate vials of transformation-competent E. coli
cells and were mixed gently. This mixture was put on ice
for 30 minutes then heat-shocked at 42°C for 30 seconds
without shaking. The transformed E. coli was put on ice for
2 minutes. 250 μL of room temperature SOC medium was
added to the vial of E. coli. This vial was incubated shaking
horizontally at 55 rpms at 37°C for 1 hour. Following
the incubation, the various tubes of transformed E. coli
were plated on separate solid LB medium plates with
spectinomycin at a concentration of 50 μg/mL. The plates
were incubated overnight at 37°C. Because of the presence
of spectinomycin on the plates and the plasmid’s resistance
to spectinomycin, the colonies that grew on the plate
overnight had to contain the target plasmid.
Once the colonies formed, 12 colonies were isolated
and grown individually in 3.0 mL of LB medium with
spectinomycin at a concentration of 50 μg/mL overnight.
The plasmid was isolated from these vials of transformed
E. coli using the Spin Miniprep Kit (QIAprep). The plasmid
was digested by EcoRI and BamHI. Gel electrophoresis
was conducted to determine whether or not the plasmid
incorporated the target gene properly (Fig. 2d). Culture
6 replicated the desired plasmid as seen by the bands at
4.5kb and 1.8kb, so the remaining plasmid that was not
run through the gel was used to transform Synechococcus
elongatus UTEX L 2973.
Figure 3a. Two colonies transformed with only
vector in the presence of 10 μg/mL spectinomycin.
Figure 3b. Six colonies overexpressing dnaJ in the
selective presence of spectinomycin.
3.2 – Transformation
The cyanobacteria were transformed using the protocol
corresponding to the GeneArt Synechococcus Engineering
Kit. Following transformation, the cyanobacteria
were plated on solid BG-11 media with 10 μg/mL
spectinomycin under normal conditions. Colonies formed
and overexpressed dnaJ, and those that were transformed
with only pSyn_6 plasmid grew (Fig. 3a & 3b). All of
these colonies were numbered and then inoculated into
flasks containing liquid BG-11 media with 10 µg/mL
spectinomycin.
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3.3 – Growth Assays
tested, it appeared as if the overexpression resulted in
increased rates in both conditions (Fig. 5a & 5b).
Figure 4a. Flasks with varying optical densities. The
three flasks on the left were cultured for the longest
time and thus, had the highest optical densities. The
flasks on the right had grown more recently and
were not as dark.
Figure 4b. Optical density values of corollary flasks.
Higher optical densities correspond to darker flasks.
In order to determine the effects of dnaJ’s overexpression
on growth rates within cyanobacteria, optical density
measurements were taken from different cultures at 745
nanometers (nm) at varying temperatures. This is an
appropriate wavelength because optical density measures
turbidity instead of absorbance. The absorbance of the
selected wavelength should be negligible in order for the
measurements to strictly account for the reflection of light
off of the cells in the solution (Martin, 2014).
There were 7 flasks of cyanobacteria before
transformation with varying optical densities (Fig. 4a).
In order to demonstrate what color and darkness of flasks
correlates to OD745 values, optical density measurements
corresponding to cyanobacteria culture were graphed (Fig.
4b). From the left to right, the optical density values were:
.250, .133, .292, .119, .144, .022, .014. The darkest flasks
evidently have the highest optical density measurements.
This growth assay measures the total increase in optical
density over time. The higher the change in optical density
is, the higher the rate of growth for the colony is. Thus,
when testing the two different transformed strains of
Synechococcus elongatus UTEX L 2973, the transformed
strain overexpressing dnaJ should have the higher change
in optical density if the heat shock protein overexpressed
through dnaJ truly increases photosynthetic and growth
rates.
Because dnaJ codes for a heat shock protein, it
was suspected that the growth rates of the strain
overexpressing this gene would be significantly greater
in only heat stressed conditions in comparison to the
cyanobacteria only transformed with the vector. It was
believed that the growth rate in normal conditions would
not be affected greatly by the heat shock protein because
the overexpression would not be necessary to withstand
high temperatures. However, once the growth rates were
Figure 5a. Graph of optical density (745nm) of control
stain and dnaJ overexpressing strain 30° Celsius. The
data suggest dnaJ significantly increases growth
rates.
Figure 5b. The colonies were grown at 40° for 9 days.
There was a trend in the data that indicates dnaJ
promotes faster growth, but after the colony was
exposed to a higher temperature, 42°, the control
stain did not grow whereas the dnaJ strain continued
normal growth. Data became significant two days
after increased temperature.
The overexpression of dnaJ in normal conditions of
30°C and 12-hour light cycles increased the growth rate
of the cyanobacteria significantly in comparison to the
control. This significance was seen as early as day 8. The
average OD745 of the dnaJ strain after 12 days was .39 in
comparison to the vector strain that had an average OD745
of .25. This increase in optical density is attributed to the
overexpression of dnaJ.
DnaJ’s overexpression within cyanobacteria in heat
stressed conditions of 40°C and 12-hour light cycles also
tended to increase growth rates. After 9 days, the average
14 | 2018-2019 | Broad Street Scientific BIOLOGY

OD745 of the overexpressing strain was .58 while the other
strain had an average of only .52; however, the standard
deviation within each of the sample groups was too high
to conclude significance at 40°. When the temperature
in the Percival Incubator was increased to 42°, the dnaJ
overexpressing strain grew normally, whereas the control
strain’s average optical density decreased. The average
optical density of the dnaJ overexpressing strain after
19 days was 1.35, and the control strain had an average
optical density of .35. After just two days being exposed
to the higher temperature, the difference between the two
strains was significant, suggesting that the overexpression
of dnaJ provided heat resistance to the transformed
strain of cyanobacteria. There is a visual difference in
optical density at day 19 in comparison to day 5, which
demonstrates dnaJ’s potential to increase growth rates and
provide heat resistance (Fig. 6).
Figure 6. The photo of the flasks in the top panel was
taken on day 5. The flasks have similar tints of green.
The last photo was taken on day 19. In the eight flasks
on the left, the dnaJ overexpressing cultures have a
much darker color than the control flasks.
4. Discussion
Essentially, this research sought to create a unique
strain of cyanobacteria through genetic transformation.
The specific plasmid utilized in the experimentation
had not been used to transform Synechococcus elongatus
UTEX L 2973 previously. The successful transformation
as seen from the colony growth in the selective presence
of spectinomycin demonstrates the competence of the
plasmid pSyn_6 in transforming the experiment’s specific
strain.
Despite the successful outcome of the research,
there were several limitations in the experiment due to
equipment and budget restrictions. One such limitation
was the inability to determine the difference between
the rates of oxygen evolution in the two strains. This
would have led to a more precise measurement of the
photosynthetic rate because oxygen is directly produced in
photosynthesis. Optical density is a less direct measurement
of this rate, but accurate, nonetheless. Without the
generation of sugars through photosynthesis, the strains
BIOLOGY
could not grow. Because of this, higher photosynthetic
rates should correspond to higher growth rates. Another
limitation of this experiment was the inability to confirm
gene expression in the transformed strains. However,
confirming the correct plasmid makes it reasonable to
assume that the growth rates increased on account of dnaJ
overexpression.
This beneficial genetic overexpression has many
potential applications in both the agriculture and energy
industries. Because cyanobacteria are currently the most
photosynthetically efficient organisms on the planet,
this modification could lead to future applications in
agriculture or more economic biofuel production that will
capitalize on their efficiency (Hunt, 2003). One possible
application could be the production and secretion of
sugars for consumption. Because cyanobacteria are not
seasonal like sugar cane, they could produce sugars more
consistently and more efficiently, especially following
genetic engineering. Clearly, isolation of sugar from a
cyanobacteria solution would have to be much cheaper
for this to be a viable contender with sugar cane, but
nonetheless, this could be a potential application of
genetically engineered cyanobacteria. Beyond sugars,
cyanobacteria’s products have been manipulated to
produce ethanol (Chow et al., 2015). Producing ethanol
could prove to be a disruptive application of cyanobacteria
in the energy industry, especially when paired with dnaJ
overexpression.
Another possible application could be overexpressing
heat shock proteins in other photosynthetic organisms to
determine their effect on growth and photosynthetic rates.
Overexpressing either dnaJ or corollary proteins specific
to certain species within corn, rice, or soybeans could
lead to increased production of these crops both in fertile
geographies and in regions that are currently considered
arid. Because heat shock proteins increased growth in
Synechococcus elongatus UTEX L 2973 even in heat stressed
conditions, it could be possible to genetically engineer
cash crops to make them resistant to higher temperatures.
This resistance could lead to the cultivation of previously
infertile land, feeding millions more people worldwide.
Further experimentation must be done to conclude the
viability of any of these applications.
5. Acknowledgements
I would like to thank Dr. Monahan for teaching
me the research process and guiding me through the
fickle experimentation that is molecular biology. Thanks
to her instruction and her patience with my stubborn
commitment to this project, I was able to persevere
through obstacles and accomplish my dream of genetically
engineering cyanobacteria. I would like to thank Dr.
Sheck for supervising me while I spent hours in the sterile
Broad Street Scientific | 2018-2019 | 15

hood working with my cyanobacteria. I would also like to
thank the rest of my Research in Biology colleagues for
encouraging me throughout my time researching. I would
like to thank Kevin Zhang and Tyler Edwards who were
lab assistants during the Glaxo Summer Research Fellows
Program. Finally, I want to thank the North Carolina School
of Science and Mathematics and the Glaxo Endowment for
blessing me with the opportunity to experience research in
high school. I have learned many lessons that I will carry
with me through the rest of my career in both research and
other fields.
6. References
Al-Haj, L., Lui, Y. T., Abed, R. M. M., Gomaa, M. A.
& Purton, S. Cyanobacteria as Chassis for Industrial
Biotechnology: Progress and Prospects. Life (Basel) 6,
(2016).
Algae, U. C. C. of. UTEX L 2973 Synechococcus elongatus.
UTEX Culture Collection of Algae Available at: https://
utex.org/products/utex-l-2973. (Accessed: 25th January
2018)
Biolabs, N. E. Protocol for OneTaq Hot Start DNA
Polymerase (M0481). New England Biolabs: Reagents
for the Life Sciences Industry Available at: https://www.
neb.com/protocols/2012/09/05/one-taq-hot-start-dnapolymerase-m0481.
(Accessed: 27th October 2018)
Biolabs, N. E. Taq 2X Master Mix. New England Biolabs:
Reagents for the Life Sciences Industry Available at:
https://www.neb.com/products/m0270-taq-2x-mastermix#Product
Information. (Accessed: 7th October 2018)
Chow, T.J. et al. Using recombinant cyanobacterium
(Synechococcus elongatus) with increased carbohydrate
productivity as feedstock for bioethanol production via
separate hydrolysis and fermentation process. Bioresource
Technology 184, 33–41 (2015).
GeneArt Synechococcus Protein Expression Vector.
Thermo Fisher Scientific Available at: https://www.
thermofisher.com/order/catalog/product/A24230.
(Accessed: 7th October 2018)
Hihara, Y., Kamei, A., Kanehisa, M., Kaplan, A. & Ikeuchi,
M. DNA Microarray Analysis of Cyanobacterial Gene
Expression during Acclimation to High Light. Plant Cell
13, 793–806 (2001).
Home - Synechococcus elongatus PCC 7942. Available
at:https://genome.jgi.doe.gov/portal/synel/synel.home.
html. (Accessed: 21st January 2018)
Hunt, S. Measurements of photosynthesis and respiration
in plants. Physiol Plant 117, 314–325 (2003).
Kufryk, G. I., Sachet, M., Schmetterer, G. & Vermaas, W.
F. J. Transformation of the cyanobacterium Synechocystis
sp. PCC 6803 as a tool for genetic mapping: optimization
of efficiency. FEMS Microbiology Letters 206, 215–219
(2002).
Martin, A., Researchgate. Available at: https://www.
researchgate.net/post/When_measuring_cyanobacterial_
growth_when_do_I_use_which_wavelength.
Martin, S. World will run out of food by 2050 thanks
to population boom. Express.co.uk (2017). Available
at: https://www.express.co.uk/news/science/803791/
World-will-run-out-of-food-by-2050-population-boom.
Minda, Renu, et al. “The Evolutionary Significance of
‘Obligate’ Photoautotrophy of Cyanobacteria.” Current
Science, vol. 94, no. 7, 10 April 2008, pp. 850-852.
Occhialini, A., Lin, M. T., Andralojc, P. J., Hanson, M. R.
& Parry, M. A. J. Transgenic tobacco plants with improved
cyanobacterial Rubisco expression but no extra assembly
factors grow at near wild-type rates if provided with
elevated CO2. The Plant Journal 85, 148–160 (2015).
Parmar, A., Singh, N. K., Pandey, A., Gnansounou, E. &
Madamwar, D. Cyanobacteria and microalgae: A positive
prospect for biofuels. Bioresource Technology 102, 10163–
10172 (2011).
QIAGEN. Quick-Start Protocol: QIAamp DNA Mini
Kit. Confidence in Your PCR Results - The Certainty of
Internal Controls - QIAGEN Available at: https://www.
qiagen.com/us/resources/resourcedetail?id=566f1cb1-
4ffe-4225-a6de-6bd3261dc920&lang=en.
QIAprep Spin Miniprep Kit. Confidence in Your PCR
Results - The Certainty of Internal Controls - QIAGEN
Available at: https://www.qiagen.com/us/shop/sampletechnologies/dna/plasmid-dna/qiaprep-spin-miniprepkit/#orderinginformation.
QIAquick Gel Extraction Kit. Confidence in Your PCR
Results - The Certainty of Internal Controls - QIAGEN
Available at: https://www.qiagen.com/us/shop/sampletechnologies/dna/dna-clean-up/qiaquick-gel-extractionkit/#orderinginformation.
Restriction Endonuclease Products | NEB. Available
at: https://www.neb.com/products/restrictionendonucleases.
(Accessed: 2nd February 2018)
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Shestakov, S. V. & Khyen, N. T. Evidence for genetic
transformation in blue-green alga Anacystis nidulans.
Molec. Gen. Genet. 107, 372–375 (1970).
Synechococcus sp. UTEX 2973, complete genome. (2015).
Watanabe, S., Sato, M., Nimura-Matsune, K., Chibazakura,
T. & Yoshikawa, H. Protection of psbAII transcript from
ribonuclease degradation in vitro by DnaK2 and DnaJ2
chaperones of the cyanobacterium Synechococcus elongatus
PCC 7942. Biosci. Biotechnol. Biochem. 71, 279–282
(2007).
BIOLOGY
Broad Street Scientific | 2018-2019 | 17

HYPOGLYCEMIC EFFECT OF Momordica charantia
AGAINST TYPE 2 DIABETES MODELED IN Bombyx mori
Aarushi Venkatakrishnan
Abstract
Diabetes is a disease that affects millions across the world, occurring when there are high levels of glucose in the blood.
Currently, treatments for Type 2 Diabetes include lifestyle and diet changes, medication, and insulin injections; however,
natural treatments, such as the vegetable bitter melon, have become more popular in recent years. As it is abundantly
grown in Asia, which houses 60% of the world’s diabetics, this finding can be very effective. Using a silkworm model, the
hypoglycemic effect of bitter melon was quantified by measuring the silkworm’s hemolymph glucose concentration with
the phenol sulfuric acid method. Injections of saline, insulin, and bitter melon solutions were made at the first proleg of
the silkworms. Hyperglycemia was induced after two days of a 10% high glucose diet, and human insulin significantly
counteracted the effect. There were no changes to mass or length between the hyperglycemic and normal silkworms.
After comparing its hypoglycemic effect to insulin, a known hypoglycemic agent, the most effective tested dose of bitter
melon was found to be 175 µg/mL, 5 times greater than the corresponding insulin dose, 35 µg/mL. With further trials to
determine the symptoms and overall effects to human health, bitter melon can potentially be recommended as an addition
to the diet for diabetes treatment.
1. Background
1.1 Introduction
Diabetes mellitus is a disease which is characterized by
high levels of sugar in the blood, hyperglycemia, resulting
from the body unable to use blood glucose for energy
(Drive, n.d.). Typical symptoms include increased thirst,
unexplained weight loss, and frequent infections (Drive,
n.d.). This disease occurs when the body is unable to
effectively use insulin, a hormone made by the pancreas,
to process glucose, and thus causing an increase in blood
sugar (“Insulin, Medicines, & Other Diabetes Treatments,”
2016). There are two types ranging in severity: Type 1 and
Type 2. Type 1 diabetes is an autoimmune disease in which
the immune system destroys islet cells resulting in the body
being unable to make insulin (Jin Yang & Mook Choi,
2015). Type 2 diabetes is a chronic condition that changes
how the body is able to metabolize glucose, caused by the
pancreas either not producing enough insulin or the body
becoming resistant to insulin (Matsumoto et al., 2011).
The current treatment for Type 1 is administering insulin
exogenically with numerous insulin treatments available,
such as an insulin pump, pen, or an inhaler. These vary in
terms of how fast they act, the quickest being 15 minutes
after injection and the longest being several hours, but
correspondingly the duration of the effect differs (“Insulin,
Medicines, & Other Diabetes Treatments,” 2016). Type 2
diabetes treatment includes maintaining a healthy lifestyle
and monitoring blood glucose levels (Matsumoto et al.,
2011). However, Type 2 diabetic patients can even take
insulin treatments to make up for that not produced in the
body; metformin is a commonly prescribed medicine first
given to diabetic patients to lower the amount of glucose
produced by the liver and help the body process insulin
better (“Insulin, Medicines, & Other Diabetes Treatments,”
2016).
The number of people being affected by this condition
has been increasing rapidly. In 2015, 1.5 million new cases
were diagnosed, and in the United States alone, there were
30.2 million Americans with some form of diabetes in 2017
(“CDC Press Releases,” 2016). With this rise, the demand
for diabetes treatments has increased. The development
of new ways to introduce or stimulate insulin secretion
is necessary as it has the potential to help the millions of
people afflicted with diabetes live healthier lives.
Although there are a variety of drugs in the market
for Type 2 Diabetes, the desire for herbal medicines
has increased as they can often be more accessible than
traditional forms. In addition, these natural remedies are
often more available and accepted than Western Medicine.
There has always been a sector of herbal medicines called
Complementary and Alternative Medicine (CAM); one
of the oldest and most-well known practices is Ayurvedic
medicine, which originates in India. Many herbs, fruits,
and vegetables used in Ayurvedic medicine have shown
promising results against diseases involving high blood
pressure, anxiety, cancer, and more (Axe, 2015). One
notable vegetable used is Momordica charantia, otherwise
known as bitter melon. Numerous studies have been
conducted that suggest bitter melon has hypoglycemic
effects (Fuangchan, 2011; Jin Yan, 2015).
Jin Yang et al. treated diabetic rats with bitter melon
and found three functional components of bitter melon
that were likely causing a hypoglycemic effect: charantin,
vicine, and polypeptide-p (2015). By using three groups:
a high fat control, high fat and 1% bitter melon, and high
fat and 3% bitter melon, bitter melon had significantly
18 | 2018-2019 | Broad Street Scientific BIOLOGY

improved glucose tolerance and insulin sensitivity. In the
3% bitter melon, they found that it increased the levels
of two insulin receptors, (phosphor-insulin receptor
substreate-1 (Tyr612) and phosphor-Akt (Ser473), likely
stimulating the hypoglycemic effect (Jin Yang & Mook
Choi, 2015).
Furthermore, bitter melon has been used in clinical
studies using human patients with Type 2 Diabetes.
Fuangchan et al. investigated the effects of varying doses
of bitter melon (500 mg/day, 1000 mg/day, 2000 mg/day)
when comparing it to metformin (1000 mg/day), a current
diabetes medication (2011). By measuring the fructosamine
concentrations over a 2-week time period from baseline to
endpoint, they found that the 500 mg/day and 1000 mg/
day doses did not significantly impact glucose levels, while
the 2000 mg/day dose did. When compared to metformin,
the effects of bitter melon were still less (Fuangchan, 2011).
Both groups did not experience extreme adverse effects;
only mild headaches, dizziness, and increased hunger
were experienced in the 2000 mg/day bitter melon group
(Fuangchan, 2011). The drawbacks of this study include
the limited time as it was only conducted for 4 weeks, and
because effects were only seen for the 2000 mg/day dose,
higher dose levels would need to be tested.
1.2 – Silkworm Model
Although bitter melon is known to have hypoglycemic
effects, research surrounding the topic is not standardized
and hard to compare. With very minimal clinical trials,
the side effects of bitter melon are difficult to determine
as well. In Matsumoto et al., scientists established the
silkworm as a reliable model of diabetes (Matsumoto et al.,
2011). While silkworms do not have blood like humans,
they have hemolymph which is a fluid “equivalent” to
blood. In this study, glucose levels after treatment with a
high glucose diet were higher than that of the silkworms
fed a normal diet. By treating the hyperglycemic silkworms
with insulin, glucose levels returned to normal. Moreover,
they also tested an herbal extract, jiou, and found that it
could mimic the effects of insulin by reducing glucose
concentrations.
Based on this research, the silkworm model could be
used to determine the hypoglycemic effects of bitter melon.
Here we show hyperglycemic silkworms that are treated
with bitter melon extract, to study if their hemolymph
sugar levels will go down without adverse reactions in
terms of body size, body mass, or lifespan because bitter
melon has been known to have hypoglycemic properties
as used in ayurvedic medicine. This hypoglycemic effect
is likely as bitter melon has the identified components
charantin, vicine, and polypeptide-p and has been a cultural
remedy as used in Ayurvedic medicine.
BIOLOGY
Figure 1. Anatomy of a silkworm. Length
measurements were made from the thorax to the
caudal leg. Injections were made in between the first
proleg and the second proleg from the head capsule.
2. Methods
This study consisted of two preliminary experiments and
two main experiments. The two preliminary experiments
determined the equation for the Beer’s Law Plot to be
used when calculating the D-glucose concentration of
silkworms and established that a high glucose diet raised
the D-glucose levels of silkworms. The main experiments
tested the effect of insulin when compared to the same dose
of bitter melon and evaluated the optimal concentration
of bitter melon. The experiment unit was the addition
and kind of hypoglycemic agent, measuring the change in
average D-glucose levels. For the main experiments, the
positive control was the hyperglycemic silkworm treated
with insulin, a known hypoglycemic agent. The negative
control was the silkworm fed a normal diet and injected
with saline, to mimic the effect of an injection without the
addition of a chemical agent.
2.1 – Silkworm Diet
The essentials of the silkworm diet consist of mulberry
leaves. To create the silkworm diet, Carolina® Silkworm
Diet was purchased from Carolina Biological. In a 2000
mL glass beaker, ½ pound of the mulberry powdered diet
was added to 720 mL (roughly 3 cups) of tap water. Using
a stirring rod, the substances were thoroughly mixed to a
uniform consistency. It was then covered with plastic wrap
and secured with a rubber band. The beaker was placed in
the microwave at high heat until the mixture came to a
boil, usually after 1-2 minutes. This caused the mixture to
rise and bubbles appeared on the surface. Once the mixture
boiled, the beaker was removed from the microwave and
stirred to again ensure uniform consistency. It was then
placed back in the microwave to repeat the process. After
the second boil and mixture, plastic wrap was tightly placed
against the surface of the mixture to ensure no moisture
escaped. Time was allowed for the beaker and substances
to cool down. Then, the top of the beaker was secured
with plastic wrap and a rubber band. It was placed in the
Broad Street Scientific | 2018-2019 | 19

efrigerator to store.
2.2 – Silkworm Maintenance
Silkworm eggs were purchased from Carolina
Biological. They were placed in petri dishes and incubated
at 29 °C. After roughly a week, the eggs hatched, and they
were disposed of. The larva was transferred to a fresh plate
with mulberry powdered diet placed on a paper towel.
Feedings were made every other day to clean out feces and
remove dried food. The experiment was performed during
the fifth instar (around 4 weeks after hatching). Raising
the temperature increased growth, whereas lowering the
temperature delayed growth.
2.3 – High Glucose Diet
To induce hyperglycemic conditions, a high glucose diet
of the Mulberry Chow was created by mixing appropriate
amounts of D-Glucose and the Mulberry Chow. D-Glucose
was added to the Mulberry Chow in a beaker, and then
mixed until all contents were dissolved. A 10% and 15%
D-Glucose diet were created.
2.4 – Injection
50 µl of each solution was injected into the hemolymph
at the second abdominal segment of the larva after the
first proleg using 1 mL syringes (Fig. 2). Injections were
done on 12-hour cycles for 2 days after 2 days of the high
glucose diet for the preliminary experiments. Injections
were performed once 24 hours before extraction for the
main experiments. The total treatment lasted 4 days with
measurements taken on Day 5.
was made with 0.9% NaCl and 0.1% acetic acid. A stock
solution of bitter melon was created by combining 0.50
grams of powdered bitter melon with 50 mL of distilled
water to make a 0.1 g/mL solution. It was heated at 40
°C, for 15 minutes and left overnight for 2 days. Then,
vacuum filtration was performed 3 times to filter out
particulates. It was then appropriately diluted to the
varying concentrations used in the experiment.
2.6 – Glucose Quantification
Hemolymph was collected from the larvae through a cut
on the first proleg after they had developed to the fifth instar.
Precipitated proteins were removed by centrifugation at
3000 rpm for 10 min. 175 µl of the supernatant was diluted
with 175 µl distilled water for sugar quantification (350 µl
total). The total sugar in the hemolymph was determined
using the 0.05 % phenol-sulfuric acid (PSA) method.
Hemolymph extract (350 µl) was mixed vigorously with
1050 µl 70% sulfuric acid. Immediately, 210 µl of 5% phenol
aqueous solution were added and mixed. The test tubes
were held in a water bath at 90 °C. The samples were then
cooled to room temperature. The absorbance at 490 nm
was measured using a spectrophotometer. Serially diluted
glucose solution was used as a standard.
2.7 – Statistical Measurements
Measurements of the mass (g) and length (cm) of
the silkworms were taken prior to experimentation.
They were then monitored throughout the trial days
and recorded until extraction. Data were analyzed using
unpaired student t-tests with unequal variance, as sample
size differed across the trials. Error bars were calculated
using standard error of the mean (SEM).
2.8 – Comparing the Effects of Insulin and Bitter Melon
Figure 2. Injection site after the first proleg.
Hemolymph was extracted from this same site as
well.
To determine whether bitter melon has hypoglycemic
effects, a silkworm model was used as it has been previously
identified as a workable model for diabetes research
(Fuangchan, 2011). Three characteristics were measured to
determine the effectiveness of the bitter melon treatment:
body mass, body length, and hemolymph sugar levels. Each
trial consisted of 6 treatments, separated into high-glucose
and normal diet models. In addition to these treatments,
the effect of insulin on both the hyperglycemic and normal
silkworm was used to provide a standard of comparison to
see the success of the bitter melon extract (Table 1.1).
2.5 – Injection Solutions
A 35 µg/mL solution of insulin was created by diluting
a 20 mg/mL solution to 15 mL. The dilution solution
20 | 2018-2019 | Broad Street Scientific BIOLOGY

Table 1.1. Experimental design comparing effect of
equal dose bitter melon
Diet
Treatment Normal Diet High Glucose Diet
Saline “Normal” with
Saline (NS)
“High” with
Saline (HS)
Insulin “Normal” with
Insulin (NI)
“High” with
Insulin (HI)
Bitter
Melon
“Normal” with
Bitter Melon
(NB)
“High” with
Bitter Melon
(HB)
A.
B.
2.9 – Determining the Ideal Concentration of Bitter Melon
Following the experimental model from the Injections,
varying concentrations of bitter melon were tested in the
silkworms to determine which concentration of bitter
melon has the largest effect on the sugar concentration in
silkworms (Table 1.2).
Table 1.2. Experimental design comparing effect of
varying doses of bitter melon
Diet
Treatment Normal Diet High Glucose Diet
Saline “Normal” with
Saline (NS)
“High” with Saline
(HS)
Insulin - “High” with
Insulin (HI)
Bitter
Melon 1
- “High” with Bitter
Melon 1 (HB1)
Bitter
Melon 2
- “High” with Bitter
Melon 2 (HB2)
Bitter
Melon 3
- “High” with Bitter
Melon 3 (HB3)
Figure 3. (A, B) Glucose standards undergoing phenolaqueous
protocol and depicted visually with a
gradient of yellow colors, shown from left to right as
(1) Blank, (2) 1.00 M D-Glucose, (3) 0.055 M D-Glucose,
(4) 0.0275 M D-Glucose
3.2 – High Glucose Diet
Before proceeding with the experiment, a baseline of a
high glucose diet needed to be tested. In this preliminary
experiment, three treatments were tested: a normal diet
of mulberry chow, a 10% glucose diet after 24 hours, and
the same diet after 48 hours. A sample size of 9 silkworms
was used for the normal diet. Five silkworms were used for
both of the 10% glucose diet treatments. Average glucose
levels across the hemolymphs of the silkworms are shown
(Fig. 4).
3. Results
3.1 – Glucose Quantification
To understand and best utilize the phenol aqueous
method, a series of D-glucose standards were used to
create a Beer’s Law plot (Fig. 3A,B). Different D-Glucose
concentrations were used to generate a standard. These
included 0.0275 M, 0.055 M, and 1.000 M.
BIOLOGY
Broad Street Scientific | 2018-2019 | 21

A.
B.
3.3 – Comparing the Effects of Insulin and Bitter Melon
After establishing that a hyperglycemic diet could
induce high glucose concentrations in silkworms, the
effect of insulin was tested on a normal and high glucose
diet. This standard concentration would also be replicated
by an equal dose of bitter melon extract. Based on the
results of the previous experiments, silkworms were fed a
high glucose diet for 2 days to induce hyperglycemia (Fig.
4). On Day 3 of the diet, injections were performed with
the various treatments. Then, on Day 4, their hemolymphs
were extracted and quantified for glucose concentration.
C.
Figure 4. (A) Average D-glucose concentration. (B)
Average mass. (C) Average length. Three different
treatment groups were measured: Normal (mulberry
diet); High Day 1 (mulberry + 10% glucose for 24
hours); High Day 2 (mulberry to 10% glucose for 48
hours). (p < 0.05= *, p < 0.01= **, p < 0.001 = ***, p > 0.05=
ns). Error bars ± SEM.
The average glucose concentration of a normal
silkworm is about 30.0 mg/mL (Fig. 4A). With the addition
of a high glucose diet, the average glucose concentration is
52.4 mg/mL after one day and 79.1 mg/mL after two days.
This means that after 48 hours, there is almost a 2.5-fold
increase. After conducting a t-test for further statistical
analysis, p-values were calculated. The only statistically
significant difference is between the normal diet and two
days of the high glucose diet, indicating that 48 hours at
a minimal of 10% D-glucose diet is required to increase
hemolymph glucose levels significantly. There was no
statistically significant difference between the mass and
length of the normal silkworms and the two tested trials
(Fig. 4B and 4C).
Figure 5. Average glucose concentrations across
various treatments. Six different treatment groups
were measured: Normal with Saline (mulberry diet
+ insect saline, n=8), Normal with Insulin (mulberry
diet + 35 µg/mL insulin, n=7), Normal with Bitter
Melon (mulberry diet + 35 µg/mL bitter melon
extract, n=9), High with Saline (mulberry diet + 15%
glucose for 84 hours + insect saline, n=9), High with
Insulin (mulberry diet + 15% glucose for 84 hours +
35 µg/mL insulin, n=10), and High with Bitter Melon
(mulberry diet + 15% glucose for 84 hours + 35 µg/mL
bitter melon extract, n=9). (p < 0.05= *, p < 0.01= **, p <
0.001 = ***, p > 0.05 = ns). Error bars ± SEM.
The average glucose concentration for each of the
treatments are as follows (Fig. 5): 40.595 mg/mL (Normal
diet with Saline), 26.929 mg/mL (Normal diet with 35
µg/mL Insulin), 34.366 mg/mL (Normal diet with 35 µg/
mL Bitter Melon), 62.905 mg/mL (15% High glucose diet
with Saline), 33.287 mg/mL (15% High glucose diet with
Insulin), and 50.579 mg/mL (15% High glucose diet with
bitter melon). As can be seen from the p-values, there was
a statistically significant difference between the normal
with saline and high with saline, and one between the
high with saline and high with insulin. This corresponds
to the predicted control values. There was no statistically
significant difference between the high with saline and
high with bitter melon.
22 | 2018-2019 | Broad Street Scientific BIOLOGY

3.4 – Revised Standard Curve
Using a different series of D-glucose solutions and a
new spectrophotometer, a new standard curve was created
(Fig. 6).
A.
B.
Figure 6. New Glucose Standard Curve. Using
concentrations of 12.5 mg/mL and 25 mg/mL, the
standard curve for glucose was created.
The linear fit was used to evaluate the following
experiment in terms of finding the ideal dose of bitter
melon for hyperglycemic silkworms.
3.5 – Determining the Ideal Concentration of Bitter Melon
Ultimately, a 35 µg/mL concentration of bitter melon
was not effective, but it did show a decrease from the
hyperglycemic silkworms (Fig. 5). By adjusting the
concentration of bitter melon, the downward trend could
be quantified further.
The average values for each treatment were: 26.046
mg/mL (Normal with Saline), 37.111 mg/mL (15% High
glucose diet with Saline), 25.043 mg/mL (15% High glucose
diet with 35 µg/mL Insulin), 24.029 mg/mL (15% High
glucose diet with 35 µg/mL Bitter melon), 33.459 mg/mL
(15% High glucose diet with 87.5 µg/mL Bitter melon),
20.006 mg/mL (15% High glucose diet with 175 µg/mL
Bitter melon), and 18.265 mg/mL (15% High glucose diet
with 350 µg/mL bitter melon) (Fig. 7A).
Insulin significantly reduced the glucose concentrations
of the high glucose diet to the levels of the normal diet. Two
bitter melon treatments yielded statistically significant
results, with the 175 µg/mL bitter melon extract having a
p-value that most closely resembled insulin (0.00303 and
0.002954).
Figure 7. (A) Determining a Statistically Significant
Bitter Melon dose. Seven different treatment groups
were measured: Normal with Saline (mulberry diet
+ insect saline, n=8), High with Saline (mulberry diet
+ 15% glucose for 84 hours + insect saline, n=9), High
with Insulin (mulberry diet + 15% glucose for 84 hours
+ 35 µg/mL insulin, n=7, High with 35 µg/mL Bitter
Melon (mulberry diet + 15% glucose for 84 hours +
35 µg/mL bitter melon extract, n=5), High with 87.5
µg/mL Bitter Melon (mulberry diet + 15% glucose
for 84 hours + 87.5 µg/mL bitter melon extract, n=8),
High with 175 µg/mL Bitter Melon (mulberry diet
+ 15% glucose for 84 hours + 175 µg/mL bitter melon
extract, n=6), and High with 350 µg/mL Bitter Melon
(mulberry diet + 15% glucose for 84 hours + 350 µg/
mL bitter melon extract, n=5). (p < 0.05= *, p < 0.01=
**, p > 0.05 = ns). Error bars ± SEM. (B) (Left) 350 µg/
mL bitter melon diet fed silkworm exhibiting a
yellowish color and less rigid than (Right) Normal
diet fed silkworm.
4. Discussion
4.1 – Bitter Melon’s Effect on Hyperglycemia
The results confirm Matsumoto et al.’s conclusion that
a silkworm model can exhibit hyperglycemia (Fig. 4). By
feeding a 10% glucose mulberry diet, the hemolymph sugar
levels increased significantly. For the convenience of the
model, the addition of glucose was increased to 15% to
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Broad Street Scientific | 2018-2019 | 23

ensure that the intake across samples would be the same
and that the effect was the greatest. Additionally, this
figure also examines the mass and length across treatments.
Matsumoto et al. claimed that mass and length differed with
the addition of glucose to the diet, however, no significant
variation in these metrics were found, indicating these
metrics were not good indicators of health (2011).
From there, insulin was added as a control treatment
to compare the effect of bitter melon. The 35 µg/mL was
appropriately scaled by the average insulin treatment for
humans, with guidance from Matsumoto et al. (2011).
There was a significant decrease in glucose levels, again
confirming the silkworm model. New treatments were
tested with a 15% glucose mulberry diet instead of the
10% glucose mulberry diet (Fig. 4 & Fig. 5). With an equal
concentration of bitter melon, 35 µg/mL, there was no
significance in the data (p = 0.12). However, bitter melon
did reduce the glucose levels from the high glucose and
saline sample. From this, it could be concluded that bitter
melon requires a larger dose than insulin does to perform
a hypoglycemic effect.
This prediction was tested (Fig. 7). With four varying
concentrations of bitter melon – 35 µg/mL, 87.5 µg/
mL, 175 µg/mL, and 350 µg/mL – the relationship of
bitter melon doses and the hypoglycemic effect were
discovered. The most effective dose out of the trials was
175 µg/mL bitter melon, as it produced a similar p-value
to the insulin treatment. However, the trend created
with increasing doses did not suggest a linear trend, like
predicted. Instead, it presented with a curved shape that
is likely because of small sample size. The sample sizes of
the various treatments ranged from 5 to 9, indicating that
more samples would be necessary to determine if a linear
trend exists.
4.2 – Limitations
Although the metrics of mass and length were not
appropriate in quantifying the effect of bitter melon,
qualitative observations of behavior helped define the
health when compared to normal silkworms. With a high
glucose mulberry diet, silkworms appeared lethargic and
did not move as fast or eat as much as the normal diet
silkworms. This could speak to food aversion or a toxicity
of glucose in the diet. Silkworms have been frequently
studied as a model of toxicity as they lack an adaptive
immune system (Chen & Lu, 2018). They possess PGs and
LPS, immune stimulators that silkworms have developed
based on their cell walls (Chen & Lu, 2018). This allows
silkworms to defend against pathogens and infections. If
they had a similar response to the insulin or glucose diet,
the model would not be ideal to study. With the addition of
insulin, the worms were still slightly affected by this effect.
In addition, silkworms in the bitter melon trials exhibited
a yellowish tinge (Fig. 7B). The higher the dose, the higher
the mortality rate. The study consisted of trials with 10
initial worms, however, the sample sizes are significantly
lower for the 35 µg/mL trial and the 350 µg/mL trial, as
only 50% of the silkworms in those trials survived (Fig.
7A).
In addition, the administration of treatment also
impacted the survival rate of the silkworms. As they
have a limited hemolymph volume, injections caused
severe hemolymph loss. Bruises and strain along the head
and thorax were very visible. With extra pressure from
the injections, silkworms often refrained from eating
as they could not perform movement. This method of
administering was rather ineffective as many samples
could not be used for analysis.
Lastly, the spectrophotometer used for the first half
of the experiment was heavily used and therefore yielded
unpredictable results. Therefore, results from the first
part (Fig. 2 and 3) cannot be compared to results from the
second part (Fig. 5), as there were two new standard curves
created. Overall, similar results were yielded throughout
the trials, which allows the general effect of the treatments
to be compared.
5. Conclusion and Future Work
By using a silkworm model, diabetes could be effectively
modeled. The most effective dose of bitter melon was
determined to be 175 µg/mL, which had effects that closely
resembled those of the insulin treatment. The data do not
confirm a linear relationship between dose of bitter melon
and hypoglycemic effect, as there was variation in the data.
With this knowledge, future work is necessary before
bitter melon can be marketed as a hypoglycemic agent. At
this dose, side effects and symptoms should be generated to
understand how it would impact human health. This can be
done through mice and human clinical trials. Additionally,
different methods of preparing the extract should be
performed. A liquid extract was prepared with distilled
water and a powdered form of bitter melon to make the
injection solutions in the previously mentioned trials.
The difference between powdered and fresh bitter melon
should be studied, with the different parts of bitter melon
as well (the core and the exterior). With the combination
of all of these factors, the doses may vary depending on
what is optimal.
Bitter melon does not only show potential as a
hypoglycemic agent, but also as a potential cancer
and osteoarthritis therapy (Raina, 2016; Soo May,
2018). Guided by bitter melon’s targeted effect against
Type 2 Diabetes, Raina et al. attempted to provide a
comprehensive view of the bioactivity of bitter melon’s
different components and determine if they are applicable
to cancer treatment (Raina et al., 2016). Specifically, they
focus on how bitter melon interacts with other drugs.
This is an important aspect to consider concerning
24 | 2018-2019 | Broad Street Scientific BIOLOGY

diabetes as well, to see how bitter melon interacts with
the mechanisms of insulin (Raina et al., 2016). Soo May
et al. focus on bitter melon’s anti-inflammatory effects and
how they can potentially reduce knee pain in osteoarthritis
patients (Soo May et al., 2018). They concluded that with
3 months of supplementation, bitter melon can reduce
the need for analgesia consumption, while also showing
reductions in body weight, body mass index, and fasting
blood glucose (Soo May et al., 2018). Overall, bitter melon
has a variety of beneficial effects that are not well studied,
so it is important to understand how it affects the body to
better recommend this natural remedy.
Once this has been completed, health care providers
can use this information, especially in Asian countries, to
inform their patients about additional foods to include into
their diet, with the appropriate intake. As there are many
different vegetables and roots that are said to exhibit this
hypoglycemic effect, they can be tested similarly to how it
has been done in this paper and examine the effects before
formally recommending inclusion into the diet.
6. Acknowledgments
I would like to thank Dr. Kimberly Monahan for being
an encouraging mentor and guiding me through the
research process. Thank you to the Research in Biology
class of 2019 for providing support throughout this project.
Thank you to Kevin Zhang and Tyler Edwards for being
my lab assistants over the summer. Finally, I would like to
thank Dr. Sheck, the North Carolina School of Science and
Mathematics, and the Glaxo Endowment for allowing me
the opportunity to experience research.
7. References
Fuangchan, A. (2011) Hypoglycemic effect of bitter melon
compared with metformin in newly diagnosed type 2
diabetes patients. Journal of Ethnopharmacology, 134(2),
422–428. https://doi.org/10.1016/j.jep.2010.12.045
Insulin, Medicines, & Other Diabetes Treatments. (2016,
November 01). Retrieved January 27, 2018, from https://
www.niddk.nih.gov/health-information/diabetes/
overview/insulin-medicines-treatments
Jin Yang, S., Mook Choi, Jung. (2015). Preventive effects
of bitter melon (Momordica charantia) against insulin
resistance and diabetes are associated with the inhibition
of NF-κB and JNK pathways in high-fat-fed OLETF rats.
The Journal of Nutritional Biochemistry, 26(3), 234–240.
https://doi.org/10.1016/j.jnutbio.2014.10.010
Matsumoto, Y., Sumiya, E., Sugita, T., & Sekimizu, K.
(2011). An Invertebrate Hyperglycemic Model for the
Identification of Anti-Diabetic Drugs. PLOS ONE, 6(3),
e18292. https://doi.org/10.1371/journal.pone.0018292
Raina, K., Kumar, D., & Agarwal, R. (2016). Promise
of bitter melon (Momordica charantia) bioactives in
cancer prevention and therapy. Seminars in Cancer
Biology, 40–41, 116–129. https://doi.org/10.1016/j.
semcancer.2016.07.002
Soo May, L., Sanip, Z., Ahmed Shokri, A., Abdul Kadir,
A., & Md Lazin, M. R. (2018). The effects of Momordica
charantia (bitter melon) supplementation in patients with
primary knee osteoarthritis: A single-blinded, randomized
controlled trial. Complementary Therapies in Clinical Practice,
32, 181–186. https://doi.org/10.1016/j.ctcp.2018.06.012
Axe, J. (2015, August 29). 7 Benefits of Ayurvedic Med
icine: Lower Stress, Blood Pressure & More. (n.d.).
Retrieved September 22, 2018, from https://draxe.com/
ayurvedic-medicine/
CDC Press Releases. (2016, January 1). Retrieved
January 27, 2018, from https://www.cdc.gov/media/
releases/2017/p0718-diabetes-report.html
Chen, K., & Lu, Z. (2018). Immune responses to bacterial
and fungal infections in the silkworm, Bombyx mori.
Developmental & Comparative Immunology, 83, 3–11. https://
doi.org/10.1016/j.dci.2017.12.024
Drive, A. D. A. 2451 C., Arlington, S. 900, & Va 22202
1-800-Diabetes. (n.d.). Diabetes Symptoms. Retrieved
October 26, 2018, from http://www.diabetes.org/
diabetes-basics/symptoms/
BIOLOGY
Broad Street Scientific | 2018-2019 | 25

TETRAETHYL ORTHOSILICATE-POLYACRYLONITRILE
HYBRID MEMBRANES AND THEIR APPLICATION IN
REDOX FLOW BATTERIES
Ethan Frey
Abstract
Redox flow batteries (RFBs) are a reliable solution to long term energy storage, but lack an inexpensive and effective
proton exchange membrane. Polyacrylonitrile (PAN) nanoporous membranes have a high chemical stability but
low hydrophilicity when compared to Nafion, the standard membrane. The addition of tetraethyl orthosilicate (TEOS)
increases the mechanical and thermal properties of membranes and may also increase their hydrophilicity due to the
presence of hydrophilic silicon hydroxide bonds. Therefore, doping a nanoporous hydrophobic PAN membrane with
TEOS is hypothesized to increase the hydrophilicity of the membrane, while still maintaining a high chemical stability
and low vanadium crossover. Membranes of Nafion 212, nanoporous PAN, and a nanoporous hybrid TEOS/PAN were
prepared through a phase inversion method and tested for chemical stability, proton and vanadium crossover in a model
RFB, and water contact angle. The TEOS/PAN hybrid membrane had a higher hydrophilicity than both PAN and Nafion.
The addition of TEOS had no impact on chemical stability. However, the TEOS/PAN hybrid membrane did have a higher
vanadium crossover and lower proton/vanadium selectivity. It was concluded that TEOS can increase hydrophilicity,
but more research needs to be done to improve proton/vanadium selectivity, potentially by optimizing pore size. Since
TEOS was proven as an effective additive to membranes, progress was made towards the development of an ideal proton
exchange membrane and a solution to long-term energy storage.
1. Introduction
Recently, polyacrylonitrile (PAN) nanofiltration
membranes have proven to be a promising alternative to
Nafion membranes due to their high chemical stability,
and inexpensive cost. However, PAN membranes have
been found to lack the proton conductivity of Nafion, a
property that could be increased through the addition of
additives to a PAN membrane. The addition of tetraethyl
orthosilicate to a PAN membrane may not only increase
the hydrophilicity and proton conductivity of PAN, but
also improve the membrane’s mechanical strength and
thermal properties, while still maintaining the chemical
stability of PAN. The creation of a hybrid membrane of
PAN and TEOS could make progress towards the creation
of a cheaper membrane with properties comparable to that
of Nafion.
As renewable energy has become increasingly popular,
demand for long term energy storage increased as well. As
a result, a lot of attention has been given to redox flow
batteries (RFBs) due to their ability to store energy for
an indefinite period of time. What differentiates a RFB
from other battery types is that it behaves essentially as a
reversible fuel cell.
Figure 1. Redox Flow Battery Design: Two different
oxidation states of vanadium are stored in the tanks
on either side of the battery and pumped into two
adjacent half cells where the vanadium is reduced or
oxidized and a flow of electrons is created. However,
a proton exchange membrane is essential to allow
this reaction to occur.
The fuel is stored in tanks separate from where the
oxidation and reduction occurs (Fig. 1). This fuel is
pumped into two adjacent half cells separated by a proton
exchange membrane. The vanadium on one side of the
half cell is reduced and the other side is oxidized before
being pumped back into the fuel tank. The battery is
finished charging or discharging when all of the fuel has
been reduced or oxidized. Commonly used batteries, such
as lithium-ion batteries, can slowly discharge while not in
use, resulting in a loss of charge over time. This is due to
the fuel being stored where the reduction and oxidation
occurs, allowing spontaneous reactions to take place even
26 | 2018-2019 | Broad Street Scientific CHEMISTRY

when the battery is not in use. Since the fuel in RFBs is
stored externally, the battery cannot slowly discharge over
time while not in use, and energy can be stored for an
indefinite period of time. Vanadium is most typically used
in RFBs due to its multiple oxidation states and large ion
size (Alotto et al., 2014).
The expensive proton exchange membrane prevents
the use of RFBs on a commercial scale. The most widely
used membrane is Nafion. This membrane is expensive and
its properties could still be improved upon. It still exhibits
vanadium ion crossover, and a higher hydrophilicity and
proton conductivity could increase its efficiency. However,
it is challenging to manipulate these properties while still
maintaining a high level of chemical stability. Vanadium
ion crossover is difficult to decrease while still maintaining
proton conductivity. Similarly, proton conductivity is
difficult to increase without decreasing chemical stability
or increasing vanadium crossover. A membrane must
be both hydrophobic to maintain chemical stability and
hydrophilic to conduct protons. An alternative is to create
a membrane that is simply very hydrophobic and has
nanopores to allow protons to pass through. However, an
extremely hydrophobic membrane struggles to keep the
nanopores big enough to allow protons to pass through
but small enough to prevent vanadium crossover. Nafion is
designed (Fig. 2) such that it has a fluorinated carbon chain
that allows for high chemical stability and hydrophobicity.
Yet, Nafion still has a S-OH bond that allows for some
hydrophilicity.
exceeding 170°, indicating its high chemical stability (Feng
et al., 2002). However, high hydrophobicity can become
problematic when it prevents the membrane from
conducting protons. Polyacrylonitrile membranes with
nanopores from a phase inversion method (Zhang et al.,
2011) and conditioning in an alkali solution (Karpushkin
et al., 2017) have been investigated. These investigations
found that, as expected, polyacrylonitrile lacks the proton
conductivity of Nafion. Therefore, doping PAN to
increase its hydrophilicity could create a membrane that
is comparable to Nafion.
Doping Nafion with metal oxides to improve its
hydrophilicity has been explored repeatedly and proven
successful (Noto et al., 2007). Specifically, silicon dioxide
has been proven effective due to its ability to significantly
increase the thermal properties and hydrophilicity
of Nafion (Yu et al., 2007). Doping PAN with metal
oxides should also increase its hydrophilicity. Tetraethyl
orthosilicate (TEOS) has been explored as an additive to
a polyvinylidene fluoride membrane (Liu et al., 2008).
However, only the enhanced mechanical properties and
effect on pore size were explored and the doped PVDF
membrane was not tested in application for RFBs. TEOS
has also been tested and used for the creation of a super
hydrophilic surface in photovoltaic cells, proving its use as
a hydrophilic material (Yan et al., 2015). Its hydrophilicity
is due to the presence of hydroxide bonds after being
polymerized and hydrolyzed, like the ones in Nafion (Fig.
3).
Figure 2. Nafion Structure: Nafion contains
a hydrophobic fluorinated backbone with a
hydrophilic sulfur hydroxide bond.
As a result of its structure, Nafion maintains a high
chemical stability while still allowing protons to cross over
the membrane. The cost of Nafion is mainly due to the
manufacturing cost of making fluorinated membranes.
Therefore, non-fluorinated membranes have been
investigated as a cheaper alternative. However, many
lack the chemical stability of fluorinated membranes,
which poses a challenge for their application in vanadium
RFBs. Polyacrylonitrile has recently been recognized
as a promising option for non-fluorinated membranes
due to its high chemical stability despite the absence of
fluorine. In fact, PAN has been explored in applications as
a superhydrophobic polymer with a water contact angle
CHEMISTRY
Figure 3. Hydrolyzed and Polymerized TEOS: Just
like Nafion’s hydrophilic sulfur hydroxide bonds,
TEOS contains hydrophilic silicon hydroxide bonds.
Doping PAN with TEOS should have the same effect
that adding a metal oxide, like silicon oxide, would have.
TEOS has also demonstrated an increase in the thermal
stability of membranes (Liu et al., 2008). Therefore,
doping PAN with TEOS should combine the superhydrophobicity
and chemical stability of PAN with the
super-hydrophilicity, thermal stability, and high tensile
strength of TEOS without compromising the high
chemical stability or proton/vanadium selectivity of PAN.
Engineering a more efficient and less expensive proton
exchange membrane will allow energy to be generated
and stored for an indefinite period of time, making
Broad Street Scientific | 2018-2019 | 27

enewable energy much more reliable and allowing entire
cities to depend on it. The future of RFB membranes lies
in the development of a non-fluorinated membrane, due
to the cheaper manufacturing cost. Through testing how
to improve the properties of a promising non-fluorinated
membrane, progress is made towards engineering an ideal
proton-exchange membrane.
2. Methods
2.1 – Preparing the Membranes
The following procedure was adapted from Liu (2008).
The nanoporous PAN membrane was prepared by casting
a 15 wt% PAN (M w
= 150,000), 3 wt% LiCl, and 4 wt%
polyvinylpyrrolidone (PVP) solution in DMSO on a glass
plate and leveling it with an RDS40 wire round rod (RD
Specialties, USA). A normal phase inversion was then
conducted using a water bath at room temperature. The
membrane was left in the water bath for 1-2 days to
remove any remaining solvents. The hybrid membrane
was prepared by lowering the weight percentages to 12.5
wt% PAN, 2.5 wt% LiCl, 3.25 wt% PVP, and adding 6.7
wt% TEOS. A normal phase inversion was then conducted
in an acid bath (pH = 1), to allow the polymerization of
TEOS, and then transferred to a water bath for 1-2 days.
2.2 – Model Redox Flow Battery
The model redox flow battery was designed using
two mini-variable flow peristaltic pumps (Fisher) and
a modified fuel cell (Heliocentris). The fuel cell was
composed of graphite, two carbon felt electrodes, and a
membrane. The design is shown below (Fig. 4).
60-90°C. After the dissolution of V 2
O 5
, temperature was
maintained while .7mL of glycerol was stirred in. Once a
uniform blue color was obtained, indicating the formation
of V 4+ , the reaction was completed.
2.4 – Proton/Vanadium Selectivity Test
Proton vanadium selectivity was tested by filling one
side of the fuel cell with water and the other side with
2M VO 2
+
and 7M HCl. The pumps were run for 45
minutes with samples being taken every 5 minutes. The
concentration of vanadium in these samples was measured
using a spectrophotometer. The absorption at 765nm
was measured and Beer’s law was used to calculate the
concentration using a molar absorptivity of 13.40 (Choi
et al., 2013). The concentration of protons was measured
through pH measurement using a pH meter (Vernier). All
data were recorded in LoggerPro (Vernier).
2.5 – Chemical Stability
The chemical stability of the membranes was estimated
by placing the membranes in a solution that consisted of
1M V 2
O 5
and 5M HCl at 50°C for 30 days. The presence of
VO 2
+
indicated that the membrane had been oxidized. The
stability of the membrane was determined by calculating
the percentage of VO 2
+
in the sample in comparison to a
control solution without a membrane.
3. Results
3.1 – Water Contact Angle
Figure 4. Model Redox Flow Battery Design: The
design consists of two peristaltic pumps, two fuel
tanks, and two adjacent half cells with electrodes
separated by a membrane.
2.3 – Vanadium 4+ Preparation
All fuel was prepared through the reduction of V 2
O 5
to VO 2
+
using glycerol in the presence of HCl (Small et
al., 2017). 38.9 mL of deionized water, 50.0 mL of 12.1M
HCl, and 5.0g of V 2
O 5
was added to a beaker and stirred at
Figure 5. Water contact angle of a drop of water on
the membranes. The photo was taken on an IPhone
6s and the angles were measured using Logger Pro.
(A) Nafion (B) PAN (C) Hybrid
28 | 2018-2019 | Broad Street Scientific CHEMISTRY

Hydrophilicity of Nafion, PAN, and the hybrid
membrane was demonstrated by measuring the contact
angle of a water droplet (Fig. 5). It was found that Nafion
had the largest water contact angle of 87.09° followed by
PAN at 55.01° and the hybrid membrane at 42.27°.
3.2 – Proton and Vanadium Crossover
membrane the highest (Fig. 6A). The TEOS/PAN hybrid
membrane also had the highest proton conductivity (Fig.
6B). The overall proton/vanadium selectivity was similar
for the Nafion and PAN membranes. However, the hybrid
membrane had a much lower selectivity (Fig. 6C).
3.3 – Chemical Stability
Table 1. The percent of V 5+ reduced to V 4+ .This
indicated ongoing oxidation of the membrane
and therefore can be used to analyze the chemical
stability of the membrane. Concentrations were
measured using a spectrophotometer.
Percent
Vanadium
Reduced (%)
Percent
Reduced
Compared
to reference
Nafion PAN Hybrid Reference
4.72% 1.20% 1.67% 2.41%
96.06% -49.94% -30.54% ________
The chemical stability of the prepared membranes was
measured as the percent of the original vanadium that was
reduced (Table 1), indicating ongoing oxidation of the
membrane. The percent of vanadium reduced was highest
for Nafion with 4.72% followed by the hybrid membrane
with 1.67% and the PAN membrane with 1.20%. However,
2.41% of the vanadium in the reference sample (the sample
without a membrane) was reduced. When comparing the
measured percentages to the reference percentages, it is
found that the percent reduced in the Nafion was 96%
higher than that of the reference sample, PAN was 49.9%
smaller, and the hybrid was 30.5% smaller.
4. Discussion and Conclusion
Figure 6. (A) Vanadium Crossover (B) Proton
Crossover (C) Proton/Vanadium Selectivity
The vanadium and proton crossovers were measured
over a 45 minute period. A model redox flow battery
was used. An acidic V 4+ solution was placed on one side
of the battery and deionized water on the other side.
The concentration of vanadium was measured over time
using a spectrophotometer and the proton concentration
was measured using a Vernier pH probe. The proton/
vanadium selectivity was determined as the ratio of the
proton crossover to the vanadium crossover.
Nafion was found to have the lowest vanadium
crossover, PAN the second highest, and the hybrid
The goal of this project was to demonstrate that
hydrolyzed and polymerized TEOS could effectively
increase hydrophilicity and provide a suitable substitute
for Nafion in a vanadium redox flow battery. The results
of the experiments are summarized in Table 2. Introducing
TEOS to the PAN membrane improved its hydrophilicity
as demonstrated by the water contact angle test (Fig. 5).
The smaller the water contact angle, the more hydrophilic
the material, because the water is not as repelled to the
polymer. The hybrid membrane had a smaller water
contact angle than both PAN and Nafion, indicating a
high hydrophilicity. Its high hydrophilicity was further
demonstrated when tested in a model redox flow battery.
The hybrid membrane showed a higher proton crossover
than both Nafion and PAN (Fig. 6). These tests show that
the proton conductivity of the PAN membrane was most
likely successfully increased. The chemical stability of
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Table 2. Data Summary: The water contact angle, vanadium crossover, proton crossover, proton/vanadium
selectivity, and chemical stability of Nafion, PAN, and the hybrid TEOS/PAN membrane.
Water
Contact
Angle (°)
Permeability to
V 4+ (cm 2 min -1 )
Permeability to
H + (cm 2 min -1 )
Proton/
Vanadium
Selectivity
Chemical Stability (% Reduced
Compared to Reference)
Nafion 87.09 7.54x10 -5 3.77x10 -4 18.19 96.06%
PAN 55.01 1.57x10 -4 7.83x10 -4 15.74 -49.94%
Hybrid 42.27 2.37x10 -4 1.18x10 -5 8.75 -30.54%
the membrane was also maintained with the addition of
TEOS, as none of the membranes had a significant amount
of oxidation occur in the presence of a strong oxidizer.
However, the TEOS-PAN hybrid did show increased
vanadium crossover. Prevention of vanadium crossover
is an essential function of a proton-exchange membrane.
The different oxidation states of vanadium on either side of
the membrane need to remain unmixed while still allowing
protons to cross over. Therefore, proton/vanadium
selectivity is measured as the ability of the membrane to
allow protons to cross over but prevent vanadium ions
from crossing over. A higher proton/vanadium selectivity
is ideal. However, the hybrid membrane displayed a
lower proton/vanadium selectivity than both Nafion
and the PAN membrane. Further optimization will need
to be performed in order to improve proton/vanadium
selectivity.
There are several areas that can be explored to improve
upon this research. The PAN and TEOS-PAN membranes
were cast through a phase inversion method and developed
nanopores, which allow these ions to cross over. The size
of the nanopores has a significant effect on the selectivity
of the membrane. To aid in the casting process, a lower
polymer concentration was used for the hybrid membrane.
However, this may have resulted in an increased pore size,
causing the decreased selectivity and increased vanadium
crossover. This could be examined with scanning electron
microscopy to verify the pore sizes. It could be inferred
that if the increased vanadium crossover is only due to an
increased pore size, then the increased proton crossover
is also only due to an increased pore size. However, it was
demonstrated that the membrane was more hydrophilic
in the water contact angle test. Therefore, the hybrid
membrane should easily allow protons to cross over even
with a reduced pore size.
This study successfully demonstrated that the addition
of hydrolyzed and polymerized TEOS to a PAN membrane
was effective in increasing membrane hydrophilicity.
Further research needs to be done to investigate if the
addition of TEOS results in an increased vanadium crossover
or if this could be overcome through the optimization of
the pore size of the hybrid membrane. The membranes’
properties should also be tested in a functional redox flow
battery to test the effects of the increased properties on the
efficiency of the battery. TEOS was proven as an effective
additive to membranes in increasing their mechanical and
thermal properties and hydrophilicity. A hybrid TEOS-
PAN membrane with an optimized pore size may create
a membrane with properties comparable to that of Nafion
at a cheaper cost.
5. Acknowledgments
I would like to thank Dr. Michael Bruno for his help
and mentorship throughout the research project as
well as the help and support of my fellow Research in
Chemistry peers. Finally, I would like to thank the NCSSM
Foundation for funding my research project as it has been
an invaluable experience.
6. References
Alotto, P., Guarnieri, M., Moro, F. (2014). Redox flow
batteries for the storage of renewable energy: A review.
Renewable and Sustainable Energy Reviews, 29, 325-335.
doi:10.1016/j.rser.2013.08.001
Choi, N. H., Kwon, S., Kim, H. (2013). Analysis of the
Oxidation of the V(II) by Dissolved Oxygen Using UV-
Visible Spectrophotometry in a Vanadium Redox Flow
Battery. Journal of The Electrochemical Society, 160(6).
doi:10.1149/2.145306jes
Feng, L., Li, S., Li, H., Zhai, J., Song, Y., Jiang, L., Zhu,
D. (2002). Super-Hydrophobic Surface of Aligned
Polyacrylonitrile Nanofibers. Angewandte Chemie
International Edition, 41(7), 1221-1223. doi:10.1002/1521-
3773(20020402)41:73.0.co;2-g
Karpushkin, E. A., Gvozdik, N. A., Stevenson, K. J.,
Sergeyev, V. G. (2017). Membranes based on carboxylcontaining
polyacrylonitrile for applications in vanadium
redox-flow batteries. Mendeleev Communications,
27(4), 390-391. doi:10.1016/j.mencom.2017.07.024
Liu, X., Peng, Y., Ji, S. (2008). A new method to prepare
organic–inorganic hybrid membranes. Desalination,
221(1-3), 376-382. doi:10.1016/j.desal.2007.02.056
30 | 2018-2019 | Broad Street Scientific CHEMISTRY

Noto, V. D., Gliubizzi, R., Negro, E., Vittadello,
M., Pace, G. (2007). Hybrid inorganic–organic proton
conducting membranes based on Nafion and 5wt.% of
M x
O y
(M=Ti, Zr, Hf, Ta and W). Electrochimica Acta,
53(4), 1618-1627. doi:10.1016/j.electacta.2007.05.00
Small, L. J., Pratt, H., Staiger, C., Martin, R. I., Anderson, T.
M., Chalamala, B., Subarmanian, V. R. (2017). Vanadium
Flow Battery Electrolyte Synthesis via Chemical Reduction
of V 2
O 5
in Aqueous HCl and H 2
SO 4
. doi:10.2172/1342368
Yan, H., Yuanhao, W., Hongxing, Y. (2015). TEOS/Silane-
Coupling Agent Composed Double Layers Structure: A
Novel Super-hydrophilic Surface. Energy Procedia, 75,
349-354. doi:10.1016/j.egypro.2015.07.384
Yu, J., Pan, M., Yuan, R. (2007). Nafion/Silicon oxide
composite membrane for high temperature proton
exchange membrane fuel cell. Journal of Wuhan
University of Technology- Mater. Sci. Ed., 22(3), 478-481.
doi:10.1007/s11595-006-3478-3
Zhang, H., Zhang, H., Li, X., Mai, Z., Zhang, J. (2011).
Nanofiltration (NF) membranes: The next generation
separators for all vanadium redox flow batteries (VRBs)?
Energy Environmental Science, 4(5), 1676. doi:10.1039/
c1ee.
CHEMISTRY
Broad Street Scientific | 2018-2019 | 31

NOVEL SYNERGISTIC ANTIOXIDATIVE
INTERACTIONS BETWEEN SOY LECITHIN AND
CYCLODEXTRIN-ENCAPSULATED QUERCETIN IN A
LIPID MATRIX
Anirudh Hari
Abstract
Food oils stale via multiple mechanisms, the most damaging being oxidation by free radicals through reaction with oxygen
in the air. Antioxidants are used to combat this oxidation, but many that are commonly used have carcinogenic properties.
Quercetin is a safer polyphenolic phytochemical known to possess antioxidative properties in lipid matrices. Soy lecithin,
a common food emulsifier primarily composed of phospholipids, also possesses antioxidative properties in lipid matrices,
one of its primary mechanisms being the dispersion of less lipid-soluble antioxidants in the matrix. Phosphatidylcholine,
the primary component of soy lecithin, is capable of forming a hydrogen bond from its polar head to a hydroxyl group of
quercetin to create a complex known as a phenolipid. This phenolipid has a greater antioxidative effect than soy lecithin
or quercetin do alone. However, one issue that remains prevalent is rapid degradation of quercetin in the lipid matrix.
Beta-cyclodextrin is a ring-shaped molecule which can encapsulate quercetin, but it has not been tested for its ability to
protect quercetin against degradation in oils.
A novel phenolipid was formulated between a quercetin-cyclodextrin complex and soy lecithin, thus doubly encapsulating
quercetin in order to potentially increase antioxidative lifetime by protecting the molecule while still maintaining the
dispersive effect of lecithin. An accelerated oxidation test was conducted and time points were analyzed for radical
scavenging activity. Results revealed that the novel phenolipid scavenged radicals more effectively than quercetin or
lecithin by themselves, and also had a greater antioxidative lifetime, showing much higher radical scavenging activity than
the quercetin-lecithin phenolipid and quercetin or lecithin alone after 12 days of the oxidation test. This implies novel
applications for beta-cyclodextrins in the protection of polyphenolic antioxidants in lipid matrices.
1. Introduction
The oxidation of lipids is a major concern in the food
industry, especially with unsaturated and polyunsaturated
fats which are very sensitive to degradation (Ramadan et
al., 2012). When excited by light, molecular oxygen in the
air forms the superoxide anion, a free radical that oxidizes
molecules in the oil, causing a radical chain reaction that
results in cleavage of the double bonds in unsaturated fatty
acids, resulting in their degradation into aldehydes and
ketones. This process, known as oxidative rancidification,
is responsible for the characteristic stale smell of old oils.
While there are a number of ways to prevent oxidative
rancidification, including wrapping containers with foil
to prevent reactions catalyzed by sunlight and vacuumsealing
containers to prevent interactions with oxygen,
the most effective way to protect oils is the addition of
antioxidants to scavenge free radicals (Judde et al., 2003).
Antioxidants are used in the food industry to protect
oils by reducing reactive free radicals. The addition of
antioxidants to oils inhibits oxidative rancidification,
slowing the rate of decline in oil quality (Ramadan et
al., 2012). However, many of the most commonly used
synthetic antioxidants, including butylated hydroxyanisole,
butylated hydroxytoluene, propyl gallate, and tert-butyl
hydroquinone, have been shown to promote carcinogenesis
(National Toxicology Program).
Flavonoids are a group of natural polyphenolic
phytochemicals consisting of more than 4000
molecules that vary in structure and properties.
3,5,7,3′,4′-pentahydroxyflavone, also known as quercetin,
is a yellow-colored flavonoid that possesses antioxidative
properties in lipid matrices and is considered safe at much
higher doses than most common synthetic antioxidants.
Quercetin is used in the food industry as an alternative to
synthetic antioxidants, but the degradation of quercetin
via glycosylation at its hydroxyl groups is a major limit
to its application in foods. The structural feature of
quercetin most involved in its antioxidative mechanism is
the hydroxyl group on the 4′ carbon, which can donate a
hydrogen atom to a free radical to reduce it (Ozgen et al.,
2016) (Fig. 1).
Figure 1. Quercetin reduces a free radical, labelled R,
by donating a hydrogen atom from its 4′ hydroxyl
group to form a stable radical 4′-quercetin.
32 | 2018-2019 | Broad Street Scientific CHEMISTRY

Phospholipids are another class of antioxidants that
have different antioxidative mechanisms than flavonoids.
Soy lecithin is a mixture of amphipathic phospholipids,
primarily phosphatidylcholine, and is a common
emulsifying agent that also possesses antioxidative
properties in lipid matrices. Soy lecithin has multiple
antioxidative mechanisms by itself. The choline group on
the phospholipid head of phosphatidylcholine is capable
of accepting a free electron from radical molecules.
Phospholipids also form an oxygen barrier at the
atmospheric interface of oils to prevent oxidation (Judde
et al., 2003).
It has been shown that soy lecithin also helps to
disperse other antioxidants present within the oil to allow
them to scavenge radicals more efficiently. Quercetin
and soy lecithin exhibit higher radical scavenging activity
when mixed together than when tested individually. The
catechol group on the 3′ and 4′ carbons of quercetin allows
for intramolecular and intermolecular hydrogen bonding
with phosphatidylcholine to create a “phenolipid” between
quercetin and the phospholipid (Fig. 2). This phenolipid is
fat soluble, increasing the accessibility of quercetin in oil.
However, although soy lecithin fully surrounds quercetin
in the phenolipid formation, it does not inhibit the
breakdown of quercetin, which remains a limiting factor
in its application (Ramadan et al., 2012).
of beta-cyclodextrin may be able to bond with soy lecithin
through hydrogen bonds to form a novel phenolipid,
increasing the solubility of a complex of quercetin and
beta-cyclodextrin in oil. This would form a double
encapsulation of quercetin (Fig. 3). Beta-cyclodextrin
could prevent the degradation of quercetin with its
encapsulation of the molecule, while soy lecithin facilitates
its dispersion in oil, allowing this novel phenolipid to have
a higher antioxidative effect compared to quercetin or
lecithin by themselves as well as an increased antioxidative
lifetime. This could be important in controlling the rate of
oxidation of quercetin both in food protection and medical
applications.
Figure 3. Potential double encapsulation of quercetin
by beta-cyclodextrin and phosphatidylcholine.
Figure 2. Quercetin-phosphatidylcholine phenolipid
complex.
Cyclodextrins are ring-shaped molecules that can
encapsulate certain molecules through hydrogen bonding.
Such encapsulation has been performed with quercetin
and has shown an increase in solubility (Zheng et al.,
2005). However, an important potential application of
the cyclodextrin-quercetin complex that has not been
previously investigated is the possible protection of
quercetin from degradation.
Since beta-cyclodextrin increases the water solubility
of quercetin, it would decrease the lipid solubility, making
the cyclodextrin-quercetin complex unsuitable for use in a
lipid matrix by itself. However, the outer hydroxyl groups
It was hypothesized that a phenolipid between lecithin
and the quercetin-cyclodextrin complex would increase
availability of quercetin in sunflower oil, and that this
phenolipid would have a greater antioxidative lifetime
than the phenolipid made of quercetin and lecithin.
Alternatively, the double encapsulation may prevent
degradation of quercetin without increasing the availability
of quercetin in sunflower oil.
In the present study, a molecular docking model of the
encapsulation of quercetin by beta-cyclodextrin indicated
that in the most stable conformation, the 4′ hydroxyl group
important to the antioxidative mechanism of quercetin is
not encompassed by the cyclodextrin, while the rest of
the quercetin molecule is, suggesting that quercetin could
retain its antioxidative ability in the beta-cyclodextrin
complex.
The novel phenolipid was prepared along with
the quercetin-lecithin phenolipid and the quercetincyclodextrin
complex. Each antioxidant sample was mixed
in sunflower oil and incubated in an oven to accelerate
oxidation. Radical scavenging activity assay was conducted
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periodically to measure reduction in antioxidant
effectiveness over time. Results from radical scavenging
activity assay indicate that the doubly encapsulated
quercetin does have a greater antioxidative lifetime than
the quercetin-lecithin phenolipid, and it also has a greater
initial ability to scavenge radicals than quercetin or soy
lecithin alone. This suggests a new potential application of
beta-cyclodextrins to allow antioxidants to last longer in
oils, which would also increase the lifetime of the oils due
to longer term protection from oxidative rancidification.
2. Materials and Methods
2.1 – Molecular Modeling
Before experimentation, the encapsulation of quercetin
by beta-cyclodextrin was computationally modelled
by molecular docking using PatchDock. PDB files for
quercetin and beta-cyclodextrin were obtained and fed
into the server, which found the most stable conformation
of quercetin inside beta-cyclodextrin using shape
complementarity and electrostatic interactions.
2.2 – Encapsulation of Quercetin in Beta-Cyclodextrin
Quercetin dihydrate, 97% (Alfa Aesar) was encapsulated
in beta-cyclodextrin hydrate, 99% (Acros Organics) using
physical kneading. An equimolar ratio of quercetin and
beta-cyclodextrin powder was mixed in a mortar using a
pestle for 10 minutes. Then, a small amount of ethanol
(Fisher Scientific) was added and the mixture was kneaded
for 40 more minutes. After kneading, the mixture was
dried in a vacuum desiccator for 24 hours.
50 mg of the dried mixture was dissolved in 50 mL
of acetonitrile (Fisher Scientific), causing the betacyclodextrin
and quercetin+beta-cyclodextrin complexes
to precipitate, while the free quercetin that did not
get complexed remained in solution. The absorbance
spectrum of quercetin was taken using a Vernier UV-
Vis spectrophotometer in a Hellma QS 282 1.000 quartz
cuvette, showing 2 UV peaks: one at 260 nm and one at
370 nm. A standard curve was made with absorption at
370 nm as a function of quercetin concentration (Santos et
al., 2015) (Fig. 4).
Figure 4. Standard curve of quercetin in acetonitrile
at 370 nm.
The solution of complex in acetonitrile was allowed
to settle for 3 days. The concentration of free quercetin
in solution was determined using the standard curve.
This concentration was compared to the total quercetin
concentration in the solution, and the entrapment
efficiency (EE) was determined using the following
equation:
free quercetin concentration
EE = 1 -
total quercetin concentration
2.3 – Formation of Phenolipid Complexes
The complex was removed from acetonitrile solution
by vacuum filtration and mixed with soy lecithin (Alfa
Aesar) at a 3:97 ratio complex to lecithin by mass. The
complex was then dissolved in 10 mL ethyl acetate (Fisher
Scientific). Several control groups were also dissolved
in ethyl acetate: quercetin, quercetin with lecithin 3:97
(phenolipid), and quercetin encapsulated in cyclodextrin
without lecithin.
Each sample was incubated at 40°C for 24 hours to
facilitate dissolution. The samples were then dried by
creating a vacuum within a chamber using a Chemglass
Scientific Apparatus Vacuum for 2 hours.
2.4 – Accelerated Oxidation
Each sample was added to 100% sunflower oil (Loriva,
cold pressed) at a concentration of 500 parts per million.
The Schaal oven accelerated oxidation test was run on the
4 samples as well as a sample with only sunflower oil as
a negative control. Each mixture was placed in a 20 mL
clear glass bottle. Each bottle was completely sealed and
incubated in an oven at 60°C (Ramadan et al., 2012).
Samples were withdrawn at 0, 3, 9, and 12 days and
analyzed by Radical Scavenging Activity (RSA) assay.
1,1-Diphenyl-2-picrylhydrazyl (DPPH) radical (Alfa Aesar)
was dissolved in reagent grade toluene (Fisher Scientific)
at a concentration of 10-4 M. 10 mg of each experimental
sample was dissolved in 100 µL of toluene. This solution
was mixed with 390 µL of the DPPH solution, and the
mixture was vortexed at maximum speed for 20 seconds
at ambient temperature. The decrease in absorbance at
515 nm between the time of making the mixture and 1
hour later was measured in a quartz cuvette using a UV-
Vis spectrophotometer. As a control, radical scavenging
activity towards the toluenic DPPH solution was measured
without addition of sample. Percent inhibition was
calculated by comparing the absorbance after 1 hour of the
control to each of the test samples:
% inhibition =
abs of control - abs of test sample
abs of control
RSA was measured as the difference in 515 nm
absorption between the beginning and end of the assay.
RSA was compared between each time-point taken for
each sample (Ramadan et al., 2012).
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3. Results and Discussion
In order to determine if quercetin would likely maintain
its antioxidative properties while encapsulated by betacyclodextrin,
molecular docking was computationally
modelled. In the lowest energy conformation, the 4′
hydroxyl group of quercetin, shown in light blue, extends
out of the cyclodextrin ring, while the rest of the molecule
sits inside the cyclodextrin (Fig. 5). This suggests that
beta-cyclodextrin can protect quercetin from degradation
without compromising its effectiveness as an antioxidant.
radical scavenging activity with the least decrease in
activity over time, while the samples that did not include
cyclodextrin scavenged radicals less effectively after 12
days, degrading more quickly. The quercetin encapsulated
with cyclodextrin without lecithin also showed increased
antioxidative lifetime compared to quercetin alone (Fig. 7,
8).
Figure 6. Radical scavenging activity assay was
conducted immediately after mixing the antioxidant
formulations in sunflower oil.
Figure 5. Molecular docking model of quercetin
in beta-cyclodextrin. Beta-cyclodextrin is shown
in pink, quercetin is shown in yellow, and the
4′ hydroxyl group of quercetin is shown in light
blue. The 4′ hydroxyl group is key to quercetin’s
antioxidative effect.
According to the hypothesis, the doubly encapsulated
quercetin formulation would scavenge radicals more
effectively than quercetin or lecithin alone before the
acceleration test, and have a smaller decrease in radical
scavenging activity over time than the quercetin-lecithin
phenolipid formulation. The entrapment of quercetin
in beta-cyclodextrin was successful, and the entrapment
efficiency was determined by UV absorbance to be 45%.
Radical scavenging activity assay conducted on the
day the complexes were mixed in sunflower oil revealed
that the quercetin-lecithin phenolipid formulation had
the highest radical scavenging activity, followed by the
novel double encapsulation formulation. Quercetin and
soy lecithin alone had similar radical scavenging activity
results (Fig. 6).
Samples in the Schaal oven accelerated oxidation test
were withdrawn at 3, 6, and 12 days and assayed for
radical scavenging activity. After incubation for 12 days,
the doubly encapsulated quercetin sample had the highest
Figure 7. Radical scavenging activity was assayed
at 3, 6, and 12 days after initiating the accelerated
oxidation test.
Figure 8. Decrease of RSA after 12 days of oxidation
test compared to RSA before oxidation test was
begun.
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The higher initial RSA of the doubly-encapsulated
quercetin compared to quercetin and lecithin alone
suggests that the polar head of phosphatidylcholine did
hydrogen bond to the exterior hydroxyl groups of the
quercetin-cyclodextrin complex, dispersing the quercetin
in the sunflower oil as hypothesized (Fig. 6). The initial
RSA of the quercetin-cyclodextrin complex without
lecithin was lowest of the groups tested, which was
expected since cyclodextrin increases the water-solubility
of quercetin, decreasing its availability in sunflower oil.
The higher antioxidative lifetimes of both the
doubly encapsulated quercetin and the single quercetincyclodextrin
complex suggest that beta-cyclodextrin
provides protection to quercetin from degradation in
sunflower oil, consistent with the hypothesis (Fig. 6, 7).
4. Conclusion
The use of cyclodextrins in the protection of flavonoidclass
antioxidants from degradation in lipid matrices has
been unexplored, as have phenolipid bonds between
cyclodextrins and phospholipids. The novel phenolipid
formulation constructed in this experiment, consisting of
quercetin doubly encapsulated in beta-cyclodextrin and
soy lecithin, had a higher radical scavenging activity than
quercetin or soy lecithin alone and a higher antioxidative
lifetime than known phenolipid formulations of quercetin
and lecithin. These results indicate that cyclodextrins
can increase the antioxidative lifetime of flavonoids
without compromising antioxidative ability if paired
with a phospholipid to disperse the complex in the
lipid matrix, opening up new avenues of lipid oxidation
research with applications in food oils. Future work
would include repeating the accelerated oxidation test
and radical scavenging activity assays for improved
statistical significance, as well as testing different types of
polyphenols, phospholipids, and oils to determine whether
the same effects are observed.
5. Acknowledgments
I would like to thank Dr. Michael Bruno for selecting
me for the Research in Chemistry program and providing
guidance throughout the development and execution of my
project. I would also like to thank the NCSSM Foundation
for providing funding for the purchase of materials and
equipment used in my experimentation.
6. References
Di Donato, C., et al. (2016). Alpha- and Beta-Cyclodextrin
Inclusion Complexes with 5-Fluorouracil: Characterization
and Cytotoxic Activity Evaluation. Molecules, 21(12),
1644. doi:10.3390/molecules21121644
Judde, A., Villeneuve, P., Rossignol-Castera, A., & Guillou,
A. L. (2003). Antioxidant effect of soy lecithins on vegetable
oil stability and their synergism with tocopherols. Journal
of the American Oil Chemists Society, 80(12), 1209-1215.
doi:10.1007/s11746-003-0844-4
Kahveci, D., Laguerre, M., & Villeneuve, P. (2015).
Phenolipids as New Antioxidants: Production, Activity,
and Potential Applications. Polar Lipids, 185-214.
doi:10.1016/b978-1-63067-044-3.50011-x
National Toxicology Program (2001). Carcinogens
Nominated for 11th Report on Carcinogens. JNCI Journal
of the National Cancer Institute, 93(18), 1372-1372.
doi:10.1093/jnci/93.18.1372-a
Ozgen, S., Kilinc, O. K., & Selamoğlu, Z. (2016). Antioxidant
Activity of Quercetin: A Mechanistic Review. Turkish
Journal of Agriculture - Food Science and Technology,
4(12), 1134. doi:10.24925/turjaf.v4i12.1134-1138.1069
Panya, A., Laguerre, M., Bayrasy, C., Lecomte, J.,
Villeneuve, P., Mcclements, D. J., & Decker, E. A. (2012).
An Investigation of the Versatile Antioxidant Mechanisms
of Action of Rosmarinate Alkyl Esters in Oil-in-Water
Emulsions. Journal of Agricultural and Food Chemistry,
60(10), 2692-2700. doi:10.1021/jf204848b
Ramadan, M. F. (2012). Antioxidant characteristics
of phenolipids (quercetin-enriched lecithin) in lipid
matrices. Industrial Crops and Products, 36(1), 363-369.
doi:10.1016/j.indcrop.2011.10.008
Santos, E. H., Kamimura, J. A., Hill, L. E., & Gomes, C.
L. (2015). Characterization of carvacrol beta-cyclodextrin
inclusion complexes as delivery systems for antibacterial
and antioxidant applications. LWT - Food Science and
Technology, 60(1), 583-592. doi:10.1016/j.lwt.2014.08.046
Tanhuanpää, K., Cheng, K. H., Anttonen, K., Virtanen,
J. A., & Somerharju, P. (2001). Characteristics of Pyrene
Phospholipid/ γ -Cyclodextrin Complex. Biophysical
Journal, 81(3), 1501-1510. doi:10.1016/s0006-
3495(01)75804-3
Zheng, Y., Haworth, I. S., Zuo, Z., Chow, M. S., &
Chow, A. H. (2005). Physicochemical and Structural
Characterization of Quercetin-β-Cyclodextrin Complexes.
Journal of Pharmaceutical Sciences, 94(5), 1079-1089.
doi:10.1002/jps.20325
36 | 2018-2019 | Broad Street Scientific CHEMISTRY

UTILIZATION OF ATOMIC LAYER DEPOSITION TO
CREATE NOVEL METAL OXIDE PHOTOANODES FOR
SOLAR-DRIVEN WATER SPLITTING
Annie Wang
Abstract
A major obstacle of dye-sensitized photoelectrosynthesis cells is the recombination of 60% of the injected electrons from
the dye into the photoanode. Creating core/shell structures is one technique of slowing down electron recombination.
There has been no work done on TiO 2
/SnO 2
structures or on TiO 2
/TiO 2
structures using atomic layer deposition, so the
aim of the project was to successfully deposit these materials, optimize the deposition, and compare the behavior of the
structures to the standard SnO 2
/TiO 2
core/shell. Novel deposition of TiO 2
and SnO 2
onto mesoporous TiO 2
thin films
was achieved using atomic layer deposition with the TDMAT and TDMASn precursors. Subsequently, the dye loading
capabilities of the core/shell structures were measured after being loaded with the RuP chromophore. The samples were
characterized through XPS after varying deposition parameters to optimize deposition conditions in order to create TiO 2
and SnO 2
shells of comparable thicknesses. Dye loading onto TiO 2
/TiO 2
was found to be affected by parameters other
than pore size, including type of TiO 2
used and processing conditions. Deposition of SnO 2
initially resulted in SnO, but
TiO 2
/SnO 2
structures were able to be synthesized by using dyesol TiO 2
instead of mixed-phase TiO 2
. The successfully
created TiO 2
/SnO 2
and TiO 2
/TiO 2
core/shells can be studied to differentiate competing electron recombination theories.
1. Introduction
As the world is becoming increasingly dependent on
our dwindling supply of nonrenewable sources of energy,
clean energy is the only viable long-term option. A
promising method for solar energy conversion is the use
of dye-sensitized photoelectrosynthesis cells (DSPECs)
(Brennaman et al., 2016). The DSPEC shares similar design
features and applies similar principles as the dye-sensitized
solar cell (DSSC), and although less developed, holds
much promise for the future of solar energy conversion.
Photoelectrosynthesis cells convert light to chemical
energy in the form of stored hydrogen fuel. Rather than
producing electrical energy as in solar cells, DSPECs use
photons from sunlight to split water into hydrogen and
oxygen gases (Fujishima & Honda, 1972). The oxidation
of water occurs at the anode and the reduction of hydrogen
occurs at the cathode. The key advantage of this model
is that hydrogen is able to be stored as chemical fuel for
future use. Photoanodes used in these cells are often made
of metal oxide semiconductors due to their ability to form
high surface area films, ability to accept photoinjected
electrons from dye molecules, and transparency in the
visible spectrum because of their optimally high band gap
energies. (Ashford et al., 2015).
In addition, a crucial component of the DSPEC is the
electron injection from chromophores (dye molecules)
attached to the surface of the mesoporous (containing
pores with diameters between 2 and 50 nm) film into
the semiconductor. It is therefore essential to minimize
undesired back electron transfer (BET) in these devices.
Back electron transfer/electron recombination occurs
CHEMISTRY
when electrons injected into the semiconductor conduction
band recombine with the oxidized dye, which ultimately
results in lower DSPEC performance because the electrons
are not able to travel to the cathode to reduce hydrogen.
One technique used to slow BET rates in DSPECs is
the application of SnO 2
/TiO 2
core/shell photoanode
structures (Bakke et al., 2011). Core/shell structures
allow for electron injection without interference, while
maintaining a barrier against electron recombination. It
has been proven by many past studies that these structures
greatly reduce back electron transfer and enhance DSPEC
efficiencies (Gish et al., 2016). There is still much debate
over the underlying theory of how electron recombination
is reduced in core/shell structures. Two competing
theories shown in Figure 1a and 1b include the band edge
offset model (proposing an energy barrier created by the
difference in band edge between the core and shell) and a
model proposing the existence of a unique electronic state
at the core/shell interface (James et al., 2018).
To study this more closely, it is therefore necessary to
create samples with different band edges for the core and
shell as well as structures with the core and shell made
of the same material in order to compare their electron
kinetics. In addition, the different samples must have
comparable shell thicknesses.
Broad Street Scientific | 2018-2019 | 37

Figure 1a. In the band edge model, an energy barrier
created by conduction band (CB) edge differences
prevents electrons from traveling back and
recombining from the fluorine doped tin oxide
(FTO).
Figure 1b. In this model, a unique electronic state
between the core and shell (left) exhibits special
properties that cause a change in electron transfer
behavior, in contrast to electronic states within the
core and shell (right).
Atomic layer deposition (ALD) is one method of
creating core/shell structures (George, 2010). The
technique involves depositing the shell layer onto
nanoparticles through successive self-limiting reactions on
the surface of the material. ALD consists of multiple cycles
of precursor pulsing and purging to obtain extremely
precise monolayers on the Angstrom scale. Due to its selflimiting
nature, ALD produces very smooth, conformal
films because all parts of the surface react completely with
the precursor to grow the film (Wang et al., 2017). ALD
has been used widely to create metal oxide films such as
Al 2
O 3
, TiO 2
, ZnO, ZrO 2
, SiO 2
, and VO 2
(George, 2010).
This study will mainly focus on deposition of SnO 2
and
TiO 2
on TiO 2
. TiO 2
has thus far produced the highest light
conversion efficiencies out of all the metal oxides, and is
widely used in DSSCs as a photoanode (Jafari et al., 2016).
SnO 2
also has favorable characteristics for its anodic
abilities, such as its stability, high reversible capacity, nontoxicity
and low cost (Knauf et al., 2015).
The goal of this study was to successfully synthesize
and characterize TiO 2
/SnO 2
and TiO 2
/TiO 2
core/
shell nanostructures using tetrakis(dimethylamido)
titanium (TDMAT) and tetrakis(dimethylamido)tin(IV)
(TDMASn) precursors. Since TiO 2
/SnO 2
has not been
created before, the hypothesis was that TiO 2
/SnO 2
would
behave similarly to the more common SnO 2
/TiO 2
core
shells and would help differentiate the mechanism actually
in use by core/shell structures to inhibit recombination.
Previously, it had been common practice to deposit TiO 2
onto TiO 2
by treating the TiO 2
thin film with a TiCl 4
chemical bath deposition, which was demonstrated to
reduce back electron transfer (Lee et al., 2012). However,
this method is very unreliable and difficult to control.
According to the hypothesis, it would be possible to
create TiO 2
/TiO 2
core/shell structures using ALD for
the first time which would allow a much more controlled
deposition while still reducing electron recombination.
The second aim of this project was therefore to deposit
TiO 2
on TiO 2
using solely atomic layer deposition, a much
more controllable and reproducible method.
The TiO 2
-TiO 2
deposition was in fact found to be
successful without necessitating the TiCl 4
treatment which
was previously utilized to create TiO 2
/TiO 2
structures.
It was also found that using the TDMASn precursor to
deposit tin resulted in stannous oxide (SnO) rather than
the expected SnO 2
. After thorough studies, the stannous
oxide was successfully removed by using pure anatase
dyesol TiO 2
paste, a commercial paste, for the thin films
instead of mixed-phase TiO 2
. In addition, dye loading was
measured for each of the samples. It was found that dye
loading in TiO 2
/TiO 2
slides does not decrease consistently
as in SnO 2
/TiO 2
slides, so there are other factors besides
pore size that have an effect on dye loading.
2. Materials and Methods
2.1 – Thin Film Preparation
FTO (fluorine doped tin oxide) glass plates were
washed in an ultrasonic bath immersed in ethanol, then
acetone, for 20 minutes each. Previously prepared TiO 2
paste was coated on the slides through doctor blading
and tape-casting. The thin films were stored in a 125°C
oven to prevent water adsorption on the TiO 2
. They were
then sintered at 450°C for 60 minutes with a 120 minute
ramp-up time. Selected films were annealed at 450°C for
30 minutes with a 120 minute ramp up time.
38 | 2018-2019 | Broad Street Scientific CHEMISTRY

2.2 – Atomic Layer Deposition
Atomic layer deposition was conducted using
an Ultratech/Cambridge Nanotech Savannah S200.
TDMASn and TDMAT precursor reactant gases were
transported to the reactor chamber through heated gas
lines using nitrogen carrier flow. Nitrogen gas was used
to purge the reactant chamber after each precursor step.
Deposition was performed at 150°C while TDMAT and
TDMASn were held at 75 °C and 60°C, respectively. Gas
flow and purge times were controlled electronically by a
LabVIEW sequencer.
minimized with additional shell coatings. After examining
the results, it can be concluded that the change in pore size
is not the only factor affecting dye loading levels. Rather,
it is hypothesized that there is an uneven preferential
deposition of TiO 2
onto the TiO 2
causing increased dye
loading which does not occur on the SnO 2
thin films.
The decrease in dye loading from 25 to 45 cycles can be
attributed to the decreased pore size, the effect of which
eventually overbears that of the preferential deposition
and leads to an overall decrease in dye loading.
2.3 – Dye Loading
The RuP chromophore was loaded to the films by
soaking the slides in anhydrous methanol solutions
containing 0.0003 M RuP for several days. The slides were
removed and subsequently soaked in methanol to remove
unadsorbed dye. UV-vis absorbances of the dye-loaded
thin films were taken in 0.1 M HClO 4
using a Cary 60 UV−
vis absorbance spectrophotometer.
2.4 – Characterization
Profilometry measurements were done with a Bruker
Optics DektakXT® stylus profiler. All films were between
4-6 μm thick. Characterization of the deposited thin films
was done through infrared spectroscopy using a Bruker
Optics Alpha FTIR Spectrometer, transmission electron
microscopy using a TEM JEOL 2010F-FasTEM, X-ray
photoelectron spectroscopy (XPS) using a Kratos Axis
Ultra DLD X-ray Photoelectron Spectrometer, and Raman
spectroscopy using a Renishaw inVia Raman microscope.
Ellipsometry to measure ALD-deposited shell thickness
was also conducted using a JA Woollam ellipsometer. All
data were analyzed using Igor Pro (WaveMetrics Inc.).
Figure 2a. Infrared spectrum of TiO 2
/TiO 2
core/
shells of various numbers of ALD cycles confirming
successful deposition.
3. Results
The goal of this project was to deposit both SnO 2
and
TiO 2
onto mesoporous TiO 2
thin films using atomic layer
deposition (ALD).
3.1 – TiO 2
/TiO 2
Deposition
The TiO 2
/TiO 2
deposition was successfully achieved
using ALD with the TDMAT and water precursors.
The slides were characterized using FTIR and TEM and
confirmed to have shells made of the correct material (Fig.
2). Following this, the dye loading of the samples was
collected (Fig. 3). The results reveal different trends from
those of the more commonly studied SnO 2
/TiO 2
core/
shell structures. While the data show a clear continuous
decrease in dye loading of SnO 2
/TiO 2
with increasing
ALD cycles, the dye loading of TiO 2
/TiO 2
increases from
0 to 25 cycles and then decreases. This is inconsistent
with previous theories that suggested dye loading always
decreases with increasing ALD cycles because pore sizes are
CHEMISTRY
Figure 2b. TEM image of an anatase TiO 2
nanoparticle
with an amorphous TiO 2
shell created using 20 ALD
cycles.
Broad Street Scientific | 2018-2019 | 39

Figure 3. Dye loading of mixed phase TiO 2
/TiO 2
samples and SnO 2
/TiO 2
samples.
This phenomenon of an initial increase then decrease in
dye loading was further studied with dyesol (pure-phase)
TiO 2
/TiO 2
samples, annealed and unannealed, as well as
annealed mixed phase TiO 2
/TiO 2
samples (Fig. 4). Dyesol
TiO 2
contains larger pores and anneals more easily than
mixed-phase TiO 2
. In addition, mixed-phase TiO 2
creates
a less well-connected film. All of the samples exhibited
higher dye loading than the unannealed mixed phase TiO 2
/
TiO 2
samples. The data clearly display an overall trend for
each sample type. The unannealed dyesol slides increase
initially in dye loading but decrease starting at 35 cycles,
while the annealed dyesol slides demonstrate the same
behavior but do not decrease in dye loading until 40 cycles.
These results are consistent with the trends observed
for the unannealed mixed phase TiO 2
/TiO 2
structures.
The annealed mixed phase TiO 2
/TiO 2
samples, however,
continuously decrease in dye loading from 0 all the way
to 50 cycles, suggesting that annealing the samples affects
the dye loading behavior of mixed phase TiO 2
. Based on
the results, it can be concluded that dye loading is not
solely determined based on pore size and can be affected
by different processing conditions as well as the type of
TiO 2
used.
Figure 4a. Dye loading on dyesol TiO 2
/TiO 2
slides
created with dyesol TiO 2
paste, unannealed.
Figure 4b. Dye loading on dyesol TiO 2
/TiO 2
slides
created with dyesol TiO 2
paste, annealed.
Figure 4c. Dye loading on TiO 2
/TiO 2
slides created
with mixed phase TiO 2
paste, annealed.
3.2 – TiO 2
/SnO 2
Deposition
The TDMASn precursor deposition was initially
performed with the standard recipe used for the mixed
phase TiO 2
/TiO 2
structures and resulted in a brown layer
on the slides, which is not the normal appearance of SnO 2
shells. Upon further characterization, the layer was found
to be SnO. The SnO formation can be attributed to the
poor oxidative properties of water. Furthermore, the ALD
growth rate of SnO 2
is naturally higher than that of TiO 2
.
When the same recipe is used for depositing both SnO 2
40 | 2018-2019 | Broad Street Scientific CHEMISTRY

and TiO 2
, there is a larger growth per cycle for SnO 2
. Thus,
it was necessary to vary the ALD conditions in order to
gain a better understanding of how each parameter affects
growth so the SnO 2
growth per cycle could be equalized to
the TiO 2
growth per cycle.
Numerous attempts were made to first convert the
SnO to SnO 2
by changing the deposition parameters.
The TDMASn deposition was initially attempted using
an ozone precursor and using a combination of water
and ozone precursors, but both approaches still resulted
in SnO shells instead of SnO 2
. In addition, an increase
of the ALD reactor chamber temperature from 150°C to
250°C resulted in an uncontrolled island-like growth of
the SnO, as calculated from ellipsometry measurements of
the shell thicknesses. The exponential growth of the SnO
thicknesses for the 250°C samples (Fig. 5) indicates the
uncontrolled nature of the deposition, which often results
in island-like growth rather than a smooth conformal
coating as desired.
After testing the effects of increasing the reactor
temperature and using the ozone precursor, a postdeposition
heat treatment was administered at 210°C in an
attempt to remove the SnO, but this was unsuccessful and
resulted in increased SnO peaks in the Raman spectra of
the sample (Fig. 6). Next, the films were annealed at 450°C
in an effort to convert the existing SnO to SnO 2
. Although
the SnO was successfully converted, the annealing process
led to delamination of the TiO 2
. This occurred because
the extreme heat induced expansion of the TiO 2
, but
the rigidity of the crystal structure forced the TiO 2
to
eventually crack and delaminate from the slide due to
internal pressure.
Figure 5. Comparison of growth rates of SnO on
planar silicon at 150°C and 250°C based on ellipsometry
of shell thickness.
Figure 6. Raman spectra characterizing TiO 2
/SnO 2
samples before and after heat treatments.
The SnO 2
deposition was then attempted using a
H 2
O 2
precursor instead of the water precursor with other
varying parameters. H 2
O 2
is a stronger oxidant than water
and does not degrade as easily as ozone, so it offered a
possible option to convert the SnO to SnO 2
during the
ALD process. In order to study the effects of varying each
parameter, samples with varying precursor pulse, hold,
and purge times were created and analyzed through XPS
and ellipsometry on planar silicon. X-ray photoelectron
spectroscopy (XPS) is a spectroscopic technique that is
used to analyze the elemental composition of the surface
of a material by measuring the kinetic energy of escaped
electrons after focusing a beam of X-rays into the material,
while ellipsometry is an optical technique used to measure
thin film thickness.
Table 1. XPS atomic concentrations obtained for
each sample created with different ALD deposition
parameters using the H 2
O 2
precursor.
TD-
MASn
Pulse
H 2
O 2
Pulse
Ti
Atomic
Concentration
(%)
Sn
Atomic
Concentration
(%)
Sn/Ti
Atomic
Ratio
0.5 sec 0.02 sec 10.84 18.89 1.74
0.5 sec 0.1 sec 13.6 16.98 1.25
0.5 sec 1.0 sec 6.1 24.54 4.02
0.1 sec 1.0 sec 9.69 21.01 2.17
0.5 sec 0.02 sec,
40 sec
hold
0.5 sec 0.5 sec,
60 sec
hold
15.75 15.28 0.97
15.66 15.13 0.97
CHEMISTRY
Broad Street Scientific | 2018-2019 | 41

Table 1 shows the atomic concentrations and Sn/
Ti ratio obtained through the XPS analysis. The atomic
concentrations for Sn using the H 2
O 2
precursor were
much higher than the typical values encountered during
ALD deposition, indicating that the precursor is extremely
reactive and causing highly uncontrolled growth onto the
films. In this case, increasing the TDMASn pulse increased
growth. Increasing the H 2
O 2
precursor pulse from 0.02
seconds to 0.1 seconds did not have much effect on growth,
but increasing its pulse time from 0.1 seconds to 1.0 seconds
increased SnO 2
deposition significantly. Based on the data,
it is clear that H 2
O 2
results in heavy growth of the shells,
but the growth is most likely uneven. Another weakness
of H 2
O 2
is its inconsistency as a precursor because of its
tendency to disproportionate in the precursor cylinder to
water and O 2
. H 2
O 2
is overall not an optimal precursor to
use in SnO 2
deposition on TiO 2
for the purposes of this
study, but holds promise for future research.
The deposition was further optimized by utilizing
dyesol TiO 2
paste to doctor blade the slides instead of
mixed-phase TiO 2
, because of the characteristics of dyesol
TiO 2
as a pure phase substance. This left a slight amount
of SnO on the films immediately after deposition, but the
SnO was completely removed after heating slightly at
200°C. Unlike the mixed phase TiO 2
/SnO 2
structures, the
dyesol TiO 2
/SnO 2
did not require annealing to convert the
SnO to SnO 2
, which would have been impractical for realworld
purposes.
The dyesol TiO 2
/SnO 2
was then characterized using
XPS to confirm that the correct form of the material was
deposited. The correct peak for Sn 4+ was observed at 486.3
eV (Fig. 7), which was extremely close to the recorded
value of 486.6 eV (Stranick & Moskwa, 1993).
confirming that the correct form of Sn 4+ was formed and
not Sn 2+ .
Table 2. Atomic concentrations of Ti, Sn, O obtained
through XPS of dyesol TiO 2
/SnO 2
samples.
ALD
Cycles
Ti
Atomic
Conc.(%)
Sn
Atomic
Conc.(%)
O Atomic
Conc.
(%)
(Ti% +
Sn%) /
O%
30 8.17 24.27 61.96 0.52
40 3.48 30.78 59.63 0.57
50 3.91 30.47 60.18 0.57
Samples created using varied parameters were analyzed
again using XPS and ellipsometry to determine the effect
of changing each condition on deposition of SnO 2
using
dyesol TiO 2
. Figure 8 shows the effect of changing each
ALD parameter other than temperature on both the
thickness of SnO 2
deposited on planar silicon obtained
through ellipsometry as well as the ratio of Sn to Ti atomic
concentrations from TiO 2
/SnO 2
samples determined by
XPS. A lower growth rate is desired for this deposition
because the SnO 2
shell naturally is thicker than the TiO 2
shell, but they should be similar thicknesses in order to
compare their electron transfer kinetics. The optimal hold
time is around 60 seconds for decreasing SnO 2
thickness.
The decreased growth caused by both increased hold
and purge time is likely due to removal of moisture and
impurities introduced into the chamber during the pulse
and hold times. The lowest growth rate occurred on the
sample with 0.1 second TDMASn pulse, 0.02 second H 2
O
pulse, 20 second hold time, 60 second purge time. This
recipe resulted in a growth rate of 0.07 nm per cycle, which
decreased from the 0.09 nm per cycle growth rate achieved
with the standard recipe used for TiO 2
deposition.
Figure 7. XPS spectra of Sn 3d region, displaying peak
at 486.3 eV.
In addition, the atomic concentrations were collected
of Ti, Sn, and O (Table 2). If the deposited material was
all SnO 2
, the ratio of (Ti % + Sn %):O% should be 1:2. The
ratios calculated for the samples were all very close to 0.5,
Figure 8. SnO 2
shell thickness determined by
ellipsometry (left axis) and atomic ratio of Sn to Ti
determined by XPS (right axis) with varying ALD
conditions, at 15 cycles.
42 | 2018-2019 | Broad Street Scientific CHEMISTRY

4. Conclusion
Atomic layer deposition was conducted to create
novel TiO 2
/TiO 2
and TiO 2
/SnO 2
core/shell structures.
Dye loading studies conducted on TiO 2
/TiO 2
with the
RuP chromophore revealed that dye loading in TiO 2
/
TiO 2
increases to a certain point, and then decreases,
contradicting the trends of SnO 2
/TiO 2
which show
continuously decreasing dye loading which was attributed
to decreasing pore size. This inconsistency suggests the
importance of multiple other factors such as processing
conditions and the type of TiO 2
used to synthesize the
core. Moreover, initial attempts to create TiO 2
/SnO 2
resulted in the formation of SnO, but this was removed
by using dyesol TiO 2
to create the thin films rather than
mixed phase TiO 2
. The effects of each ALD parameter
were studied to create films of similar thicknesses for both
TiO 2
/SnO 2
and TiO 2
/TiO 2
, and the growth rate of the
SnO 2
was able to be decreased from the standard recipe.
Future directions will include the conduction of transient
absorption spectroscopy in order to understand the
differences in the dynamics of interfacial electron kinetics
between the TiO 2
/TiO 2
and TiO 2
/SnO 2
structures. In
addition, the electron kinetics should be studied in core/
shells of various other oxide materials.
5. Acknowledgments
We would like to thank Dr. Jillian Dempsey as well as
Michael Mortelliti for their incredible mentorship over
this project. This work was performed in part at the
Chapel Hill Analytical and Nanofabrication Laboratory,
CHANL, a member of the North Carolina Research
Triangle Nanotechnology Network, RTNN, which is
supported by the National Science Foundation, Grant
ECCS-1542015, as part of the National Nanotechnology
Coordinated Infrastructure, NNCI. In addition, the
project was funded by a grant from the RTNN Kickstarter
Program for fabrication & analytical costs.
6. References
Fujishima, A., & Honda, K. (1972). Electrochemical
Photolysis of Water at a Semiconductor Electrode. Nature,
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George, S. M. (2010). Atomic Layer Deposition: An
Overview. Chemical Reviews, 110(1), 111–131. https://
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Gish, M. K., Lapides, A. M., Brennaman, M. K., Templeton,
J. L., Meyer, T. J., & Papanikolas, J. M. (2016). Ultrafast
Recombination Dynamics in Dye-Sensitized SnO 2
/TiO 2
Core/Shell Films. The Journal of Physical Chemistry
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Jafari, T., Moharreri, E., Amin, A. S., Miao, R., Song, W.,
& Suib, S. L. (2016). Photocatalytic water splitting - The
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James, E. M., Barr, T. J., & Meyer, G. J. (2018). Evidence
for an Electronic State at the Interface between the SnO 2
Core and the TiO 2
Shell in Mesoporous SnO 2
/TiO 2
Thin
Films. ACS Applied Energy Materials, acsaem.7b00274.
https://doi.org/10.1021/acsaem.7b00274
Knauf, R. R., Kalanyan, B., Parsons, G. N., & Dempsey, J.
L. (2015). Charge Recombination Dynamics in Sensitized
SnO 2
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by XPS.
Surface Science Spectra, 2(1), 50–54. https://doi.
org/10.1116/1.1247724
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Assemblies for Dye-Sensitized Photoelectrosynthesis
Cells Prepared by Atomic Layer Deposition. Journal of
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Cells. Journal of the American Chemical Society, 138(40),
13085–13102. https://doi.org/10.1021/jacs.6b06466
CHEMISTRY
Broad Street Scientific | 2018-2019 | 43

USING A HYBRID MACHINE LEARNING APPROACH
FOR TEST COST OPTIMIZATION IN SCAN CHAIN
TESTING
Luke Duan
Abstract
Continual technological advances have led to more complex microchip designs, which in turn, have led to the need for
more complex fault testing. As a result, higher testing costs (increased test time and data volume) have emerged as well.
This work examines one application of hybrid machine learning (ML) to optimize the costs of scan chain testing. We
used fifty-one benchmark circuits to train the models and analyze their performances. We generated training data by
performing scan chain test simulations on each of these circuits using MentorGraphics tools DFTAdvisor and FastScan
and compiled them into files readable by the ML framework Weka. We then trained three individual ML models and
evaluated their accuracies by comparing them against a test set. Finally, we created a hybrid model by combining these
individual models, with different weights allotted to each model based on their individual accuracy. Findings showed that
there was a slight increase in performance by using a hybrid approach. We concluded that this method can be improved
by using larger training sets and better heuristic algorithms when assigning weights. This research could be useful for the
microchip industry by reducing time-to-market.
1. Introduction
Technological advances in the field of engineering have
allowed integrated circuit/microchip design companies
to figure out how to continuously add more and more
transistors (along with gates) onto smaller and smaller
devices. In order to completely test for all the possible faults
in a microchip, more complex and costly testing is needed
on these denser designs (Bushnell & Agrawal, 2005).
One procedure for fault testing occurs during the design
phase of chips - in the form of scan chain testing. In this
type of testing, a certain number of scan chains are chosen
for insertion into a circuit, with varying numbers of scan
chains having different test costs. It can become extremely
tedious to test all possible scan chain numbers, and
manually pick out the most cost-efficient number to use.
In order to make that decision, machine learning models
can be trained with circuit data, along with the number
of scan chains inserted. Then, when provided with a new
circuit, they would be able to predict the best number of
scan chains to use. (Zipeng & Chakrabarty, 2016) proposed
a method to optimize test cost by choosing parameters,
such as scan chain length, using a support vector regression
(SVR) machine learning model. In this work, we will
examine the parameter optimization of the number of
scan chains. The primary focus is to explore how well a
hybrid machine learning model performs in predicting the
optimal number of scan chains to use in scan chain testing.
1.1 – Design for Testability (DFT)
Design for Testability, or DFT, can be described as the
set of methods that make testing for faults in microchips
easier. In the next section, we break down DFT and explain
the connections between digital logic, data flip-flops, shift
registers, and scan chain testing.
1.1.1 – Context
There exist two types of digital logic: combinational and
sequential, with the latter involving a memory component
as well as a clock signal for regulation. The physical
manifestation of digital logic can be found in digital circuits.
A flip-flop (FF) is a prime example of a component in a
sequential digital circuit. It is not uncommon for instances
of sequential logic/circuits to incorporate combinational
logic.
The Data FF (Fig. 1), or DFF, is the simplest type of
FF, and consists of an input (D), a clock signal (CLK) and
an output (Q). The “scan-enabled” DFF comes with an
additional scan-in and scan-out port (scan-out port not
pictured).
Figure 1. A typical scan-enabled flip-flop (Gupta, 2014)
It is a basic storage element in sequential logic, able to
hold a stable state of either 0 or 1. The DFF may receive
an input, but unless the clock signal is turned “on,” the
output will not change. This reduces the occurrence of
any unnecessary output changes, thus saving power. A
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shift register is essentially a linear chain of these DFF’s,
all connected to and regulated by the same clock signal.
The output of one DFF is directly connected to the input
of the next. The input can be controlled, and the output of
the register can be observed. For our purposes, we do not
worry about what happens within the register.
1.1.2 – Scan Chain Testing
Scan chain testing (Fig. 2) is a common method for testing
for faults in silicon when manufacturing circuits. Either
one or multiple scan enabled shift registers are formed,
with each DFF being replaced with their “scan-enabled”
versions, which simply means they come equipped with
scan-in and scan-out ports. The total number of flip-flops
are divided as equally as possible over the number of scan
chains in a circuit. A clock signal is established, and testing
begins. An input test pattern generated by pseudo-random
methods is scanned in by each register, and the scannedout
output will be compared to the expected output.
The expected output is the output that would have been
reached if all gates in the combinatorial logic had been
working correctly. If the two outputs do not match, then
a fault is detected. Scan chain testing can be characterized
by its test application time (time for the test to occur),
and test data volume (number of test patterns inserted to
test for all faults) (Gupta, 2014). These costs can change
depending on the number of scan chains used.
connected to every single neuron in the next layer. The
input values, each multiplied by a unique weight, are
summed up and passed through an activation function.
If above a certain value, the neuron “fires” (information
is passed on to the next layer). A neural network uses
feedback (comparison to actual value) to learn and slowly
correct itself to become the best predictor it can be
(Mitchell, 1997).
Figure 3. A visual representation of an artificial
neural network; two hidden layers.
Random forests (Fig. 4) essentially take a collection
of decision trees, and output either the mode or mean
predictions of the individual trees. Decision trees work by
breaking a dataset into smaller pieces and formulating a set
of rules for decision-making based on previous data. They
have the ability to decide which features are important and
which features can be dropped (as they contribute little to
the prediction process) (Donges, 2018).
Figure 2. A typical scan chain (Gupta, 2014)
1.2 – Machine Learning (ML)
1.2.1 – Basic Principles
Machine learning (ML) is a subset of artificial
intelligence, which is built around the idea of self-learning
and self-improvement. To begin, a ML model is trained
with a set of training data. In supervised learning, both the
input and expected output are fed into the model. After
becoming sufficiently trained, the model can be tested
against a test set. Accuracies for the model can be found
by comparing the predicted outputs from the model to the
actual outputs of the test set (Mitchell, 1997).
1.2.2 – Machine Learning Model Descriptions
The artificial neural network (NN) (Fig. 3) consists of
an input layer, one or several hidden layers, and an output
layer. Each layer consists of several neurons, which are
Figure 4. A visual representation of a random forest;
two separate decision trees - red nodes represent
the individual output of each tree, which are then
combined in some way to form the output of the
random forest (Donges, 2018).
Support vector regression (SVR) (Fig. 5) works by
optimizing a line between two sets or classes of data. In
other words, while learning, it attempts to minimize
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error by adjusting a hyperplane. The accuracy is generally
dependent on setting good parameters (Cortes and
Vapnik, 1995).
A formula for a Test Cost (TC) may be obtained from Test
Application Time (TT) and Test Data Volume (TV):
TT max
and TV max
represented the maximum test
application time and maximum test data volume for a
circuit, respectively. This was to normalize a value for TC
(Zipeng and Chakrabarty, 2016).
Figure 5. A visual representation of SVR applied to
two classes of data (black circles and blue squares);
hyperplane represented by the green line.
1.2.3 – Weka Software
Weka is a software tool that provides a collection of
many developed ML models, including neural networks,
random forests, and support vector regression. This
application contains a user interface, which simplifies the
experience when working with and applying ML to data
(Weka Machine Learning Group, n.d.).
2. Methodology
This project was divided into four phases: Training Data
Generation, Individual ML Model Training, Allotment of
Weights, and Hybrid ML Model Performance.
2.1 – Training Data Generation
In this phase, the tools DFTAdvisor (MentorGraphics,
n.d.) (to insert scan chains) and FastScan (MentorGraphics,
n.d) (to generate and compare test patterns) were applied
on a collection of 51 pre-constructed benchmark digital
circuits from the ISCAS89 library. With each circuit, we
recorded several features: the number of primary inputs,
the number of primary outputs, the number of gates,
the number of flip-flops, and the number of scan chains
inserted. Five variations of each circuit were tested, from
one scan chain inserted to five scan chains inserted.
For context, the features had the following ranges
(Table 1):
Table 1. Range of values for features.
# of Primary Inputs 6 - 80
# of Primary Outputs 1 - 320
# of Gates 26 - 26115
# of Flip-Flops 3 - 1728
# of Scan Chains Inserted 1 - 5 for each circuit
We also took note of the test application time and test
data volume in performing each scan chain test.
2.2 – Individual ML Model Training
In this phase, Weka was used to individually train three
types of regression ML models: artificial neural networks,
random forest, and SVR. Out of the 51 total circuits that
were given, 42 circuits were used for training the models,
while the remaining 9 circuits were used for testing. A true
random number generator was used to select the circuits
in each set. The ML model was trained and run against the
testing set. The outputted TC was compared to a manually
calculated TC from the actual FastScan data.
2.3 – Allotment of Weights
In this phase, the weights that each individual ML
model will have in the hybrid model were empirically
selected. This was performed on the following basis: the
higher the accuracy, the more weight it had. There were
many different methods for weight selection, which left
this phase open to a lot of trial and error.
2.4 – Hybrid ML Model Performance
In this phase, the hybrid model was fed a different
set of training data and tested against a different testing
set (though still chosen out of the same collection of
benchmark circuits). The minimum TC was chosen,
and the scan chain number correlated with that TC was
compared to the actual FastScan output. The accuracy of
the hybrid model was evaluated.
3. Data Analysis
We performed tests on the 9 circuits not used for
training.
3.1 – Weighting (Individual Models)
For each individual model, results were labeled with the
following:
• Off if the scan chain number correlating with the
lowest ML test cost prediction didn’t match the scan
chain number correlating with the lowest actual
FastScan output (Table 2)
• Success if the scan chain number correlating with
the lowest ML test cost prediction did match the
scan chain number correlating with the lowest actual
FastScan output (Table 3)
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Example of Off for a test circuit:
Table 2. Comparison between actual and predicted
test cost example 1 - from NN.
The scan chain number correlating with the lowest
ML test cost prediction (0.9474) is 1, while the scan chain
number correlating with the lowest actual FastScan output
(0.8733) is 4.
Example of Success for a test circuit:
random forest had a weight of 0.8000, and the support
vector regression had a weight 0.1000 (a 1:8:1 ratio).
3.2 – Hybrid Model
Both hybrid models had 3 Successes, so further
evaluation had to be completed. Specifically, the total
difference between the actual test cost corresponding
with the predicted SC number and the actual lowest test
cost was found for the 9 testing circuits. A lower total
difference is indicative of a more accurate model.
The differences with the first weighting combination
(2:3:1) are shown in Table 5.
Table 5. Hybrid model (Weights 2:3:1) total differences.
Table 3. Comparison between actual and predicted
test cost example 2 - from NN.
The scan chain number correlating with the lowest ML
test cost prediction (0.9951) is 5, matching the scan chain
number correlating with the lowest actual FastScan output
(0.9504).
The lowest values for Test Cost are highlighted in
boldface. If the lowest Predicted Test Cost does not
match the lowest Actual Test Cost, then Off. If the lowest
Predicted TC matched the lowest Actual TC, then Success.
We only focus the lowest values of cost, because this is the
main objective of our optimization.
Weights for the hybrid model were assigned based on
the number of Successes (Table 4).
Note: A difference of 0.0000 means Success.
The total difference for the hybrid model with weights
2:3:1 is 0.3502.
The differences with the second weighting combination
(1:8:1) are shown in Table 6.
Table 6. Hybrid model (Weights 1:8:1) total differences.
Table 4. Number of Successes for each model.
The total difference for the hybrid model with weights
1:8:1 is 0.3560.
Thus, our initial weighting of the hybrid model was in
a 2:3:1 ratio. The artificial neural network had a weight of
0.3333, the random forest had a weight of 0.5000, and the
support vector regression had a weight 0.1667 in the hybrid
model. We also decided to investigate heavily weighting
the best-performing individual model as compared to the
other two models. In this weighting of the hybrid model,
the artificial neural network had a weight of 0.1000, the
We next compare these differences to those of the
individual models. The Artificial Neural Network isn’t
considered in these comparisons, due to predicting invalid
test costs.
The differences for the random forest model are shown
in Table 7.
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Table 7. Random forest model total differences.
optimized weights. There could very well exist a weight
set for the hybrid model that provides an even better
performance. Moreover, we hope that with promising
results, this methodology may be applied to industriallevel
circuits for real-world use.
5. Acknowledgments
The total difference for the random forest model is 0.3560.
The differences for the support vector regression model
are shown in Table 8.
Table 8. Support vector regression model total
differences.
I would like to express my sincerest thanks towards
Dr. Jonathan Bennett for his constant encouragement
and accepting me into the Research in Physics program
at NCSSM. I would also like to acknowledge Dr. Sarah
Shoemaker for organizing and directing the Summer
Research Internship Program.
I am very thankful to Dr. Krishnendu Chakrabarty for
granting me permission to work with his research group
at Duke University.
I would like to thank Zhanwei Zhong, Shi Jin, Thomas
Napoles, and the Duke Office of Information Technology
for their assistance with local issues.
Last but not least, I would like to express my gratitude
towards my mentor, Arjun Chaudhuri, for his patience
and dedication in guiding and challenging me.
6. References
The total difference for the support vector regression
model is 0.4894.
The hybrid model with weights 2:3:1 had lower total
differences compared to the total differences of the
individual models, as well as a hybrid model with
nonoptimal weighting, showing evidence of a slightly
better performance. This provides basic evidence that
there is, in fact, an improvement in accuracy by using a
hybrid ML method.
4. Conclusion and Future Work
4.1 – Conclusion
This work offered the possibility of using a hybrid
machine learning model to predict the best number of scan
chains to use for cost optimization. Though individual
ML models, such as the artificial neural network, random
forest, and support vector regression work well on their
own, a hybrid model with correct weighting appears to
offer a slightly better performance. With this in mind,
microchip testers could potentially use this new method
to further decrease test costs and improve time-to-market.
4.2 – Future Work
Running a program or algorithm may offer further
Bushnell, M., Agrawal, V. (2005). Essentials of Electronic
Testing, Springer.
Zipeng, L., Chakrabarty, K. (2016). Test Cost Optimization
in a Scan-Compression Architecture using Support-
Vector Regression. Proc. IEEE Test Symposium (VTS).
Gupta, N. (2014). Overview and Dynamics of Scan
Chain Testing, Retrieved from https://anysilicon.com/
overview-and-dynamics-of-scan-testing/
Mitchell, T.M. (1997). Machine Learning, McGraw-Hill.
Donges, S. (2018). The Random Forest Algorithm.
Retrieved from https://towardsdatascience.com/therandom-forest-algorithm-d457d499ffcd
Cortes C., Vapnik V. (1995). In Support-vector networks,
Machine Learning (vol. 20, pp. 273-297).
Machine Learning Group. (n.d). Weka 3: Data Mining
Software in Java, University of Waikato.
DFTAdvisor Reference Manual. (n.d). MentorGraphics.
FastScan and FlexTest Reference Manual. (n.d).
MentorGraphics.
48 | 2018-2019 | Broad Street Scientific ENGINEERING

NOVEL WATER DESALINATION FILTER UTILIZING
GRANULAR ACTIVATED CARBON
Geoffrey Fylak
Abstract
As the human population continues increasing, so does the demand for freshwater resources. The scarcity of freshwater
will likely impact one-third of the world’s population within the next decade. While there are many proven methods of
water desalination, most are cost- and energy-intensive. Our research seeks to improve upon capacitive deionization:
an emerging, yet proven, scalable method of desalination that removes charged species from water using low levels of
electricity. The filter utilizes granular activated carbon (GAC), an affordable, naturally abundant material commonly used
in industrial Brita® water filters to remove uncharged contaminants. We anticipate that GAC’s electrically conductive
properties will enable the material to adsorb sodium chloride. Our goal is to determine and enhance the performance
capabilities of GAC by altering operational parameters and system design. Initial tests demonstrated low performance
due to inadequate operational parameters and design flaws. Through systematic improvements, researchers have greatly
increased system performance. The filter’s charge efficiency has increased from 13% to 63% while the adsorption capacity
has increased from 10.3 µg/g to 452.0 µg/g. Based upon success in removing sodium chloride, our filter’s application could
be extended to remove more harmful, charged water contaminants in the future.
1. Introduction
1.1 – Significance
As the human population continues increasing, so
does the demand for freshwater resources. The scarcity
of freshwater will likely impact one-third of the world’s
population within the next decade. While there are many
proven methods of water desalination, most are cost
and energy-intensive. Our research seeks to improve
upon a novel desalination technique, which would
expand available drinking water sources on a global
scale. The technology investigated is based on capacitive
deionization (CDI), an emerging, yet proven, scalable
method of desalination that removes charged species from
water using low levels of electricity. The filter will utilize
granular activated carbon (GAC), an affordable, naturally
abundant material commonly used in industrial Brita®
water filters to remove uncharged contaminants. We
anticipate that GAC’s electrically conductive properties
will enable the material to adsorb sodium chloride.
Our goal is to determine and enhance the performance
capabilities of GAC by altering operational parameters
and system design. Emerging contaminants widely exist
in raw and treated drinking water and present an ongoing
threat to human health and the planet. Certain substances,
such as PFAS, are suspected carcinogens and pose a risk to
humans even at trace levels (ng/L to µg/L). Thus, there
exists a need to develop viable methods and technologies
to remove charged contaminants from water resources.
Ultimately, our filter’s application can be extended to
remove more harmful charged contaminants in the future.
1.2 – Background Literature Review
Water treatment is a broad field consisting of many
different methods and focuses. Water desalination is a
sub-field which focuses on removing salt from water.
Many industrial scale water desalination techniques
exist, such as reverse osmosis and thermal distillation;
however, these techniques are highly energy intensive.
CDI technology improves upon these other techniques
through its low energy requirement.
CDI cells operate based off of the electrochemical
principles of charge. Essentially, saltwater is a solution
containing two sets of molecules: salt compounds and
water molecules. Salt compounds are composed of two
types of ions: positively charged sodium ions and negatively
charged chloride ions. Moreover, when opposite electrical
charges are given to two parallel plates, an electric field is
created. This electric field will immobilize sodium chloride
ions and separate them based off of their respective
electrical charge, directing the positively charged ions to
attach to the negatively charged plate and vice versa for
the negatively charged ions. However, the most crucial
component of a CDI system is the electrode, the part that
captures the charged salt ions, thus removing them from
the water, resulting in pure water (Suss et al., 2015).
Previous research has proven CDI technology to
successfully remove salt on the lab scale (Porada et al.,
2013) and industrial scale (Welgemoed & Schutte, 2005).
These experiments describe the salt removal process, as
well as detail the various essentials of a successful CDI
system. The most important physical component is the
electrode material, as the resistivity and specific surface
area of the material determine the amount of salt that can
be adsorbed. Materials with high specific surface areas and
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porosity are most efficient at removing salt.
As researchers attempt to expand the applicability of
CDI technology, they are experimenting with a variety
of electrode materials. One particular electrode material,
granular activated carbon, is contained within Brita®
water filters, removing uncharged contaminants with its
desirable properties. Researchers determined granular
activated carbon (GAC) to have a promising surface
conductivity and adsorption capacity (Jia & Zhang, 2016).
Another set of researchers packed an electrode chamber
with granular activated carbon and discovered up to two
and a half times more salt removal (Bian et al., 2015).
However, their research did not assess the potential of
GAC as a primary electrode material. Our study seeks
to determine performance metrics, as well as compare
our findings with pre-existing data. In doing so, we will
be able to gain a holistic view of the efficiency of GAC
as an electrode material. Since many industrial water
filters, such as Brita®’s, utilize GAC, the transition to an
industrial-scale desalination system will be feasible if GAC
is proven to be efficient.
However, to accurately assess the efficiency of GAC
as an electrode material, we must first ensure that the
CDI system’s design is sufficient. Charge efficiency
is an important, quantifiable indication of a system’s
effectiveness. A system’s charge efficiency is a measurement
in the form of a percentage, which demonstrates the moles
of salt removed per moles of electrical charge emitted
to electrodes. A system with a charge efficiency of 100%
removes one mole of salt per mole of electrical charge.
One set of researchers discovered that CDI cells must be
charged at a positive voltage to achieve the highest charge
efficiency (Avraham et al., 2009). Therefore, our project
will utilize critical findings to ensure that the electrode
parameters are under enable the maximum performance
of GAC.
Though there is substantial research surrounding
the CDI process, there is no significant information
concerning the efficiency of GAC as an electrode material.
By conducting this research, GAC could potentially prove
to be a useful electrode material, consequently sparking
feasible industrial filter production. Conversely, GAC
could prove to be inefficient, allowing researchers to
focus on other potential modifications. The purpose of
this study is to determine the efficiency of the electrode
material granular activated carbon in comparison with
pre-existing materials.
2. Materials
2.1 – Novel CDI System Design
The novel filter was designed, modeled, and assembled
using materials funded by the Call Lab at NC State
University. As a novel design, each material and component
must be considered to achieve optimal functionality.
The assembled and disassembled GAC filter design is
illustrated below (Fig. 1, Fig. 2). Certain materials such
as the hex nuts, screws, and barbed tube fittings did not
require modification; however, the polycarbonate plate,
graphite plates, rubber gaskets, and glass fibre prefilters
needed to be cut. Each part plays an instrumental role
in adapting GAC to carry electrical charge and remove
sodium chloride.
Figure 1. A rendered model of the assembled filter.
Figure 2. A disassembled model of the GAC filter.
Numbers coincide with different parts and materials:
1. Rubber gaskets and glass fibre prefilter; 2. Nylon
screws; 3. Barbed Tube Fittings; 4. Polycarbonate
plates; 5. Graphite plates 1/8” thick; 6. Graphite plates
1” thick.
Water will enter through the top barbed tube fitting
and exit through the bottom, passing through the
cylindrical chambers that contain the electrode material.
An electrical charge must be given to the system through
an anode and a cathode. Hence, the 1/8” thick graphite
plates have an extended area designated for anode and
cathode attachment. Graphite was chosen as the material
to house the granular activated carbon (GAC) because it
is electrically conductive. However, since two oppositely
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charged chambers are created, they must be separated
to ensure the system does not short-circuit. A series of
glass fibre prefilters (spacers) accomplishes this goal. The
middle spacer separates the anode and cathode chambers,
ensuring the GACs in either chamber do not touch and
cause system failure.
Gaskets are used in combination with the spacers to
prevent leakage from occurring. Each of these components
is held together by two nylon screws. It is essential to use
nylon, plastic, or any other non-conductive material so
that the system does not short-circuit when an object is in
contact with both the anode and cathode chambers at the
same time. The nylon hex nuts allow researchers to tighten
the system, preventing leakages and pressure build-ups.
With computer-aided design, the 3D model was
converted into 2D sketches and each individual part
was able to be cut in NC State’s Machine Shop. Lastly, a
3D-printer in the NCSSM Fabrication Lab was used to
create a stand to hold the filter upright and prevent the
filter from lying horizontally (Fig. 3).
Figure 4. A top view of the resistance experienced
from the anode/cathode connection sites to various
locations within the electrode chamber.
Figure 5 shows a few photos of the GAC filter
completely assembled.
Figure 5. The GAC filter completely assembled, from
a variety of angles.
3. Specific Aims and Research Design
We seek to address the following research questions:
Figure 3. A red, 3D-printed stand supports the GAC
filter and enhances the system’s vertical flow path.
Aside from flow path, system resistance was a challenge
that the design needed to overcome. Thus, researchers
filled the chambers with GAC and measured the resistance
from the anode or cathode connection points to various
locations within the chamber (Fig. 4). These data
demonstrate that graphite sufficiently emits charge to all
of the electrode material. Although resistance increases in
areas furthest away from the graphite, electrical charge can
still travel to those areas and facilitate salt removal (Fig. 4).
3.1 – Specific Aim 1
Determine the relationship between flow rate and CDI
system performance by running tests with different flow
rates and comparing the respective performances.
3.2 – Rationale and Hypothesis
The flow rate of water through a CDI system impacts
the volume of salt entering the system. Exposure to higher
salt concentrations should enable electrodes to capture
more salt. However, increased flow rates facilitate pressure
build-ups and leakage issues that may negatively impact
system performance. By analyzing the impact of flow
rate on system efficiency, researchers can discover the
operational parameters necessary to yield maximum salt
removal.
Typical lab-scale, flow-by CDI cells utilize 0.200 g of
electrode material; however, this novel design incorporates
20.0409 g of electrode materials. Due to the much higher
system volume, researchers expect higher flow rates to
increase CDI cell performance. Moreover, incremental
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changes in flow rate will likely impact performance less
because of the large volume. Thus, researchers may need
to greatly increase flow rate to produce significant changes
in performance.
3.3 – Supporting Preliminary Data
We previously analyzed the relationship between flow
rate and cell performance using flow-by CDI cells. We
concluded that increasing flow rate negatively impacted
CDI performance across all performance metrics (Table
1). Our current experiment utilizes flow-through CDI
cells; thus, our design differs from the one featured in this
study.
Nevertheless, it is important to observe the implications
of these findings on the electrochemical level, as this study
indicates that higher flow rates induce pressure build-ups
and consequently, Faradaic Reactions. Faradaic Reactions
contribute to pH fluctuations and electronic charge storage
without salt ion adsorption (Na + or Cl - ).
Table 1. Comprehensive visualization of the
impact of increasing flow rate on flow-by CDI
cell performance. Noticeably, each performance
parameter decreases as flow rate increases.
Adsorption
Capacity
Charge
Efficiency
4 mL/min 6 mL/min 8 mL/min
2.507mg/g 1.212mg/g 1.075mg/g
18.87% 9.44 % 10.07 %
3.4. – Methods
After calibrating the pump, tubing was attached from
the pump through the CDI system, then directed into a
properly labeled waste container. Next, distilled water
was pumped through the system to ensure that no leakage
occurred.
Finally, flow cells were attached outside of the system
to allow researchers to measure the conductivity of water
exiting the system (Fig. 6).
Figure 6. A visualization of the research setup,
including the pump, salt solution, CDI cell,
conductivity flow cell, pH flow cell, waste bucket,
and tubing.
With the system assembled, we created one liter of 100
mM salt solution. The 100 mM solution is then diluted
into a 10 mM salt solution and pumped through the CDI
cell. This step saves time creating solutions in the future,
as it is much easier to dilute a solution than create one.
For this specific project, we chose to test flow rates of
5 mL/min and 10 mL/min. Using the calibration which
we previously conducted, we programmed the pump to
each of these flow rates in different tests. All of our other
system parameters were kept constant during this test:
voltage during charge was 1.2 V, charge cycle time was 5
minutes, the alligator clips were positioned from anode to
cathode, and the system ran for three cycles.
We first measure the conductivity and pH of the water
before it enters the system. The flow cells containing
conductivity and pH probes are used to measure the
conductivity and pH of the water exiting the system.
Conductivity is directly related to salt concentration, so the
combination of these measurements enables researchers to
analyze salt removal over time. Each probe captures data
points one minute apart, allowing researchers to observe
the behavior of the cell over time, minute by minute.
3.5 – Data Analysis
A charge cycle occurs under an applied voltage while the
system is removing salt. However, the electrodes will reach
an adsorption capacity and cannot remove salt forever. A
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discharge cycle occurs when the voltage is removed or
reversed, allowing electrodes to flush captured salt ions
into a brine stream. During each cycle there are various
performance metrics that researchers observe to assess
system efficiency. These metrics are adsorption capacity,
adsorption rate, and charge efficiency. Adsorption capacity
refers to the mass of salt collected per mass of electrode
material. Adsorption rate is an indication of the rate of salt
adsorption as per mass of electrode. Charge efficiency is a
measurement in the form of a percentage; a ratio of moles
of salt removed per mole of electric charge.
Since conductivity is directly proportional to salt
concentration, we were able to derive each performance
metric by finding the area under the effluent conductivity
curve (Fig. 7).
Figure 7. Conductivity versus time graph that
graphically illustrates the importance of the
integral of effluent conductivity in determining salt
removed.
The following demonstrates the mathematical analysis
performed to derive each performance metric.
Adsorption Capacity:
Ultimately, these mathematical formulas are the key
to transform raw data into meaningful analysis. These
performance metrics are accepted throughout the larger
CDI community.
3.6 – Specific Aim 2
Determine the relationship between charge and
discharge cycle length and CDI cell performance by
increasing the time during which voltage is applied to the
system.
3.7 – Rationale and Hypothesis
The charge and discharge cycle length determine the
time during which salt removal will occur. However,
considering the adsorption capacity of electrodes, we
expect for salt removal rates to vary as the pores become
more filled with salt. Accordingly, proper cycle lengths
are essential for an accurate measurement of electrode
material performance. By analyzing the impact of cycle
length on system efficiency, researchers can maximize
the effectiveness of the electrode and determine the true
potential of the material.
Researchers expect longer cycle times to coincide
with increased system performance. The large volume of
electrode material should theoretically require more time
to reach maximum adsorption. However, exceedingly long
cycle times will decrease charge efficiency, as charge enters
into electrodes that are unable to hold more salt ions. Thus,
it is imperative that researchers systematically determine
the proper charge cycle to enhance system performance.
Ultimately, researchers expect cycle time to be
significantly longer than the five-minute period that is
adequate for smaller cells.
3.8 – Supporting Preliminary Data
Figure 8 illustrates the salt concentration over time
for the first test run on the CDI cell. The test run below
consisted of three, five-minute charging and discharging
cycles.
Charge Efficiency:
Figure 8. Conductivity versus time graph for a flow
rate of 5 mL/min, at 1200 mV, for 3 complete charge
and discharge cycles each 5-minutes long.
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This length was not adequate since the system was still
removing salt at the end of the charging cycle. At the end
of a charging period, effluent conductivity should return to
influent conductivity so that the system reaches maximum
adsorption and returns to a state of equilibrium. These
findings demonstrate that the CDI system needs a longer
charging cycle period, likely because of the large relative
volume of the cell. This result is limited because it does
not indicate what an adequate length would be, it merely
demonstrates that it needs to be longer than 5 minutes.
Thus, the researchers will be conducting systematic testing
to determine the appropriate charge cycle time.
3.9 – Methods
For this specific test, researchers knew that the charge
and discharge cycle needed to be longer than 5-minutes
however, they did not know how long it needed to
be. First, researchers decided to increase cycle time
gradually in order to analyze the system behavior. This
enabled researchers to analyze the system’s consistency
as well as GAC performance under different operational
parameters. Consequently, this heuristic continually
yielded an inadequate cycle time. Hence, researchers
decided to systematically determine the charge cycle by
conducting a ‘single-cycle test’. In this test, researchers set
the charge length to 300 minutes, and observed the data
to determine the time at which the electrodes had reached
their maximum adsorption and returned to equilibrium.
3.10 – Data Analysis
Researchers used the same mathematical and graphical
approach to derive the performance metrics for the CDI
cell as in Specific Aim 1.
In addition to this quantitative data analysis, this data
required graphical analysis based off of graph qualities.
Researchers focused on observing the effluent versus
influent conductivity at the end of each cycle time to
observe whether the system was at equilibrium at the end
of the cycle.
3.11 – Specific Aim 3
Determine the impact of design modifications on CDI
cell performance by decreasing the total volume of the
system.
3.12 – Rationale and Hypothesis
Although the filter was experiencing great increases
in adsorption capacity, the charge efficiency was still very
low. Charge efficiency is a measure of the percentage of
electrical charge allotted to salt removal. A low charge
efficiency indicates that much of the GAC is not removing
salt and not receiving electrical charge. Researchers
hypothesized that the large volume of the system was
contributing to a poor distribution of electrical charge.
Thus, system performance is expected to increase as the
filter’s volume decreases.
3.13 – Methods
For this specific test, researchers decided to decrease
the system’s volume by half. Researchers hypothesized that
the large volume of GAC in the filter was contributing to
the low charge efficiency, thus researchers anticipated that
this modification would improve adsorption capacity and
charge efficiency. The following image demonstrates the
design modification that occurred.
Figure 9. Graphic illustration of the design
modification that decreased the filter volume from
45.23 mL to 25.24 mL.
Researchers decided to test the filter using the 5 mL/
min flow rate because higher flow rates caused too many
leakage issues. Moreover, the applied voltage of 1.2 V
remained constant. A charge cycle time of 20 minutes was
deemed appropriate after qualitative graph analysis.
3.14 – Data Analysis
Researchers used the same mathematical and graphical
approach to derive the performance metrics for the CDI
cell as in the previous specific aims.
3.15 – Specific Aim 4
Determine the impact of design modifications on
CDI cell performance by rearranging anode and cathode
attachment locations.
3.16 – Rationale and Hypothesis:
Although the filter once again experienced an increase
in adsorption capacity, the charge efficiency decreased.
Researchers hypothesized that the arrangement of the
anode and cathode connection was not facilitating the ideal
electron flow. Thus, researchers decided that increasing
the distance between the applied voltages was necessary
for the electrical field to encompass all of the GAC within
the filter. Researchers hypothesize that this change may
increase charge efficiency and overall system performance.
3.17 – Methods
For this specific test, researchers decided to change
the location of the anode and cathode connection points.
Researchers hypothesized that this modification would
increase the reach of the electrical field, enable more GAC
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to be charged, and increase the filter’s charge efficiency.
Figure 10 demonstrates the design modification that
occurred.
Figure 10. Graphic illustration of the design
modification that increased the reach of the electric
field by moving the anode and cathode connection
plates further away from one another.
Researchers decided to keep the operational parameters
constant to ensure that the design modification was
the only factor that could contribute to differences in
performance. Thus, the flow rate remained 5 mL/min,
the voltage applied remained 1.2 V, and the cycle time
remained 20 minutes long throughout testing.
3.18 – Data Analysis
Researchers used the same mathematical and graphical
approach to derive the performance metrics for the CDI
cell as in the previous specific aims.
4. Results
to use a flow rate of 5 mL/min in future testing to avoid
these issues. Nevertheless, these tests were successful in
establishing baseline performance capabilities of GAC.
4.2 – Impact of Cycle Time on Filter Performance
The following table displays the performance of the
CDI system as the cycle time increases. As expected,
system performance increased as cycle time increased,
since the cell spent more time at peak adsorption (Table 3).
Additionally, the cell spent more time expelling salt during
discharge cycles so the GAC was able to adsorb even more
salt for a longer period of time.
Table 3. Performance metrics comparison between
elongated cycle periods demonstrates that the longer
cycle time increased performance efficiency.
Adsorption
Capacity
Charge
Efficiency
5 min 10 min 20 min 50 min
20.2
µg/g
31.9
µg/g
96.0
µg/g
155.4
µg/g
22.32% 30.65 % 35.04% 35.64%
Figure 11 displays the salt concentration over time for
the lowest charge time tested (five minutes).
4.1 – Impact of Flow Rate on Filter Performance
After testing, researchers observed that a higher flow
rate yielded more efficient filter performance. Flow rate
directly impacts the performance metrics of the flowthrough
CDI cell (Table 2). The lower flow rate was
significantly less efficient than the higher flow rate.
Table 2. The performance metrics of the flowthrough
CDI cell at two different flow rates: 5 mL/
min and 10 mL/min. Each performance metric rises
with flow rate, demonstrating that higher flow
rates increase performance.
Adsorption
Capacity
Charge
Efficiency
5 mL/min 10 mL/min
10.7 µg/g 20.2 µg/g
13.125 % 22.32 %
The novel system has a relatively large electrode
volume, causing alterations in operation parameters
to impact system performance less than expected.
Accordingly, additional testing with a higher range of flow
rate values may be necessary to cause greater variations in
performance. Moreover, the larger flow rate introduced
many leakage issues and pressure build-ups which
increased internal system resistance. Researchers chose
Figure 11. Salt concentration over time for a cycle
time of 5 minutes. Operational parameters: applied
voltage of 1.2 V, cycle time of 5 minutes, and flow rate
of 5 mL/min.
During this test, the filter was not at equilibrium at the
end of the charge and discharge cycle periods. Here, very
brief, ineffective discharge periods inhibited the amount
of salt that the electrodes were able to adsorb. From this
qualitative analysis, it was evident that cycle time must be
increased. Figure 12 displays the salt concentration over
time for an increased charge and discharge cycle length of
10 minutes.
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indication regarding the potential of GAC to adsorb salt
when operating under ideal conditions.
Figure 12. Salt concentration over time for a cycle
time of 10 minutes. Operational parameters: applied
voltage of 1.2 V, cycle time of 5 minutes, and flow rate
of 5 mL/min.
Noticeably, the discharge cycles were more effective as
the area under the curve during discharge cycles appears
much larger, which was confirmed through quantitative
analysis. However, the effluent and influent conductivities
were still not equal at the end of the respective cycle time
lengths (Fig 12). After increasing the cycle time again to
20 minutes, graphical analysis once again demonstrated
a need for increased cycle time. However, these results
were limited because they did not indicate the ideal cycle
time. Researchers conducted a ‘single-charge test’ to
finally determine the optimal cycle time. In doing so, 50
minutes was found to be ideal. The system performance
was considerably higher under the 50-minute charge and
discharge cycle time (Table 3). Figure 13 illustrates the salt
removal over time under this elongated cycle time.
Figure 13. Salt concentration over time for a cycle
time of 50-minutes. Operational parameters: applied
voltage of 1.2 V, cycle time of 5 minutes, and flow rate
of 5 mL/min.
4.3 – Impact of System Volume on Filter Performance
Due to the exceptional volume of electrode material
contained within the original design, researchers
decided to decrease system size and analyze the impact
on performance. The system design was maintained,
researchers merely decreased the volume of each large
graphite chamber to half of its original size. This change
decreased the amount of electrode material from 20.04 g
to 8.44 g. Figure 14 illustrates the salt removal over time
using the smaller system.
Figure 14. Salt concentration over time for the
system after the design modification. Operational
parameters: applied voltage of 1.2 V, flow rate of 5
mL/min, and a cycle time of 20 minutes.
Qualitative analysis demonstrates that the conductivity
was nearing equilibrium at the end of the charge and
discharge cycles, so a cycle time of 20 minutes was adequate
for the smaller system. The performance metrics of the
system were considerably higher than the larger systems,
indicating an improved performance with the design
modifications (Table 4).
Table 4. Performance metrics and size comparisons
between the two filters of different sizes illustrate
that a decrease in filter size coincides with an
increase in adsorption capacity but a decrease in
charge efficiency. Researchers attribute the decrease
in charge efficiency to an inadvertent decrease in
GAC density.
Large Filter
Small Filter
Volume 45.23 cm 3 25.24 cm 3
Mass of GAC 20.04 g 8.433 g
Density of GAC 0.433 g/cm 3 0.334 g/cm 3
In this test, GAC demonstrated the impressive ability
to remove salt at maximum adsorption for an extended
period of time (~35 min.), which is a positive indication
of GAC capability and system performance (Fig. 13). In
conclusion, the results of this experiment were a positive
Adsorption
Capacity
Charge
Efficiency
155.4 µg/g 287.7 µg/g
35.6 % 27.3 %
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The adsorption capacity increased, indicating that the
GAC in the filter adsorbed more salt than in previous tests.
However, the charge efficiency decreased which meant that
less charge was directed towards salt removal. Researchers
hypothesize that the difference in GAC densities between
the chambers caused this decrease in charge efficiency. As
the chamber becomes less dense, it is more difficult for
charge to be administered across the GAC, thus a lower
charge efficiency should coincide with a lower electrode
density. Nevertheless, the broader goal of this research
project was to study the adsorption capabilities of GAC,
using our filter as the avenue to do so. Thus, this increase
in adsorption capacity was another promising sign.
4.4 – Impact of Anode/Cathode Arrangement on Filter
Performance
In this design modification, researchers changed the
location of the anode and cathode attachments to expand
the amount of GAC impacted by the applied voltage (Fig.
10). The results from this design modification are shown
in Table 5.
Table 5. Performance metrics before and after
increasing the distance between anode and cathode
attachment plates demonstrate that a wider
electrical field significantly increases the charge
efficiency and adsorption capacity of the system.
Adsorption
Capacity
Charge
Efficiency
ENGINEERING
Previous
Design
New Design
287.7 µg/g 452.0 µg/g
7.3 % 63.1 %
This modification caused the most significant increase
in charge efficiency experienced by the filter. Additionally,
there was a large increase in adsorption capacity which was
likely due to the amount of charge contributing towards
salt removal. The distance between the applied voltages
was much larger than before, likely causing the increase
in charge efficiency. Moreover, charge efficiency reflects
the performance of the filter, while adsorption capacity
reflects the performance of the GAC. Thus, the correlation
between increases in filter performance and increases in
GAC performance indicate that GAC has even more
potential to serve as an electrode material as the system
design continues to improve.
5. Discussion and Conclusions
The aforementioned study established the efficiency
of a novel electrode material, granular activated carbon,
commonly used in portable water filters. Many industrial
water filtration companies leverage GAC’s adsorptive
capabilities to remove uncharged contaminants. Without a
preexisting design, researchers leveraged their innovation
and created a system that dispersed electrical charge
across a chamber of GAC. Throughout experimentation,
researchers have improved GAC’s adsorption capacity
from ~10 µg/g to ~450 µg/g. The filter was initially
invented as a lab-scale device aimed to determine the
potential of GAC. This profound increase in adsorption
capacity proves GAC to be a promising potential electrode
material for use on the industrial scale. Moreover, the
charge efficiency of the system was increased from ~13% to
~63% over the course of various design modifications. It is
important to consider that operational conditions are not
yet ideal, and are evidently limiting system performance.
Nevertheless, researchers proved that the electrochemical
technique capacitive deionization is compatible for use
with granular activated carbon. Thus, researchers have
created a portable device that feasibly adapts GAC for salt
removal. The low cost and energy requirements of this
desalination technique will become a valuable resource
to those impacted by the growing demand for freshwater
resources. Furthermore, though currently untested,
the device may have the potential to adapt GAC for the
removal of other, more harmful, charged contaminants.
6. Acknowledgement
My work for this project was completed at North
Carolina State University’s Environmental Engineering
Lab from June 2018- January 2019 under the mentorship
of Dr. Douglas Call and Dr. Shan Zhu. Both of my mentors
played fundamental roles in building my competency with
capacitive deionization technology. Moreover, these
mentors initially proposed the idea to design a filter that
could utilize granular activated carbon (GAC) based upon
their knowledge of the advantages of GAC. While the filter
was designed, modeled, and assembled entirely by myself,
I have sought their guidance throughout the development
of my specific research aims to ensure continual system
enhancement.
7. References
Jia, B., Zheng, W. (2016). Preparation and Application of
Electrodes in Capacitive Deionization (CD): a State-of-Art
Review. Nanoscale Research Letters, 11.
Schutteb, C. F., Welgemoeda, T. J. (2005). Capacitive
Deionization Technology TM : An Alternative Desalination
Solution. Desalination, 183, 327-340.
Avraham, E., Noked, M., Bouhadana, Y., Soffer, A.,
Aurbach, D. (2009). Limitations of Charge Efficiency in
Capacitive Deionization. Journal of the Electrochemical
Society, 156, 157-162.
Broad Street Scientific | 2018-2019 | 57

Suss, M. E., Porada, S., Sun, X., Biesheuvel, P. M., Yoon,
J., Presser, V. (2015). Water desalination via capacitive
deionization: what is it and what can we expect from it?
Energy Environmental Science, 8, 2296-2319.
Porada, S., Zhao, R., Van der Wal, A., Presser, V.,
Biesheuvel, P. M. (2013). Review on the science and
technology of water desalination by capacitive deionization.
Progress in Materials Science, 58, 1388-1442.
Bian, Y., Huang, X., Jiang, Y., Liang, P., Yang, X., Zhang, C.
(2015). Enhanced desalination performance of membrane
capacitive deionization cells by packing the flow chamber
with granular activated carbon. Water Research, 85, 371-
376.
58 | 2018-2019 | Broad Street Scientific ENGINEERING

LONG PRIME JUGGLING PATTERNS
Daniel Carter and Zach Hunter
Abstract
There are a large variety of ways to juggle balls. Different juggling patterns can be modeled by a sequence of states that
describe the positions of the balls in regular time intervals. A pattern is said to be prime if it does not repeat states more
than once per cycle. We investigate the problem of finding the longest prime pattern for a given number of balls and
maximum throw height. Solutions up to a maximum throw height of 9 were found by computer search. We completely
solve the 2-ball case and provide a very strong upper bound for all other cases. This upper bound differs by no more than
1 from every computed case.
1. Introduction
Juggling and mathematics are intricately connected.
The math YouTube channels Mathologer (Polster &
Geracitano, 2015) and Numberphile (Wright & Haran,
2017) have both released videos on juggling. This introduction
reiterates the information in those videos and introduces
the main problem of this paper.
There are many ways to juggle balls. For example, two
basic 3-ball patterns are cascade, where the balls travel in a
figure eight, and shower, where they travel in a circle. We
can represent these patterns by following which hand the
balls are in or traveling to over time in a ladder diagram,
such as the ones shown in Figure 1.1.
The left and right columns of dots represent the left
and right hands, and the lines represent the paths of the
balls. For the cascade, every ball is thrown so that it lands
in the opposite hand 3 steps later. In other words, the ball
is thrown to height 3. However, for the shower, the right
hand throws balls to height 5 and the left hand throws balls
to height 1.
Jugglers assign siteswap notation to these patterns. This
notation lists the sequence of throw heights in a pattern.
For example, cascade has a siteswap of “3” and shower has
a siteswap of “51.” It is worth noting that siteswap notation
does not distinguish the left hand from the right. In fact,
these patterns could be juggled using just one hand. Also
worth noting is that there may be multiple siteswaps that
refer to one pattern; for example, 51 and 15 represent the
same pattern. Finally, a 0 in siteswap means all balls are in
the air and there is no ball ready to be thrown.
We can also describe the states reached by a pattern.
Each state is a sequence of 1’s and 0’s representing the
positions of the balls in the air. A 1 in the kth position
indicates a ball in the air will land k steps later. At most
one ball may be in each position, because two balls in the
same position will fall into the same hand at the same time,
which isn’t allowed in basic juggling. In the cascade, the
only state is (111): one ball is always just about to land,
one will land in two steps, and one will land in three steps.
Jugglers call this state ground state, as it is the state with all
balls in the lowest position. For the shower, the two states
are (11010) before a throw of height 5 and (10101) before
a throw of height 1. Two throws of a shower are shown
diagrammatically in Figure 1.2.
Figure 1.1. Ladder diagrams of the 3-ball cascade and
3-ball shower.
MATHEMATICS AND COMPUTER SCIENCE
Broad Street Scientific | 2018-2019 | 59

e decomposed into the prime patterns 42 and 3. Prime
patterns correspond to cycles on the graph, which are
closed walks that do not repeat vertices.
The number of (not necessarily prime) patterns is wellestablished
(Takahashi, 2015). The more difficult question
of the number of prime patterns has a partial answer
(Banaian et al., 2015). We attempt to find the longest
prime pattern for each combination of balls and maximum
throw height.
2. Empirical Results and Symmetry
Figure 1.2. Converting location of balls to states.
Bolded arrows indicate throws and are labeled
with the throw height. Dotted arrows show balls
dropping due to gravity.
Reading from the bottom to the top, marking a 1 for
every ball and a 0 for every gap gives the states (11010)
and (10101). In this diagram, the balls are colored
differently for clarity. However, we will consider each ball
indistinguishable for our analysis.
As seen, throws can change the state of the balls. In
general, every throw each “1” moves left one place (i.e.
the corresponding ball falls slightly) except for a ball in
the leftmost position, which is thrown to some currently
empty spot. We can make a directed graph describing
every possible state and throw. A closed walk in this graph
is a repeating pattern of throws — a juggling pattern. The
graph for 3 balls with a maximum throw of 5 is shown in
Figure 1.3.
There are finitely many prime patterns, because for any
finite graph, there are finitely many cycles. Therefore, a
computer can search and find the longest prime pattern.
Call L(n, b) the length of the longest prime pattern for b
balls and maximum height n. The values of L(n, b) for 0 ≤ n
≤ 9 are given in Table 2.1.
Table 2.1. Lengths of longest prime patterns for max
height 9 or less.
For example, the value at b = 3, n = 5 is 8 because the
longest prime pattern has siteswap 55150530, which is
length 8. In Figure 1.3, this corresponds to the 8 states in
the center of the diagram that are arranged in an octagon.
Interestingly, the table appears symmetrical, with L(n, b) =
L(n, n−b). We will now prove this. In fact, we will prove a
somewhat stronger result.
Figure 1.3. Juggling graph from 3 balls and max height
5. Vertices represent states and edges represent
throws. Vertices are labeled with the state they
represent, and edges are labeled by throw height.
We will denote the graph for b balls with max throw
height n as J(n, b). The diagram above represents J(5,3).
If a pattern visits each state no more than once, jugglers
call it a prime pattern. This is because if a state is visited
multiple times, the pattern can be decomposed into two
or more prime patterns. For example, the pattern with
a siteswap of 423 visits the state (11100) twice and can
Theorem 2.1. There exists a bijection between patterns with b
balls and n − b balls.
Proof. Consider a valid juggling pattern for b balls with
maximum height n. List the states of this pattern in order.
Now, switch 0’s and 1’s, mirror each state left-to-right,
and reverse the order of the list. This new list is a valid
pattern for n − b balls. For example, there is a 3-ball pattern
of height 5 with siteswap 5511. The states reached are, in
order:
(11100)
(11001)
(10011)
(10110)
60 | 2018-2019 | Broad Street Scientific MATHEMATICS AND COMPUTER SCIENCE

The new list in this case is
(10010)
(00110)
(01100)
(11000)
Which are, in fact, the states reached by the 2-ball
pattern with siteswap 4004.
To see why this bijection works, consider two seemingly
unrelated questions: “What happens to the 0’s in the state
after each throw?” and “What states could have led into
some particular state?”
For the first problem, there are three cases. The first
is the case where there is a 0 in the leftmost position, so
a throw of height 0 is the only option. In this case, all 0’s
except the leftmost move left one position (i.e. fall) and
a 0 appears in the rightmost position. Next, if a throw
of maximum height is made, all 0’s simply move left one
position. Finally, for any other throw, all 0’s move left one
position, a 0 appears in the rightmost position, and one
of the 0’s disappears because it was filled by the ball just
thrown.
For the second problem, there are also three cases.
The first is if there is a 1 in the rightmost position, so the
previous throw must have been maximum height. In this
case, the previous state had the 1’s (except the rightmost 1)
moved right one step, and there was a 1 was in the leftmost
position. Next, there is the case where the previous throw
was height 0, and the previous state had all 1’s simply
moved right one position. Finally, for any other throw, all
1’s were moved right one position, a 1 was in the leftmost
slot, and one of the 1’s disappears because it has not been
thrown yet.
Clearly, these problems are equivalent! Simply swap 0
and 1 and left and right. This accounts for the swapping of
0’s and 1’s and the left-to-right mirroring in the bijection.
The reversal of the order of states is a reversal of time,
which comes from the statement of the second question.
Due to this bijection, any pattern for b balls with max
height n corresponds to a pattern for b gaps — that is, n − b
balls.
Corollary 2.2. L(n, b) = L(n, n − b).
Corollary 2.3. To construct J(n, n − b) given J(n, b), reverse
all arrows and relabel each vertex by switching 0 and 1 and
mirroring left-to-right.
Borrowing terminology from graphical linear algebra,
we call the state formed after doing the bijection the bizarro
of the initial state, denoted S * . We introduce the functions
next and prev of a state S which return the set of possible
states that could follow or precede S, respectively. From
this theorem, if S 2
∈ prev(S 1
), then S 2
*
∈ next(S 1*
).
We will derive some basic upper bounds on the lengths
of the longest prime patterns.
3. Basic Upper Bounds
Obviously, we cannot have a prime pattern with more
states than the number of possible states.
Lemma 3.1. The number of possible states is
J(n, b) has vertices.
. Equivalently,
Proof. Each state is a permutation of b copies of 1 and
n − b copies of 0. Therefore, the number of distinct states
is .
Corollary 3.2. L(n, b) ≤ .
In fact, if b > 1 and n−b > 1, this inequality is strict because
it is impossible to reach all states without repetition. This
is proven below.
Lemma 3.3. If b > 1 and n − b > 1, L(n, b) < .
Proof. Consider the state with all balls in the highest
possible position,
Because this state ends in 1, the previous throw must
have been max height and the previous state was
However, this new state also ends in 1, so the previous
throw must have been max height, and so on until all b
copies of 1 are exhausted and the state is ground state,
In other words, the only way to get to the original
state S is to do b max height throws from ground state.
However, because S begins with n − b copies of 0, the next
n − b throws must all be height 0. After those throws, we
return to ground state, closing the walk.
This means that S is only reached by a single prime
pattern. This pattern has length n, and for b > 1 and n −
b > 1, n < . In other words, the longest prime pattern
will either reach S and be length n or not reach S at all.
Therefore, if b > 1 and n − b > 1, L(n, b) < .
Now, consider the simple case where b = 2. Using a more
complex argument, stronger bounds can be constructed.
MATHEMATICS AND COMPUTER SCIENCE
Broad Street Scientific | 2018-2019 | 61

4. The Case b = 2
The argument hinges on simplifying the problem by
considering the distance between the two balls, rather than
their exact positions in the states. The distance between
two balls in a state is the difference in the position of their
corresponding 1’s. For example, the distance between the
balls in the state (01001) is 5 − 2=3, because the first 1 is in
position 2 and the second 1 is in position 5.
With only two balls, the distance between the balls and
the position of the first ball completely describe a state.
However, notice that if the first ball is not in the leftmost
position, the only possible throw is 0 until that ball falls
into the leftmost position. Therefore, any pattern that
reaches a state with some distance d necessarily reaches
the state with distance d and a 1 in the leftmost position.
This implies that each throw where height ≠ 0 in a prime
pattern must lead to a unique distance.
By considering only the states with a 1 in the leftmost
position, we can construct a weighted directed graph with
each vertex representing a unique distance and the weights
on the edges indicating the maximum number of throws
from one distance to another, using only one throw
of height > 0. For example, the graph for 2 balls with
maximum height 5 (or maximum distance 4), is shown in
Figure 4.1.
Then, an edge exists between states d and d′ if d′ < d or
d + d′ ≤ n. Its weight is
Rather than drawing the graph, it is simpler to consider
a modified adjacency matrix where the entry in row x and
column y is the W(x, y), if that edge exists. The example
n = 5 is below.
A cycle on the weighted graph does not repeat states,
so it is also a prime pattern. Its length is the sum of the
weights of the edges that it traverses. In the n = 5 case, the
longest prime pattern created using this strategy is length
8. The edges it traverses are circled in the matrix below.
In fact, there is a general pattern that gives very long
prime patterns and a lower bound on L(n,2).
Lemma 4.1.
Figure 4.1. Condensed 2-ball juggling graph with
max height 5. Vertices represent states with a 1 in
the leftmost position and edges represent throws.
Vertices are labeled with distance, and edges are
labeled with the number of states reached in the
transition from one state to another.
The edge from distance 3 to distance 2 has weight 3
because the longest path from (10010) to (10100) is length
3, given by the throws 5, 0, 0.
The edge weights can be calculated easily. Every time a
ball is thrown, it can either be thrown to a higher position
than the other ball or to a lower position. If it is thrown
higher, the next ball to land will be the second ball, which
happens in d steps. If the first ball is thrown lower, say
height h, it will be the next to land, h steps later. Let d′ be
the target distance. Then h = d - d′ . Finally, this transition
is only possible if d′ < d (so we can throw lower) or d + d′ ≤
n (so we don’t throw above max height).
Proof. Construct a sequence of distances as follows:
• Begin with distance n − 1.
• Go to .
• Alternate across n/2, each time going to the distance
closest to n/2 not yet reached. For odd n, begin by
increasing the distance, and for even n, begin by
decreasing the distance.
• When distance 1 is reached, go to distance n − 1.
For example, take n = 10. The sequence of distances
formed by this procedure is 9, 5, 4, 6, 3, 7, 2, 8, 1. Looking
at the matrix representation makes it much more obvious
what this process does. For n = 10, the edges traversed are
The sum of the weights of the edges traversed (the
circled numbers) is the length of the pattern. This sum is
62 | 2018-2019 | Broad Street Scientific MATHEMATICS AND COMPUTER SCIENCE

upper bound on L in terms of C.
For upper integer bound n, this is equal to .
Writing it in this way shows a difference of just from
the upper bound .
In fact, we will later see that the notion is
exactly L(n,2). This is due to a stronger upper bound for L
that is derived by extending the notion of distance to cases
with b > 2.
5. Extension to b > 2
For some state S with a ball in the lowest position, write
the sequence of distances between each ball and the nexthighest
ball, starting with the lowest ball. Call the sum
of this sequence m and append n − m to the sequence to
construct the distance notation of a state. We write distance
notation in brackets and without commas or space
between entries. For example, for the state (100101), the
distance notation is [321].
Distance notation is useful because after a max height
throw and all subsequent height 0 throws, the distance
notation rotates one place. Again taking the state (100110),
after the siteswap 600, the state is (1010100) and the
distance notation is [213]. The states corresponding to all
unique rotations of a distance notation and all “in-between”
states that have a 0 in the leftmost position form a subcycle:
a set of states formed when doing only max height and
height 0 throws. Each state is part of exactly one subcycle.
Subcycles are very useful for finding long prime
patterns, because a particular subcycle contains many
states that cannot be reached by and cannot reach any state
outside the subcycle. All states that end in 1 must have had
the previous throw be max height, so the previous state
was in the subcycle. Furthermore, all states that begin in 0
must have the next throw be height 0, so the next state will
be in the subcycle.
Not all subcycles have the same number of states. For
example, (1010) and (0101) form a subcycle with b = 2
and n = 4, but (1100), (1001), (0011), and (0110) are also a
subcycle with b = 2 and n = 4. If the number of states in a
subcycle is m, the ratio n/m is the multiplicity of the subcycle,
denoted with the letter x. Multiplicity can also be seen as a
property of a state and is the number of times a string of 1’s
and 0’s is repeated to form that state. For example, (1010)
has multiplicity 2 because it is (10) repeated 2 times. States
have the same multiplicity of the subcycle of which they
are part. Clearly, x must be a divisor of n. x must also be a
divisor of b, because each repetition must include the same
number of balls. Therefore, x must be a divisor of gcd(n, b).
Let C x
(n, b) be the number of subcycles of multiplicity
x with max throw n and b balls. We obtain the following
MATHEMATICS AND COMPUTER SCIENCE
Theorem 5.1. If b > 1 and n − b > 1, L(n, b) ≤
or equivalently L(n, b)≤
means α is a divisor of β.
. The notation α|β
Proof. This bound essentially states that in each subcycle,
we can hit at most one fewer state than the number of
states in that subcycle.
To see why this is true, consider all states with a 1 in
the leftmost position. For brevity, we call these states
grounded. These are the only states that can reach any state
outside the subcycle. Consider a particular grounded state
S. Then there is the next state in the subcycle S′ formed
after doing a max height throw from S. The only state that
can reach S′ is S.
Now consider a prime pattern that includes all
grounded states in a subcycle S 1
,S 2
,...,S n/x
. Unless the prime
pattern has no states outside this subcycle, at some point a
throw lower than max height must be made from one of
the grounded states S i
. However, the state after S i
in this
subcycle could not be reached without repeating S i
.
Therefore, if a prime pattern includes states from
multiple subcycles, it can hit at most one fewer than the
number of states in each subcycle. The number of states
in a subcycle of multiplicity x is n/x, so multiplying n/x
− 1 by the number of subcycles with multiplicity x, then
summing across all possible multiplicities gives the upper
bound
Equivalently, we can start with the total number of
states and subtract 1 for each cycle to get
The exceptions are when the longest prime pattern is
actually just one subcycle, and the length of that subcycle
is greater than the bound above. This only occurs when
there is only one subcycle, which happens when b = 1 or
b = 0.
We will define
for
simplicity.
How many subcycles of a particular multiplicity are
there? We can construct several recurrence relations that
uniquely define C x
.
Lemma 5.2.
Proof. Recall that x counts the number of repetitions of a
string needed to form a state with multiplicity x. Each of
these strings is also a state with b/x balls and max height
n/x. For example, (101010) is a state with 3 balls and max
Broad Street Scientific | 2018-2019 | 63

height 6, and the repeating unit (10) is a state with 1 ball
and max height 2.
Every subcycle of multiplicity 1 with b/x balls and
max height n/x uniquely determines a subcycle of
multiplicity x with b balls and max height n. Therefore,
.
Table 5.2. Upper bound on length of longest prime
pattern given by Theorem 5.1.
Let s x
(n, b) be the number of states with multiplicity x,
max height n, and b balls. Clearly, C x
(n, b) = , because
each subcycle of multiplicity x has n/x states by definition.
From the previous lemma, we have
. We
also have the following relation that involves s.
Lemma 5.3.
Proof. Each state has a unique multiplicity, so summing
across all possible multiplicities yields all states.
Table 5.3. Difference between the upper bound and
actual value of longest prime pattern.
This is enough information to calculate any value of C
and s, and therefore the upper bound on L. As an example,
we will find L≤(6,3):
In fact, L(6,3) = 15.
Below are tables for values of C 1
, L≤, and L≤ − L. C x
, and
therefore L≤, is not defined for b = 0 or n − b = 0, so those
entries are omitted.
Table 5.1. Number of subcycles with multiplicity 1.
Table 5.3 shows that in many cases, L≤ = L. However, for
cases where n = 2b and b > 2 (the central values in every
other row), L(2b, b) < L≤(2b, b). Before this is proven, we
will establish some necessary conditions to lose only 1
state in each subcycle, instead of more.
We define the first grounded state in a subcycle. As the
name implies, this is the grounded state in a subcycle that
first appears in a prime pattern. Not every grounded state
can be a first grounded state.
Lemma 5.4. If a grounded state has 1 as its last distance, it
cannot be a first grounded state.
Proof. If a state has 1 as its last distance, it must have a 1 in
the rightmost position. However, this means the previous
throw must have been a max height throw, so the previous
state was a grounded state in the same subcycle. Thus, a
state with 1 as its last distance cannot be the first grounded
state reached in a subcycle.
Now consider, for example, the state (1101000), or in
distance notation, [124]. If this is the first grounded state
and the prime pattern only misses 1 state from its subcycle,
then [241] and [412] will also be reached. The states
missed are the non-grounded states “in-between” [412]
and [124]. These are S 1
= (0001101), S 2
= (0011010), and
64 | 2018-2019 | Broad Street Scientific MATHEMATICS AND COMPUTER SCIENCE

S 3
= (0110100). Out of these, only S 2
and S 3
can be reached
from a state outside this subcycle, because S 1
has a 1 in the
rightmost position. If S 3
was reached first, then both S 1
and
S 2
will be missed. Then to miss exactly one state, assuming
[124] is the first grounded state reached in the subcycle, S 2
must be the first state reached in the subcycle.
In general, the first state reached in a subcycle must be
two states after some grounded state S G
in a subcycle, if
only 1 state is to be missed in that subcycle. We call this
state an entry state for a subcycle. The singular state missed
in that case is the state from throwing maximum height
from S G
.
Which states can reach this particular entry state? From
Theorem 2.1, this question is equivalent to asking for the
bizarro of the states that can be reached by the bizarro of
the entry state. In our example, the entry state is (0011010),
which has bizarro (1010011). There are 4 states that can
immediately follow this state: (1100110), (0110110),
(0101110), and (0100111), which have bizarros (1001100),
(1001001), (1000101), and (0001101). Obviously, we
discard the last of these, because it is in the same subcycle
as the entry state.
The distance notation for the three states that work
are [313], [331], and [421]. These would be the last states
reached in their subcycle, or the leaving states, and the
corresponding first ground states reached would be [133],
[313], and [214]. Recall our original grounded state [124].
Notice the state [133] is just [124] with the second-to-last
distance incremented and the last distance decremented.
Notice as well that the other two states both have 1 as their
second-to-last distance. These are in fact the only two
possibilities, a fact that we will prove.
Before the proof, we introduce the function entry of a
grounded state S G
, which returns the unique entry state if
the first grounded state reached in S G
’s subcycle is S G
. From
the above example, entry((1101000)) = (0011010). We also
introduce the function fg of a grounded state S H
, which
returns the unique first grounded state of S H
’s subcycle if
S H
is the leaving state. fg(S H
) is also the next grounded state
after S H
in S H
’s subcycle. If fg(S H
) = S G
, then entry(S G
) is the
state formed after a max height and height 0 throw from
S H
.
Lemma 5.5. Let S G
with distance notation [d 1
d 2
...d b−1
d b
] be the
first grounded state of a subcycle. Then let {S p1
,S p2
,...} be all states
in prev(entry(S G
)) but not in the same subcycle as S G
. For each
S pi
, let S qi
= fg(S pi
). Then the distance notation of each S qi
is either
[d 1
...d b−2
(d b−1
+ 1)(d b
− 1)], or S qi
has 1 as the second-to-last distance
and either d b
− 1 or d b
− 1 + d 1
as the last distance.
Let fg(S H
) = S G
. Then
We know the entry state is the state after a max height
throw and one throw of height 0 from S H
, so
The bizzaro is
We know
. In fact, only
entry(S G
)* is omitted in
There are three cases
for possible throws from entry(S G
)*: the aforementioned
max height throw, a throw of height 1, and every other
throw. We must consider only the latter two.
Case 1: After a throw of height 1, the state is
which has bizarro
Then
, which is
S qi
has distance notation [d 1
...d b−2
(d b−1
+ 1)(d b
− 1)]. This
is the first possibility described by the lemma.
Case 2: After a throw of height < n, the state is either
Case 2a, where the ball is thrown somewhere in the middle:
or Case 2b, where the ball is thrown close to the end:
with the circled 1 representing the thrown ball. These
two subcases are essentially the same and correspond to
the two possibilities for the last distance, d b
− 1 and d b
− 1
+ d 1
. We will only show the rest of Case 2a, but Case 2b
follows similarly.
After absorbing the circle 1 into the adjacent groups,
we have
Proof. We will begin by constructing entry(S G
). We have
MATHEMATICS AND COMPUTER SCIENCE
Broad Street Scientific | 2018-2019 | 65

which has bizarro
not work because its last distance is 1. Therefore, pfg(S 1
)
consists of exactly one state S′ 1
, which has distance notation
We have S qi
= fg(S pi
), so
Then S qi
has a 1 as its second-to-last distance and d b
− 1
as its last distance, which is the second possibility described
in the lemma. As mentioned before, Case 2b corresponds
to the final possibility described in the lemma, with 1 as the
second-to-last distance and d b
− 1 + d 1
as the last distance.
As these are the only two possibilities, the proof is
complete.
We will denote pfg as the set of these previous first
grounded states. That is, pfg(S G
) is the set of fg(S pi
) for each
S pi
in prev(entry(S G
)) but not in the same subcycle as S G
.
There is the additional constraint that any S′ ∈ pfg(S G
) must
not have 1 as its last distance, because then S′ could not be
a first grounded state from Lemma 5.4.
We have the following useful corollary.
Corollary 5.6. For any grounded state S that does not have
1 as its second-to-last distance, there is exactly one S′ where
S ∈ pfg(S′). This S′ has the same distance notation as S but with
the second-to-last distance decremented and the last distance
incremented.
We now have the groundwork to tighten the bound for
L(2b, b).
Theorem 5.7. For b > 2, L(2b, b) < L≤(2b, b).
Proof. This proof relies on the unique subcycle of
multiplicity n/2. There are 2 states in this subcycle:
From Theorem 5.1, we know that only S 1
could ever be
reached in a prime pattern, except if that pattern consists
of just S 1
and S 2
. Consider pfg(S 1
). From Lemma 5.5, each
S qi
∈ pfg(S 1
) satisfies at least one of the following criteria:
• The distance notation is
• The second-to-last distance is 1 and the last distance
is 2 − 1=1.
• The second-to-last distance is 1 and the last distance
is 2 − 1+2=3.
The third possibility is actually the same as the first
in this case. From Lemma 5.4, the second possibility does
S 1
is also the leaving state, so consider the possible
states S i
where S 1
∈ pfg(S i
). Because S 1
does not have 1 as its
second-to-last distance, Corollary 5.6 applies and the only
state S where S 1
∈ pfg(S) has distance notation
This is actually S′ 1
.
Therefore, if only one state is to be missed in each
subcycle, the subcycle containing S′ 1
must both immediately
precede and immediately succeed S 1
. The only prime
pattern that satisfies this consists of only that subcycle
minus one state and S 1
, so it has length n. For any b > 2,
this is not as long as the longest possible prime pattern, so
we miss out on S 1
. Therefore, for b > 2, L(2b, b) < L ≤(2b, b).
6. Concluding Remarks
The cases where n = 2b are not the only cases where
L

AN ANALYSIS OF A NOVEL NEURAL NETWORK
ARCHITECTURE
Vatsal Varma
Abstract
Artificial Intelligence is a rapidly growing field in computer science, and the pinnacle of this field is the Artificial Neural
Network (ANN). Modeled after neuronal connections in the brain, neural networks have proved exceptional in locating
and discriminating amongst patterns in vast datasets. Each neural network contains a multivariate function, which is
known as the error function. Using a different optimization function, the neural network attempts to reach a minimum
of its error function by reaching the respective minima of its weights and biases. This study aims to determine the effects
of four different neural network architectures (NNA) on their overall convergence rates holding all other variables
constant. The architectures are based on different types of neural networks: The Deep Residual Network (DRN), the
Multilayer Perceptron Network (MLP), the Extreme Learning Machine (ELM), and one novel design dubbed as the
Encoded Learning Machine (EncLM). A previous study used Boolean functions to determine the rate of optimization,
and the novel design topped out of the tested networks. However, this study utilizes the Modified National Institute of
Standards and Technologies (MNIST) Dataset, a dataset of images of handwritten digits. Each of the networks was run
over the 60,000 images for one epoch, and within that epoch, was optimized every 100 images using backpropagation.
It was determined that the MLP and DRN were the weakest networks for fast optimization as they took the longest to
converge. The EncLM was once again the fastest architecture to converge upon a satisfactory result.
1. Introduction
1.1 – Neural Networks
An artificial neural network (ANN) is an abstraction of
the biological nervous system, using artificial neurons and
axons to create a web and a means to solutions unfound.
The popularity of such networks stems from their ability
to adapt, learn and generalize. Due to these abilities,
artificial neural networks can solve many computational,
classification and pattern-recognition problems via a
learning-based algorithm.
In this study, every neural network is constructed and
implemented with three factors remaining constant: the
optimization method, the framework of the network, and
the data used by each network. The data that each of the
neural networks being tested will use are derived from the
Modified National Institute of Standards and Technology
(MNIST) dataset. The dataset in question is around
60,000 images of handwritten digits, each of which has
intrinsic properties that the network must derive to attain
a successful output. Before specifying the steps taken to
process the image, some notation needs to be defined. Let
(w i
, h i
, l i
), where w represents width, h represents height
and l represents length, be defined by dimension d i
. Each of
the handwritten digits comes in an uncompressed format
of d u
= (28, 28, 1). Using a program, each one of those
images was compressed to a size of d c
= (24, 24, 1) to make
computation and pooling easier for the neural networks.
There were two parts to each of the networks tested
in this study: the convolutional neural network, and the
feed forward network. The convolutional neural network
formed the back end of each of the networks, as it allowed
further compression of the handwritten digits into a onedimensional
input vector with meaningful data readable
by the feed forward layer. The feed forward layer forms
the front end of the network. The one-dimensional output
vector determined by the convolutional neural network is
then used as the input vector for the feed forward network.
The feed forward architecture is what is being tested in
this study. Thus, before describing the intricacies of each
network, it is important to know how each network works
mathematically.
Before delving into the mathematics of neural
networks, a few notation issues must be sorted out. Let n L j
define each neuron in the feed forward layer. Let o L define j
the activation of the neuron in layer L at position j and
β L define the bias of the neuron at layer L and position j.
j
Similarly, let ī L define the net input a neuron receives.
j
L
Next, let w 1 ,L 2
j,k
define the weight of the link between neuron
j of layer L 1
and neuron k of layer L 2
. Finally, let σ define
the activation function of the neuron.
Figure 1. An artificial neuron model.
MATHEMATICS AND COMPUTER SCIENCE
Broad Street Scientific | 2018-2019 | 67

Each neuron in the feed forward network is derived
from the McCulloch & Pitts neuron model (Fig. 1).
The model describes neurons as synaptically linked to
each other, and each neuron may have multiple links
to multiple other neurons. Each link to a neuron holds
a specific value, called its weight w, as described earlier.
That value represents the importance of the link to the
neuron the information is going to. To exemplify, say
there existed a neural network with two layers L 1
and L 2
.
Layer L 1
has two neurons, and L 2
has one neuron. In this
network, there would only be two links, with weights, w 1
= w 1,2 and w = 1,1 2 w1,2.
If w = 0 it would mean that the input
2,1 1
of the neuron ī 2 would remain unaffected by the output
1
o 1 . This is also reflected in the way the net input of each
neuron is calculated.
The input of each neuron in successive layers is
calculated based on the sum of the product of the output
of each neuron and the respective weight of the link
propagating that output.
A neuron not only holds its net input, but also is
responsible for calculating its net output, which is a
function of its net input ī and its bias β. Each neuron’s
output is calculated as follows where σ is representative
of the sigmoid function, and this is true for both the
convolutional neurons and the feed forward neurons.
In this model, three activation functions are used:
sigmoid σ(n), hyperbolic-tangent h(n) = tanh(n), and
exponential linear units ε(n), a modification of the rectified
linear units function.
The sigmoid activation function suppresses each of the
outputs within a range of (0,1). The hyperbolic tangent
serves a similar purpose and suppresses the outputs within
a range of (−1,1). The Exponential Linear Units serves a
different purpose. It is used on the convolutional neurons
within the convolutional neural network part of the
entire network. Since the convolutional neural network
(CNN) is tasked with compressing an image, its inherent
purpose is to process each pixel of an image. The value
of each pixel locus is the atomic number of the element
present at that location, and zero otherwise. This is not
adequately processed by the sigmoid or hyperbolic tangent
functions, as when the pixel values become larger and
larger, the hyperbolic tangent and sigmoid functions will
become more and more saturated. Furthermore, negative
pixel values are typically regarded as zero. That is why the
Convolutional Neural Network utilizes the exponential
linear units activation function instead of another.
There are two types of neurons in the CNN, the
convolutional neuron n C
and the pooling neuron n P
. The
n C
neurons operate in a similar fashion to the feed forward
neurons, but the n P
neurons have a different purpose. Each
of the n P
neurons take a (2, 2) section of the image and
finds the largest value within its section, and sets that value
as its output. This essentially carries the most important
pixel value for the next layer of processing. As the network
progresses layer by layer, the image is compressed further
and further until it becomes a one-dimensional input
vector for the fully connected layer.
The CNN, like the feed forward network, is built in
layers; however, the way those layers are designated is
completely different from the feed forward network.
The CNN operates through filters and convolutions.
Essentially, a filter is a set of weights which are applied
to sections of the image to create a net input for the
convolutional neuron that filter is sending its data to. A
convolutional layer can be described with a dimension d i
where its length represents the number of filters that layer
has. For example, the image of dimensions d c
= (24, 24, 1)
is convoluted upon to create a layer of size d L
= (24,24,3).
This means that there are three filters in that convolutional
layer, each responsible for one (24, 24) section of that
layer. To further explain how filters work, let there be
three filters f 0
, f 1
and f 2
, for the layer discussed above. Each
filter acts upon the entire depth of the input image, thus
the length of the filter must be the length of the previous
image. Say the dimension of the filter was d f
= (3, 3, 1).
Filter f 0
would operate on consecutive three by three by
one sections of the input image. In the next convolutional
layer, each filter would operate on consecutive three by
three by three sections of the previous layer, and so on.
Between convolutional layers exists a pooling layer, which
further compresses the layer. For example, if the layer
was of size (24, 24, 13) the max pooling layer would be of
size (12, 12, 13). That is essentially how a CNN operates.
Successive layers will convolute upon the previous layer’s
output image, and slowly pool the image down to a
manageable size. That output vector will then be used as
an input vector for the feed forward network.
All of the above tools, when put together, can be
68 | 2018-2019 | Broad Street Scientific MATHEMATICS AND COMPUTER SCIENCE

used to deliver an output of the network that classifies
the handwritten digit with its respective value. This is
known as the feed-forward stage. Initially that output will
be meaningless, and it will remain so until the network
is trained. The training vector t → is built using already
optimized geometries to train the network. t → will be of the
dimension of the input image. To then train the network,
the error of the network is calculated using t → and the
Mean Squared Error formula (MSE), and then that error is
backpropagated throughout the network.
If t → defines the correct/preferred output of the network,
and → ρ is the actual output of the network, MSE can be
calculated as follows.
(3)
Backpropagation has three main procedures: first, to
determine the effect that a neuron’s output has on the
error; then to determine the effect that the neuron’s bias
and net input has on that same error; and finally, using
the value calculated by the net input, to determine the
effect that each link’s weight has in that error. Through
backpropagation, the network is attempting to minimize
the error function MSE(t → , → ρ) by calculating its negative
gradient.
To do this, the network calculates the partial derivative
of each weight and bias with respect to the error function.
Symbolically, this can be represented as for bias
and for weights. By applying the chain rule we can
expand these basic equations to finish the implementation
of the entire backpropagation rule. The first step is to
calculate a δ value for each neuron which indicates the
direction the neuron’s output needs to step for it to reach
a minimum. The δ is calculated differently depending on
whether the neuron in question is an output neuron or
not.
(4)
In these functions the sigmoid activation function can
be replaced by any other activation function discussed
earlier in the Introduction.
Using this δ the network is able to calculate the
effects of the weights and biases on the total error of the
network and take a step down the gradient of the error
function. The equations below define the backpropagation
algorithm where η β
is the constant that determines the
size of the step the bias β must take, and η w
is the constant
that determines the size of the step the weight w of each
individual link must take.
(5)
(6)
All of the above will remain constant in this study.
The only variable will be the neural network architecture,
or, in other words, the number of connections and how
each network is linked together. What changes, then, is
how the gradients δ are calculated. If different neurons
are connected, then their outputs will differ based on the
outputs of the neurons they are connected to. Thus, what
happens if the neurons are connected in specific ways?
How does that architecture change the performance of
the network? Most importantly, is it possible to hybridize
two architectures and obtain properties of both? This
study is designed to test the differences between various
neural networks based purely on their architecture.
Using the image dataset, each neural network will be
run for the entirety of 60,000 iterations, during which
data corresponding to the neuron will be collected every
iteration, and data corresponding to the network will
be collected only when the total error is backpropagated
(every 100 iterations). Data will include the neuron biases
and activations, link weights and the overall network
error. The aim of this study is to find the quickest and most
efficient NNA convergence rate based on its architecture
and architecture only. Furthermore, using the knowledge
gained from the three initial networks, a novel NNA by the
name of the Encoded Learning Machine, which employs
principles of various networks in attempt to obtain faster
and more efficient convergence, can be implemented.
2. Computational Approach
The designing and visualization of these NNAs took
place in two parts. First, each neural network was designed,
implemented and tested in Java. Then, using Mathematica
and Microsoft Excel, the data were visualized and each
neural network was heuristically evaluated and given a
score relative to the other networks. A high score meant
the network converged faster than the other networks;
a lower score meant that either the network’s error was
high, or the network’s accuracy was low. However, before
delving into the object-oriented implementation of these
NNAs, an overview of the structures must be given.
MATHEMATICS AND COMPUTER SCIENCE
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2.1 – Structure Overview
sets. They have further been used to obtain "higher-quality
contact prediction” data for proteins (Wang, 2017). The
DRN most likely will not show its full potential during this
study due to all networks only being 4 layers deep, when
DRN architectures can be upwards of 100 layers.
Figure 2. A Multilayer Perceptron (MLP) model
visualized in STELLA.
There are four different NNAs used in this study:
The Multilayer Perceptron, the Deep Residual Network,
the Extreme Learning Machine, and finally the Encoded
Learning Machine. The MLP is one of the most basic
implementations of a neural network. Generally, an MLP
consists of an input layer, usually represented as a vector,
an output layer, and n hidden layers (Fig. 2). To clarify,
layers are simply objects that hold an array of neurons.
Each neuron is then connected with every neuron in the
layer in front of it with links starting from the input layer
and ending at the output layer. The MLP architecture is a
simple and efficient structure that has been proven to be
able to organize and classify data. It is often used as a part
of a larger neural network.
Figure 3. A Deep Residual Network (DRN) model
visualized in STELLA.
The DRN is quite like the MLP, but instead of only
connecting consecutive layers, it can include connections
that span more than one layer at regular intervals
throughout the network (Fig. 3). The theory behind
this network is that previous input is being forward
propagated many layers to prevent loss of data and enhance
generalization capabilities. DRN architectures have proven
adept at generalizing images and other complicated data
Figure 4. An Extreme Learning Machine (ELM)
model visualized in STELLA.
The ELM is basically a network with an input layer,
a hidden layer and an output layer. The only catch is
that there exist random forward links from each neuron
which can connect to any other neuron in the network
if the prospective neuron is not in a layer behind the
neuron requesting connection (Fig. 4). This network was
designed to reduce the slow training speed of other types
of neural networks (Ding, 2015). It has also proven to be
better at generalization and have a faster learning rate
(Ding, 2015). Furthermore, due to the stochastic nature
of the connections, the number of hidden layers becomes
arbitrary, therefore making it pointless to initialize this
network with multiple hidden layers like the others. This
network is actually trained differently from the rest of the
networks when applied in other cases; however, in this
study it remains like a network with random connections.
The design was simply an experiment to analyze how a
neural network with such connections would behave
when trained by backpropagation.
Finally, the EncLM is a hybridization of two different
types of architectures: an autoencoder and the ELM. An
autoencoder takes an input vector and transposes it to a
layer identical to it (Fig. 5). This essentially means that
it encodes the same information in a different pattern,
meaning that more intricate aspects of the data can be
seen by the network. Furthermore, due to the speedy
performance, but higher average error, of the ELM,
it became the second part of this network. Due to the
autoencoder, it was theorized that if the neural network
was able to process the same information coming from
more neurons, it would be able to step down the gradient
faster and more efficiently.
70 | 2018-2019 | Broad Street Scientific MATHEMATICS AND COMPUTER SCIENCE

Figure 5. An Encoded Learning Machine (EncLM)
model visualized in STELLA.
A convolutional neural network’s job is to compress a
two or three-dimensional input tensor, such as an image,
into a one-dimensional vector that can be processed by the
front end neural network. Each convolutional network
is based on the idea of filters, where each filter “learns”
to differentiate certain aspects of that tensor from other
aspects. For handwritten digits, filters might be used to
recognize loops or edges within the numbers. Each layer
in the convolutional neural network depends on the filter
assigned to it. Each convolutional neural network in this
study had 10 filters of size five pixels by five pixels. At the
end of the convolutional network, a pooling layer was
constructed that normalized and compressed the previous
outputs so that the front end networks had less data to
analyze, and therefore saved memory on the computer.
For this network, one convolutional layer of dimension
d L
= (24, 24, 10) was used. Ten filters of size (5, 5) pixels
were applied to this layer. After this layer determined its
output, the next layer was the max pooling layer, which
condensed the output of the convolutions into a smaller
space and allowed faster forward propagation of the
network. Each neuron in the CNN was connected to the
neurons in the previous layer based on the size of its filter.
The feed forward network had 4 layers, each with 32
neurons as the initial layer, 20 neurons, 16 neurons and
finally 10 neurons as the output layer. The input neurons
of the feed forward layers were connected to the output
neurons in the max pooling layer of the convolutional
neural network.
This is a brief overview of how the architectures were
set up in this study.
2.2 – Data Generation
The initial objective of the NNA implementation was
to write the algorithm that converted the MNIST data into
a readable form. Using a small Python script, each image
of the 60,000 images in the dataset was converted into a
MATHEMATICS AND COMPUTER SCIENCE
one-dimensional input vector and put into a file readable
by the Java ParseCSV class. Once this was complete, each
one of those images needed to be assigned a classification
vector → t . By obtaining the correct value for each image,
the ParseCSV class was able to create classification vectors
for each image. Each vector would be used to train the
network after it determined the output on the input image.
After generating the datasets, the NNAs had to be
implemented as well. To keep implementation easy
and understandable, each neural network is based on
a superclass, NeuralNetwork.java, which allowed each
subclass, corresponding to the neural networks in this
study, to be initialized by defining how they are run,
trained, and connected. All neural networks were run by
forward propagation, which involves taking all the layers
of a network, starting from the input layer, and calculating
the output or activation o L of each neuron within that
j
layer via equation 2 until it reached the final neuron,
which, when its output was calculated, would represent
the network’s integer answer to → b.
While a run operates, the neural network writes
data to its respective csv file. Data are written either
every activation cycle, or every optimization cycle.
Every activation cycle, each neuron’s activation o L j
and its net input ī L is written to a file by the name of
j
”NetworkNameNeuronData.csv” where NetworkName
would be replaced by the acronyms given to each network
in this study. Furthermore, since the weights and biases
are updated every optimization cycle, those are written in
a smaller file by the name of “NetworkNameNetworkData.
csv”. This file also contains the network error data that will
be crucial to the analysis of these NNAs. During every 100
iterations, or optimization cycle, the network is trained
through backpropagation. This is done in two steps: first,
recursively going backwards along the various links and
neurons and creating a δ value for each neuron according
to equation 4; then, again recursively back propagating
along the links and neurons to update the biases β L and j
L
weights w 1 ,L 2 L L
j,k
according to the δ j
and o j
of the neuron (see
equations 5 and 6).
This summarizes, in brief, the constants and variables
to which each neural network will be subject.
3. Results
Each network has a vast amount of data to analyze and
visualize. Therefore, to make this section more organized,
it will be split into two subsections: error & accuracy,
which will discuss the evaluation, speed and efficiency of
the networks, and visualization, which will discuss what
is being visualized and why it was chosen to represent the
neural network.
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3.1 – Error and Accuracy
The objective of this study was to determine the highest
performing network based on two parameters, accuracy a
and error e. By those two metrics, a heuristic score can be
assigned to each of the networks, where the higher score is
the better score, based on the function H as shown below.
As accuracy increases, the score increases, and as error
decreases the score increases. In other words H(a, e) ∝ a
and H(a, e) ∝ 1/e.
Before delving into the meaning of each one of those
numbers, definitions of error and accuracy are required.
Error is the average difference between the perfect output,
and the actual output of the network. It can range from
−∞ to ∞. Accuracy is the percentage of the images the
network classified correctly while training. It can only
range from 0 to 100. Finally, the prediction percentage of
the network is how sure the network is of its answer.
Table 1. Error and Accuracy Averages for the Two
Trials.
TRIAL DRN ELM MLP ENCLM
1-Error 0.030128 0.005262 0.034142 0.006175
2-Error 0.038433 0.016085 0.039846 0.03341
1-
Accuracy 0.1374 0.118417 0.113433 0.125283
2-
Accuracy 0.153573 0.095943 0.124493 0.217846
Avg.
Accuracy 0.145487 0.10718 0.118963 0.171565
Avg.
Error 0.034281 0.010674 0.036994 0.019793
Scores 424.395 1004.12 321.574 866.796
For each of these networks, interesting observations
can be gathered. Of course, if more trials were performed,
the data would reflect the actual performance of the
network more accurately. According to Wang et. al’s
paper, the DRN was particularly adept at accurately
classifying various things, especially images (Wang, 2017).
Seeing the scores, this seems to be true, as the DRN has the
second highest accuracy of all of the network architectures
tested in this study. This means that, out of every 100
predictions, about 15 predictions were correct, even if
they were predicted by a low margin. That low margin is
indicated by the relatively high error value that the DRN
has. In other words, the DRN can guess correctly, but it is
quite unsure about its guesses. For example, if an image of
a three was input into the DRN, it may guess it correctly,
but its prediction percentage for an eight would also be
relatively high.
Next, the ELM architecture was the highest scoring
of all of the networks. The random connections of the
architecture seemed to have helped it achieve the low
error. However, its high score is deceiving. The accuracy
of the ELM is the lowest of all of the network architectures
tested in this study, a mere 10.718% across 60,000 images.
Its very low error, coupled with its low accuracy, can only
be attributed to one occurrence; the network was trained
in a manner that associated several features with the wrong
values. For example, if a three was input into the network,
it would guess that eight was the answer because of the
similar features, with a very high prediction percentage. It
was sure of its answer, even if that answer was incorrect.
Third, the MLP architecture was the lowest scoring
of all of the networks. The orderly connections of the
architecture as seen in Fig. 2 seem to have inhibited the
network from learning the nuances present within the
structures of each of the handwritten digits. The MLP
had both the lowest accuracy as well as the highest error.
For example, if a three was put into the network, it would
be unsure of what the output should be, and would guess
based on whatever it found familiar, leading to a guess of
eight, nine, and sometimes, three.
Fourth and finally, the new hybrid network
architecture, EncLM, was the second highest scorer
of the four tested networks across the two trials. The
orderly connections that form its first two layers, instead
of inhibiting the network’s performance, seem to have
enhanced it. The worst performer combined with the best
performer created a hybrid network with new capabilities.
It had the highest accuracy, with the second lowest error.
Comparing this with the other architectures, if a three was
put into the EncLM architecture, the architecture would
guess three and be fairly sure of its guess, meaning that it
would have a high prediction percentage.
From these numbers, this is a summary of the
observations that can be made. The performance of each
of the networks can further be broken down when looking
at their performance over time.
3.2 – Visualization
For each one of the networks, the accuracy over time
a(t) and the error over time e(t) were plotted (Fig. 6, 7, 8,
9). The trends visible in each of the graphs indicate the
aspects of the networks discussed above, but they show the
networks’ training speed as well.
A more accurate network will have an a ′(t) slope larger
than most networks. In this case, by observation, the DRN
has the fastest increasing accuracy. Perhaps, after several
iterations over the same data, the DRN will have the
72 | 2018-2019 | Broad Street Scientific MATHEMATICS AND COMPUTER SCIENCE

highest accuracy out of all of the networks. One thing that
the a(t) graph indicates about the network is its potential
to learn within the limited vision it was given. Obtaining
a higher average accuracy is often indicative of the faster
training of the network. It is true in all cases that the
accuracy value goes up as the number of iterations goes
on. Where the real differences in the networks can be seen
is in the e(t) graphs.
The faster training network will have an e ′(t) slope
value greater in magnitude to all of the other networks.
That network will reach the error threshold, where the
error begins to flatten, much more quickly than the other
networks. During backpropagation, such a network is
more likely to take the correct step down the gradient
of its error function −∇MSE(t → , → ρ). Furthermore, another
property of the e(t) graphs is the stochastic nature of the
values, or how far they deviate from a proper curve. It is
here where the differences are quite noticeable between
networks.
As the networks trained, the data corresponding
to each error and accuracy were collected every 100
iterations. Using Wolfram Mathematica, those data were
then visualized.
Figure 8. Trial one error data for each network.
Figure 9. Trial two error data for each network.
4. Discussion
Figure 6. Trial one accuracy data for each network.
Figure 7. Trial two accuracy data for each network.
MATHEMATICS AND COMPUTER SCIENCE
Ultimately, the goal of the study is to prove that the
new hybrid network architecture is viable for use in
various situations. Furthermore, this study can open up a
new area of neural network research, where properties of
two different architectures, whether they be mathematical
or structural, can be hybridized to obtain a hybrid network
that reflects the desired properties of both networks. In
the case of the EncLM, the high accuracy of the DRN
architecture and the fast training of the ELM architecture
were the desirable properties. Over both studies, the
EncLM expressed both of these properties, becoming a
fast training and highly accurate network.
As with any hybridization, unexpected results come up.
Those results manifested themselves in the form of the
error graphs e(t) of each network.
Each error graph looks similar, but varies in one aspect,
the deviation of the error in between each iteration. The
MLP has the least deviation, and the EncLM has the most
deviation. This deviation is akin to exploration. The more
the error deviates, the more the network is exploring its
individual error function to locate its minima. Half of this
is luck. The network might reach optimized values that
could drop the error to a very low value. The other half is
Broad Street Scientific | 2018-2019 | 73

exploration, or how much the neural network is willing
to deviate from certain relative minima to find the next
lowest possible error. This feature is indicative in the
lowest error values observed within each network. The
stochastic connections within the EncLM and ELM gave
the two networks error values that were nearly a sixth of
the more orderly DRN and MLP architectures. A random
set of connections, it seems, enables a network to see the
input data as a whole, rather than seeing it in layers. This
allows the network to traverse its respective error function
rapidly. However, the one drawback is that the network
cannot determine with certainty whether the output it
creates is the correct one. For the orderly networks, this
was their strength, especially in the DRN. Even with its
high error, it was able to accurately classify each digit.
The two properties of the DRN and ELM, when
combined, seem to have amplified each of their individual
effects. The exploratory nature of the EncLM is enhanced
by the DRN’s orderly connections, and the accuracy of the
network overall is higher than all other networks in the
study.
5. Conclusion
The EncLM is, ultimately, a hybrid network architecture,
employing tools from both orderly connected networks as
well as stochastic connected networks. The end result is
very satisfactory. The error it achieves is comparable to
the error the ELM achieved, and the accuracy is higher
than all other networks.
Overall, the novel architecture proved to be an
intriguing development in neural network architectures,
as it furthered the idea of speedy and efficient convergence
to a global minimum. It is safe to say that the novel
architecture is viable in all aspects when compared to the
architectures tested in this study. To further this study,
more research will be needed to determine whether the
properties of the EncLM can be further generalized to
more complex and larger datasets, maybe involving larger
and more intricate images than handwritten digits. If this
is possible, research also needs to be done to determine
the convergence rates of the other architectures in this
study on that same dataset to determine whether a more
organized structure like that of the MLP, or DRN will
be able to notice the complicated patterns present in the
new dataset, or whether a similar pattern of stochastic
dominance in this study will extrapolate onto that dataset.
Furthermore, the possibilities of architecture mixing
could potentially have uses in business, industry and other
fields that require the management of more than one task
at the same time. Another study could be carried out to
determine the effects of mixing more architectures on a
similar dataset. This could be used to determine the hybrid
architecture that provides the best possible results for any
problem.
6. Acknowledgments
The author would like to thank Mr. Robert Gotwals for
his sincere and expertful management and his fascinating
insights into various tools and means that were used in
this paper, including Excel, Mathematica and LaTeX. The
author would also like to thank his mentor Mr. Keethan
Kleiner for interesting insights and guidance throughout
this project. Appreciation is also extended towards
the North Carolina School of Science and Math for its
investment into every one of its students.
7. References
Wang, S., Sun, S., Li, Z., Zhang, R., & Xu, J. (2017).
Accurate de novo prediction of protein contact map by
ultra-deep learning model. PLoS Computational Biology,
13(1) doi:http://dx.doi.org/10.1371/journal.pcbi.1005324
Ding, S., Zhao, H., Zhang, Y., Xu, X., & Nie, R. (2015).
Extreme learning machine: Algorithm, theory and
applications. The Artificial Intelligence Review, 44(1),
103-115. doi:http://dx.doi.org/10.1007/s10462-013-
9405-z
74 | 2018-2019 | Broad Street Scientific MATHEMATICS AND COMPUTER SCIENCE

EFFECTS OF RELATIVITY ON QUADRUPOLE
OSCILLATIONS OF COMPACT STARS
Abhijit Gupta
Abstract
In the present age of space-based photometry, telescopes such as K2 and TESS are providing pulsation frequencies of
stellar objects to unprecedented accuracy, requiring equally precise theoretical models correlating these observations to
mass- and composition-dependent characteristics of stars. At this precision, relativistic models are required for compact
objects such as white dwarfs and neutron stars. We model these stars as polytropes using the Tolman-Oppenheimer-
Volkoff equation, and compute relativistic nonradial stellar pulsations around this equilibrium state. Outside the stellar
surface, we integrate the Zerilli equation to locate resonant quasinormal modes, where ingoing gravitational radiation
vanishes. We compare the frequencies of a subset of these modes to their corresponding pressure-modes in the Newtonian
limit, as a function of the strength of relativity inside the star. Our results contribute to our understanding of the impact
of general relativity on stellar oscillations, and can be used to determine the conditions under which the Newtonian
approximation is justified.
1. Motivation
1.1 – Asteroseismology
Although stars generally evolve on extremely long
timescales, they are not static but pulsate periodically
around an equilibrium. The frequencies of these
oscillations inform us about internal characteristics of the
star, suchv as mass, radius, pressure, and density. While
these variables cannot be directly measured, telescopes can
detect luminosity deviations that stellar pulsation cause.
The frequencies of these oscillations are the frequencies of
the stellar pulsations.
Asteroseismology, the study of these stellar pulsations,
involves two components: theoretical calculations
and experimental observations. Theoretical programs
assume a particular equilibrium state, and then model
perturbations on this system. Only pulsations that satisfy
boundary conditions at both the interior and stellar surface
can possibly occur. Each pulsation can be described by a
frequency and spherical harmonic degree and mode. The
experimental observations measure periodic luminosity
oscillations of stars over long periods of time. A Fourier
transform is performed, and after filtering, spikes in
the frequency curve are used to determine potential
eigenfrequencies (Fig. 1).
Figure 1. Experimental results from the K2 mission.
The top panels show the standard and phasefolded
light curves. The bottom panel shows the
amplitude and residual spectrum after the pulsation
frequencies are removed. Red vertical lines indicate
observed pulsation frequencies (Bowman, D. M. et
al., 2018)
Given these experimentally determined frequencies,
programs can be run to determine the predicted central
density, central pressure, total mass, radius, and many
additional stellar variables. Asteroseismology presents an
additional method to calculating these variables, alongside
existing procedures. The combination yields stronger
approximations than any method individually.
1.2 – Compact Objects
In recent years, space-based telescopes such as NASA’s
Kepler spacecraft and Transiting Exoplanet Survey
Satellite (TESS) are providing pulsation frequencies of
stellar objects with unprecedented accuracy. Equally
precise theoretical models correlating these observations
to mass and composition-dependent characteristics of
stars is required to make full use of these satellites. Present
theoretical models have reduced error to less than 1 part
PHYSICS
Broad Street Scientific | 2018-2019 | 75

in 10 7 , roughly equivalent to the observational accuracy of
these telescopes (Christensen- Dalsgaard & Mullan, 1993).
However, when studying highly dense compact objects,
general relativity can have a noticeable impact on the
stellar structure and pulsations, requiring more rigorous
models.
While most stars are not substantially affected by general
relativity, a class of compact objects require general
relativistic corrections to accurately model the pulsations
to the desired accuracy due to their extreme densities.
Among compact objects, there are two main classes of
stars: white dwarfs and neutron stars. White dwarfs are
the remnants of low-mass to medium-mass stars that have
exhausted their hydrogen and helium supplies. These
stars are composed of heavier elements such as carbon
and oxygen, and support themselves against gravitational
collapse with electron degeneracy pressure. The density of
a white dwarf is some 10 6 times greater than that of our
Sun.
Even more extreme are neutron stars, formed by the
supernova explosions of stars not quite large enough to
produce black holes. Neutron stars are similar to white
dwarfs except are composed almost entirely of neutrons
and supported with neutron degeneracy pressure instead
of electron degeneracy. Physicists are still unsure exactly
what types of matter are present at the very center of a
neutron star, where density is the highest. Neutron stars
are believed to be the densest macroscopic objects in the
Universe, with densities about 10 15 times higher than that
of the Sun.
Relativistic corrections have small but noticeable impacts
on white dwarfs, but are essential to study the pulsation
frequencies of neutron stars. By better understanding the
pulsations of neutron stars, we gain a better understanding
of their interiors. Recent research even suggests that the
matter in a neutron star may be the strongest material
in the Universe, 10 billion times stronger than steel
(Caplan, Schneider, & Horowitz, 2018). Relativistic
asteroseismology can assist in evaluating the different
models attempting to describe the neutron star interior
by providing accurate experimental data on neutron star
properties.
In this paper, we analyze how general relativity impacts
the stellar pulsations of compact objects. By understanding
when the Newtonian approximation is justified for a
given error tolerance, we can improve the computational
efficiency of theoretical asteroseismology without
decreasing accuracy. On the other hand, computational
improvements to previously published algorithms make
our results potentially more accurate than existing
results. Additionally, this research has applications to
understanding the yet unknown physics governing the
dense neutron star cores.
2. Stellar Equilibrium
The radius-dependent characteristics of compact objects
affect their stellar pulsations, so an accurate model of the
equilibrium state is required before computing stellar
pulsation eigenfrequencies and other characteristics. To
simplify calculations, a polytropic model is used in both
the Newtonian and relativistic calculations (Knapp, 2011).
A polytrope is a star where pressure (p) and density (ρ) are
continuous with respect to radius, and are related by the
equation of state:
(1)
where κ is the constant of proportionality, and n is the
polytropic index. A polytropic index between 0.5 and 1
generally models a neutron star well, while white dwarfs
are modeled with a polytropic index of 3.
2.1 – Newtonian Equilibrium
In flat spacetime, the Lane-Emden equation describes
the relationship between radius and density for polytropic
stars, derived from the equation of hydrostatic equilibrium
and the mass-continuity equation (Knapp, 2011)
(2)
where θ is defined by ρ = ρ c
θ n , ρ c
being the central density.
ξ is the dimensionless radius defined by
where G is the universal gravitation constant. The
boundary conditions for this differential equation are θ(0)
= 1 and θ′(0) = 0. For n = 0, n = 1, and n = 5, analytic
solutions are available. For any other polytropic index,
numerical integration to θ = 0 is required to analyze the
equilibrium conditions of the star. Specifically, the Lane-
Emden equation can be separated into two coupled firstorder
ODEs using:
(4) (5)
Adaptive step-size fourth-order Runge-Kutta numerical
integration is run on the system until the first step where θ
< 0. Newton’s Method is then used to locate a more precise
ξ where θ = 0. At this point, pressure and density become
0, marking the outer edge of the star (Fig. 2).
(3)
76 | 2018-2019 | Broad Street Scientific PHYSICS

are used when analyzing the stellar pulsations.
2.3 – Comparison
We compare the results of the Lane-Emden Equation
and TOV Equation for a neutron star with typical
characteristics. While the shapes of the curves are similar,
there is a noticeable difference in radius and mass (integral
of density with respect to radius) in Newtonian and
relativistic spacetime (Fig. 3).
Figure 2. θ vs. ξ for varying n. n = 0 has θ decline the
fastest, while n = 5 decreases asymptotically but
never reaches θ = 0. Neutron stars have n ≈ 1, and
white dwarfs have n ≈ 3.
2.2 – Relativistic Equilibrium
While the Newtonian model is accurate in predicting
the oscillation frequencies of main sequence stars, general
relativity is needed to accurately describe compact objects
with immense densities. The quantity σ approximates
how relativistic a star is:
(6)
The greater σ, the greater the impacts of general relativity
on both the equilibrium and stellar oscillations. For a white
dwarf star, σ ≈ 0.001, while for a neutron star, σ ≈ 0.1.
In this paper, we shall consider all stars in Schwarzschild
spacetime, where spherical symmetry is assumed and there
is no stellar rotation or magnetism involved (Hartle, 2003).
The Schwarzschild metric tensor describes the spacetime:
(7)
where e −λ(r) = 1 − 2M (r)/r. e ν relates to the mass of the star,
but cannot be analytically represented for a relativistic
polytropic star. This metric tensor is given in geometric
units (c = 1, G = 1) and in standard Schwarzschild
coordinates (t, r, θ, Φ).
A relativistic equivalent of the Lane-Emden equation,
the Tolman-Oppenheimer-Volkoff (TOV) Equation, takes
into account curved spacetime in describing polytropic
stars. It calculates P, ρ, and ν as a function of radius. The
TOV Equation can be written as three coupled first-order
ODEs (Tooper, 1964).
(8) (9) (10)
With boundary conditions M(0) = 0, ν(R) = 1 − 2M/R,
and p(0) = p 0
, we solve this system very similarly to the
Lane-Emden equation. The numerical results of the
equilibrium analysis, radius-dependent p, ρ, ν, λ, and M,
Figure 3. Comparison of solutions to Lane-Emden
Equation and TOV Equation for neutron star with
polytropic index n = 1. The TOV Equation predicts
smaller radius and mass.
The TOV Equation is used in all relativistic stellar
pulsation calculations as the equilibrium model. Relativistic
effects can be attributed both to differences in the
equations governing stellar equilibrium, and differences in
the equations governing stellar pulsations.
3. Stellar Pulsations
To analyze stellar pulsations, a perturbation is applied
and propagated through the polytropic equilibrium state.
Only under certain eigenfrequencies will the solution be
continuous throughout the star. These oscillations can
be both radial or nonradial, and each have a spherical
harmonic degree l and mode m.
Furthermore, the oscillations can be grouped into
families of modes, depending on their restoring forces. The
two most important classifications are Pressure Modes
(p-modes) and Gravity Modes (g-modes). P-modes are
high frequency modes whose deviations from equilibrium
are counteracted by pressure changes in the convective
zone. G-modes are low frequency modes, counteracted by
mass movement in the radiative zone. In this research, we
focus on p-modes, although our methods apply to g-modes
as well.
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For a specific spherical harmonic degree, spherical
harmonic mode, and mode classification, there are
multiple energy eigenmodes with ascending mode number
k. The three variables, l, m, and k, along with the mode
classification, fully describe a particular stellar pulsation.
Multiple pulsations can occur simultaneously in a star,
with resonant modes resulting from superposition (Fig. 4).
perturbation variables y 1
through y 4
representing fractional
changes in radius, pressure, gravitational potential, and
gravitational acceleration. The solutions to the system are
independent of all stellar equilibrium factors, except the
polytropic index, allowing this dimensionless analysis. The
differential equations for these variables can be written as
one matrix equation (Unno, 1989).
(13)
The 1/x term in front of the matrix causes potential
singularities in the integration, and also requires further
emphasis closer to x = 0, where the system changes faster.
To improve computational accuracy, we apply a change of
variables from x to ln(x), yielding this simpler form:
Figure 4. P-mode propagation for two harmonics.
The number of reflections is the degree. The resonant
modes result from a superposition of component
waves travelling in opposite directions (Tosaka, n.d.)
These stellar pulsations have separable time, angle, and
radius dependence, given by:
(11)
(12)
where f(t,r,θ,Φ) is a perturbation function, ω is the
frequency, P lm
(cosθ) is the associated Legendre polynomial,
and N is a normalizing factor. By calculating f l
(r), the radiusdependent
perturbation for a specific eigenfrequency, the
overall nature of the oscillations can be understood. While
all degrees from 0 to ∞ could occur, in reality only the first
few have substantial amplitude. l = 2 is the first degree
at which gravitational radiation occurs in the relativistic
model, making it the most optimal case study.
4. Newtonian Quadrupole Oscillations
4.1 – Pulsations Inside the Star
In Newtonian spacetime, a set of 4 homogeneous firstorder
differential equations describe the perturbations
of radial displacement, pressure, gravitational potential,
and gravitational acceleration. Physically, these relations
are derived by maintaining continuous variables and
appropriate boundary conditions.
The system of differential equations originally is
dimensioned, but can be made dimensionless, with
(14)
A * , U, V g
, and c 1
are dimensionless stellar equilibrium
quantities as defined in Equations 15-18 below (Unno,
1989). Although they contain ρ and p, all can be simplified
to dimensionless form using ξ and θ. A * is the Eulerian
pressure perturbation, c 1
is an inverse scaled average
density, and U and V g
are common stellar variables.
(15)
(16)
(17)
(18)
x is the dimensionless radius, ranging from 0 to 1. ω refers
to the frequency of the oscillation being tested, and is made
dimensionless by multiplying the dimensioned frequency
by . ρ c
and p c
are the central density and pressure,
respectively.
The system of differential equations has central and
surface boundary conditions, defined below. These
conditions ensure the solution is physically acceptable at
both boundaries (Unno, 1989).
(19)
(20)
The differential equations are singular at both
boundaries due to division by zero-valued variables. At
the center of the star (x = 0), ln(x) is not defined, and
at the outer surface of the star (x = 1), pressure is zero
and V g
and A * approach ∞. To handle this issue, we use
the Magnus Multiple Shooting Scheme (Townsend &
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Teitler, 2013). Two arbitrary solutions satisfying the
boundary conditions are created on both boundaries, and
integrated to x = 0.5. They are inserted into a matrix, and
the determinant is computed. Eigenfrequencies are found
when the determinant of this square matrix is 0. Adaptive
step-size fourth-order Runge-Kutta integration is used to
integrate the system, and Newton’s Method is used during
root-finding to locate where det(M) = 0 with quadratic
convergence.
4.2 – Algorithmic Roadmap
In this section, we explain the specific steps taken to
accurately compute the resonant modes of Newtonian
polytropic stars. The code used to implement this
algorithm was written in Python 3.
1. The central pressure and density of the star are
provided. The polytropic index n is given as well.
From these, fourth-order Runge-Kutta integration is
used on the Lane-Emden Equation (Eq. 2).
2. For a test frequency and spherical harmonic degree,
the perturbation variables are calculated at both
boundaries using boundary conditions (Eq. 19-20).
Two possible solutions on each end are integrated to
r = 0.5R using fourth-order Runge-Kutta integration
(Eq. 14). The equations are treated in matrix form for
improved computational efficiency.
3. Using the Magnus Multiple Shooting Scheme, the
determinant of a 4x4 square matrix of partial solutions
is calculated. Each row is a single integration
from the previous step, and all 4 solutions are used. A
determinant of 0 corresponds to an eigenfrequency.
4. Steps 2 and 3 are repeated keeping the spherical
harmonic degree constant and varying the test frequency.
Newton’s Method is used to locate where
det(M) = 0 with quadratic convergence. The derivative
required for Newton’s Method is approximated by
sampling 2 points slightly above and below the test
frequency. Newton’s Method is run until a certain
threshold accuracy is obtained.
5. Steps 2 to 5 are repeated for each spherical harmonic
degree. In this paper, results for l = 2 are shown,
although others can be calculated with this algorithm.
l = 2 is of particular importance because it accounts
for the majority of gravitational radiation in the
relativistic system.
5. Newtonian Model Results and Discussion
perturbation is the second-harmonic pressure-mode. We
refer to the fundamental or lowest frequency mode in a
family as the first-harmonic. l = 2 is chosen because it is the
lowest spherical harmonic degree for which gravitational
waves occur in the relativistic model.
Figure 5 shows the results of this calculation. The
four graphs left to right and top to bottom are radial
perturbation, pressure perturbation, gravitational potential
perturbation, and gravitational field perturbation, y 1
to y 4
in the above calculations. Radial displacement and pressure
perturbations are largest near the center of the star, and all
four perturbation variables approach zero near the surface
of the star.
Figure 5. Dimensionless Perturbations as a function
of radius for l = 2 2 nd Harmonic Pressure-Mode for n=3
Polytrope. x = 0 is center of star, x = 1 is stellar surface.
While the perturbation dynamics are interesting, the
eigenfrequency at which the pulsation occurs is generally
more important, as it can be readily observed from Earth.
The eigenfrequency for a Newtonian polytrope is solely a
function of n among the equilibrium characteristics, and is
also dependent on the spherical harmonic and particular
mode.
Prior calculations by Christensen-Dalsgaard and Mullan
have yielded the first few p-mode eigenfrequencies for l =
1, l = 2, and l = 3 to high precision (Christensen-Dalsgaard
& Mullan, 1993). We compared the results of our method,
described in Section 1.3, against these literature values.
As a sample, Table 1 below shows a comparison of our
calculations against theirs for the first 5 eigenfrequencies
of a star with polytropic index n = 3 and spherical harmonic
degree l = 2.
We can visualize the normalized perturbations of a
polytrope with index n = 3 as a function of dimensionless
radius x. Although n = 3 best represents a white dwarf,
a neutron star’s pulsations could be seen with n = 1. We
use n = 3 for ease of comparison to prior calculations
for main-sequence stars, also well approximated with n
= 3. The spherical harmonic is l = 2, and this particular
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Table 1. Dimensionless Frequencies of low harmonic
pressure-modes (l = 2) for n = 3 Polytrope
Harmonic Literature Calculated Rel. Error
Fundamental 3.90687 3.90687 1.2491x10 -7
2nd Harmonic
3rd Harmonic
4th Harmonic
5th Harmonic
5.169468 5.169469 7.6588x10 -8
6.439991 6.439990 4.5185x10 -8
7.708951 7.708951 1.8080x10 -10
8.975891 8.975891 3.1879x10 -8
With higher harmonics, the perturbation variables
have a higher spatial frequency in the interior of the star,
and have more zeroes and relative extrema. This makes
numerically simulating these scenarios more complex, and
less accurate than lower harmonics for equal number of
integration steps. With increased integration steps, our
model is sufficiently accurate even for higher harmonics.
Table 2 uses the same polytropic equilibrium as Table 1,
and the same spherical harmonic degree l = 2.
Table 2. Dimensionless Frequencies of high harmonic
pressure-modes (l = 2) for n = 3 Polytrope
Harmonic Literature Calculated Rel. Error
31st Harmonic
41.5192 41.5221 6.8743x10 -5
32nd Harmonic
42.7630 42.7664 7.8022x10 -5
33rd Harmonic
44.0065 44.0104 8.7698x10 -5
34th Harmonic
45.2497 45.2541 9.7599x10 -5
35th Harmonic
46.4927 46.4977 1.0758x10 -4
Although the error in the higher harmonics is
approximately 100 times larger in magnitude than the
error in the lower harmonics, it is still 1 part in 10,000
or less. Given the strong match for both low and high
eigenfrequencies, this code can be used to calculate
frequencies for higher harmonics than previously
reported ((Christensen-Dalsgaard & Mullan, 1993) goes
to 50 th ). However, these higher harmonics require greater
energy, and thus occur at smaller amplitudes in real
compact objects. Their study is useful for understanding
patterns in stellar pulsations, but not for experimental
asteroseismology.
6. Relativistic Quadrupole Oscillations
6.1 – Perturbation Metric
Similar to the Newtonian case, we use a polytropic model
of the equilibrium structure. A perturbation is applied, and
as a result of the motion, the geometry of spacetime around
the relativistic star is no longer described by Equation (7).
Rather, the new metric, involving the perturbation metric
h uv
, becomes
(21)
In even-parity Regge-Wheeler gauge, the perturbation
metric takes the form (Thorne & Campolattaro, 1967):
(22)
The variable μ is the dimensionless radius of the star
(ranging from 0 to 1), Y = e iωt * Y lm
is the time dependence
multiplied by the spherical harmonic of the perturbation.
H 0
, H 1
, and K are functions of r only. The Regge-Wheeler
gauge is preferred for only introducing two terms outside
the main diagonal. Substituting into Equation (21), we
obtain:
(23)
6.2 – Perturbations Inside the Compact Object
Inside the star, the perturbed fluid is described by a
displacement ξ α , where:
(24) (25)
(26)
The three fluid perturbations have separable timeand
radius-dependence, allowing for calculations done
at a specified time to represent the system with the
necessary transformations. The variables W and V are
fluid perturbation variables that must be solved for to
describe the nonradial stellar pulsations. Five variables
are dependent on radius, H 0
, H 1
, K, W, and V. The first
three relate to the initial spacetime perturbation, and W
and V describe fluid perturbations (Lindblom & Detweiler,
1983).
Einstein’s Field Equations can be applied to the
spacetime metric given in Equation (23) to give differential
equations for each perturbation variable. Using these
relations, we can eliminate one variable, creating a system
of four differential equations. Following Detweiler and
Lindblom, H 1
is eliminated instead of H 0
, to avoid possible
singularities (Lindblom & Detweiler, 1985). To simplify
the resultant equations, X is defined as a function of W,
V, and H 0
:
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(27)
The four first-order differential equations for H 1
, K, W,
and X, are (Lindblom & Detweiler, 1985):
(28)
(29)
(30)
in the interior of the star. We are mainly interested in
solutions composed only of outgoing waves, as these
represent resonant oscillation and the energy radiated
from the star. These frequencies are called Quasi-Normal
Modes (QNMs), and include the relativistic equivalent of
Newtonian p-modes.
To find these specific eigenfrequencies, we analyze
the perturbation variables outside the compact object to
determine the gravitational radiation produced. In the
exterior of the star, the fluid perturbations W, V, and X
are zero and the 2 metric perturbations H 1
and K can be
combined to obtain the single second-order differential
equation known as the Zerilli equation (N. Andersson &
Shutz, 1995).
with the effective potential V Z
given by:
(32)
(31)
Equations (28) to (31) can be expressed in matrix form
similar to Equation (14), and are handled computationally
in this manner. A major difference between the
Newtonian and relativistic calculations is that the
relativistic calculations are dimensioned while Newtonian
is dimensionless. Only 2 of the 4 linearly independent
solutions to this system are well-behaved at the center of
the star (at r = 0). The perturbed pressure must vanish at r
= R, so X(R) = 0. From these conditions, a single acceptable
solution is specified for each frequency ω.
At the central boundary, r = 0, the differential equations
are singular, as they contain multiple 1/r terms that tend
the function to infinity. Since the numerical integration
cannot be started at r = 0, a power-series approximation
is used to determine an appropriate starting condition
slightly away from the center, following the procedure
described in (Lindblom & Detweiler, 1983) and (Lindblom
& Detweiler, 1985).
The power series approximations are used to r = 0.01R.
Then, the differential equations are integrated using
fourth-order Runge-Kutta integration to r = 0.5R. There
are two linearly independent solutions, labelled Y 1
and Y 2
.
Similarly, the three solutions from the exterior of the star
are iterated to the midpoint of the interval, giving Y 3
, Y 4
,
and Y 5
. A linear combination of these five solutions exists
that makes each variable H 1
, K, W, and X continuous at the
midpoint. With five solutions for four variables, there is
an extra degree of freedom. This additional degree allows
for free-scaling of the solution.
6.3 – Perturbations Outside the Compact Object
Given any spherical harmonic degree and frequency,
we can find the unique solution for the radial dependent
variables H 1
, K, W, and X that define the perturbations
The tortoise coordinate r * is defined by:
(33)
(34)
The Zerilli equation is notable because it provides
a Schrödinger-type equation for even-parity Regge-
Wheeler perturbations of Schwarzschild geometry. This
presents simplifications to the analysis of wave equations
(Fackerell, 1971). The Zerilli function is defined in terms
of the perturbations H 0
(r) and K(r)
(35)
where the functions a(r), b(r), g(r), h(r), and k(r) are
functions of the frequency, spherical harmonic degree, and
mass and radius of the compact object, given in (Lindblom
& Detweiler, 1983). We recover H 0
with the following
equation, similar to the relation defined between V and X
in Equation (27).
(36)
Using Equation (35), we obtain initial conditions for Z (r * )
and dZ (r * ) /dr * . For a given (r * , Z) coordinate, Equation
(32) can be used to calculate d 2 Z/dr *2
, and in this manner
we propagate Z through r * . In practice, we integrate Z from
r * = R * to r * = 25ω −1 (Lindblom & Detweiler, 1983). Far
away from the star, the Zerilli function can be expressed as
a combination of 2 components, namely the ingoing and
outgoing contributions. These individual solutions may be
asymptotically expressed as power series.
(37) (38)
The solution Z − represents purely outgoing gravitational
radiation, while Z + represents purely ingoing waves. The
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constants a j
and the complex conjugates ā j
are recursively
defined in (Chandrasekhar & Detweiler, 1975). A solution
to the Zerilli equation will be given by a constant linear
combination of Z + and Z − .
(39)
For Quasi-Normal Modes, all the gravitational radiation
is outgoing, so the particular solution Z should be a multiple
of Z − , with no parts Z + . At r = 25ω −1 , the Zerilli equation
numerically integrated is matched onto the asymptotic
series, with j max
= 2. We determine values of constants
β(ω) and γ(ω), and use Newton’s method to search for ω
such that γ(ω) = 0. The eigenfrequencies found are those
of quasinormal modes, a subset of which correspond to the
Newtonian Pressure-Modes.
(40)
We compare the difference in frequencies of these
corresponding modes Equation (40) against the relativity
parameter σ defined in Equation (6) to understand the
effects of general relativity on pulsation frequencies of
compact objects, the ultimate goal of this research.
6.4 – Algorithmic Roadmap
A similar approach is taken here compared to the
Newtonian model (See Section 4.2). However, there are
some key differences in the implementation. Instead
of using the Lane-Emden Equation, the Tolman-
Oppenheimer Equation is used (Eq. 8-10). After
integrating the Equations (28)-(31) in the interior of the
star, the Zerilli function and its derivatives are computed
at r = R (Eq. 32-36). Runge-Kutta integration is used to
iterate the Zerilli function far from the star where it is
matched onto the asymptotic power series expansions and
the coefficients β(ω) and γ(ω) are calculated (Eq. 39). γ(ω)
replaces det(M) in the Newtonian model, and we proceed
as before locating eigenfrequencies for various spherical
harmonics.
7. Relativistic Model Results and Discussion
We calculate the normalized perturbations of a
polytrope with n = 3 as a function of dimensionless radius
r. Although n = 1 is most optimal for a neutron star, we
use n = 3 initially to best compare to the Newtonian model.
The spherical harmonic degree is l = 2, and this particular
perturbation is the second harmonic pressure mode.
Figure 6 shows the results of this calculation. The four
graphs left to right and top to bottom are perturbation
variables X, W, K, and X 0
. Recall K and X 0
represent metric
perturbations (Eq. 23). The shape of these curves closely
match the shapes of y 3
and y 4
in the Newtonian section
(Fig. 5). X and W are different variables than y 1
and y 2
,
explaining the differences in the shapes of the top two
panels between Figure 5 and 6.
Figure 6. Perturbation variables calculated for
a specific pulsation, with corresponding Zerilli
variable integrated outside the compact object using
the Zerilli equation.
These results show strong qualitative similarities to
our previous Newtonian results, indicating the relativistic
model is successful in predicting the general behavior of
the interior perturbation variables. The single discernible
frequency and sinusoidal shape of the Zerilli function
indicate these methods can locate quasinormal modes
fairly accurately. Further research is ongoing to search
for exact quasinormal eigenfrequencies. Until then, we
cannot numerically comapre quantitative results between
the Newtonian and relativistic models. Nonetheless,
our model successfully replicates the Newtonian model
behavior within curved spacetime as well.
8. Acknowledgments
I would like to thank Mr. Reece Boston (UNC-Chapel
Hill), Dr. Charles Evans (UNC-Chapel Hill), and Dr.
Jonathan Bennett (NCSSM) for their continued support
and guidance throughout this research project.
9. References
Bowman, D. M., Buysschaert, B., Neiner, C., P ́apics, P.
I., Oksala, M. E., & Aerts, C. (2018). K2 space photometry
reveals rotational modulation and stellar pulsations in
chemically peculiar a and b stars. A&A, 616, A77. Retrieved
from https://doi.org/10.1051/0004-6361/201833037 doi:
10.1051/0004-6361/201833037
Caplan, M. E., Schneider, A. S., & Horowitz, C. J.
(2018, Sep). Elasticity of nuclear pasta. Phys. Rev. Lett.,
121, 132701. Retrieved from https://link.aps.org/
doi/10.1103/PhysRevLett.121.132701 doi: 10.1103/
PhysRevLett.121.132701
Chandrasekhar, S., & Detweiler, S. (1975). The quasinormal
modes of the schwarzschild black hole. The Royal
Society.
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Christensen-Dalsgaard, J., & Mullan, D. J. (1993). Accurate
frequencies of polytropic models. Royal Astronomical
Society.
Fackerell, E. D. (1971). Solutions of zerilli’s equation for
even-parity gravitational perturbations. The Astrophysical
Journal.
Hartle, J. B. (2003). Gravity: An introduction to einstein’s
general relativity (1st ed.). San Francisco: Addison-Wesley.
Knapp, J. (2011). Polytropes.
Lindblom, L., & Detweiler, S. L. (1983). The quadrupole
oscillations of neutron stars. The Astrophysical Journal.
Lindblom, L., & Detweiler, S. L. (1985). On the nonradial
pulsations of general relativistic stellar models. The
Astrophysical Journal.
N. Andersson, K. D. K., & Shutz, B. F. (1995). A new
numerical approach to the oscillation modes of relativistic
stars.
Thorne, K. S., & Campolattaro, A. (1967, Sep). Nonradial
pulsation of general-relativistic stellar models. i.
analytic analysis for l ≥ 2. The Astrophysical Journal,
149, 591. Retrieved from http://adsabs.harvard.edu/
abs/1967ApJ...149..591T doi: 10.1086/149288
Tooper, R. F. (1964). General relativistic polytropic fluid
spheres. The Astrophysical Journal, 140(434). Tosaka, W.
C. C.-B.-S.-. G. (n.d.).
Townsend, R., & Teitler, S. (2013). Gyre: An open-source
stellar oscillation code based on a new magnus multiple
shooting scheme.
Unno, W. (1989). Nonradial oscillations of stars (2nd ed.).
Tokyo: University of Tokyo Press.
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EFFECT OF ELLIPTIC FLOW FLUCTUATIONS ON THE
TWO- AND FOUR-PARTICLE AZIMUTHAL CUMULANT
Brian Lin
Abstract
We incorporate finite elliptic flow fluctuations for the 2-particle and 4-particle azimuthal cumulants. Starting from
expressions that include transverse momentum conservation, we consider three potential v 2
distributions: a Gaussian
distribution, a Bessel-Gaussian distribution, and a power law distribution. For the Bessel-Gaussian distribution, we find
the results are sensitive to the size of fluctuations, and c 2
{4} values at large multiplicity range from 0 to significantly
negative. Therefore, the 4-particle cumulant c 2
{4} with transverse momentum conservation can be used to study elliptic
flow fluctuations in both small and large systems.
1. Introduction
In the Pb+Pb and p+Pb collisions in heavy ion colliders,
evidence indicates a nearly perfect fluid is produced in this
system of quarks and gluons. The collective flow phenomenon
that arises from these collisions is predicted very well by
the use of hydrodynamics. Caused by the collision’s initial
geometric anisotropies, we observe azimuthal anistropy in
the produced particles, which is the clearest indicator of the
collective flow phenomenon (Nagle and Zajc, 2018).
The study of relativistic heavy ion collisions originates
from the desire to learn more about the basic origins of matter
and, in particular, a new form of QCD matter: the Quark-
Gluon Plasma (QGP). Understanding of the QGP will reveal
fundamental properties of matter in high-temperature and
high-density systems, such as systems existing in the core of
neutron stars and theorized to have existed in the early stages
of the Big Bang (Jacak and Steinberg, 2010).
Elliptic flow is an essential observable that can reveal
the equation of state of the QGP among other important
characteristics of dense matter, so accurate measurement of
elliptic flow has impactful theoretical implications (Snellings,
2011). However, momentum conservation and jet quenching
add non-flow effects to measurements of elliptic flow, so our
measured elliptic flow values contain non-flow effects. Thus,
the field of relativistic heavy ion collisions utilizes cumulants,
which suppress the effects of non-flow factors and emphasize
the true effects of collective flow. Elliptic flow reflects the
initial geometric anisotropies of the overlapping nuclei. Even
at the same centrality, the elliptic flow for each event differs
due to fluctuations. Therefore, we need to consider effects
of fluctuation on multi-particle cumulants (Bilandzic et al.,
2011).
The clearest way to remove non-flow effects from elliptic
flow coefficients is to analyze the azimuthal cumulants
associated with the collisions. However, even these azimuthal
anisotropies differ as the overlap between the two nuclei
varies. Thus, the measured elliptic flow coefficient is expected
to follow a probability distribution. This paper calculates the
effect of elliptic flow distributions on two-particle and fourparticle
cumulants, which have been calculated assuming
global transverse momentum conservation.
We calculate new expressions for c 2
{2} and c 2
{4} by
incorporating three predicted distributions of elliptic flow
that originate from geometric anisotropies between events.
We primarily analyze the the effect of the distribution
characteristics on the values of the azimuthal cumulants.
2. Methods
The two- and four-particle azimuthal cumulants are
functions of elliptic flow, v 2
, so we determine new expressions
for c 2
{k} by incorporating the v 2
fluctuations as probability
density distributions, P(v 2
). The single-event average 2-particle
and 4-particle azimuthal correlations are defined as follows,
where the brackets represent averaging over all particles in
the event:
The average 2-particle and 4-particle azimuthal correlations
over many events may be written as follows, where we
denote two averages, first over all particles in an event and
then over all events:
The single-event average 2-particle and 4-particle
azimuthal cumulants are defined as:
Due to fluctuations in the average azimuthal cumulants
between events, we calculate the event-averaged 2-particle
and 4-particle cumulant values, denoted and
respectively, by incorporating a probability distribution
on v 2
as follows:
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3. Results
3.1 – Gaussian Formulas
We begin by incorporating a Gaussian distribution of
v 2
, as follows:
We now introduce the formulas derived earlier
(Bzdak and Ma, 2018) using the assumption of transverse
momentum conservation (TMC). This assumption has a
key contribution for small systems because the last particle’s
momentum is restricted. The effect of TMC diminishes as
the number of particles, N, increases because the effect of
one particle’s momentum also decreases with N.
2.1 – TMC Formulas
For the Gaussian distribution, we have:
3.2 – Bessel-Gaussian Formulas
The Bessel-Gaussian distribution that we give v 2
is
defined as:
where I n
(x) denotes the Bessel function of the n-th kind.
For the Bessel-Gaussian distribution, we have:
The original formulas (Bzdak and Ma, 2018) contained
the variable v 2
(p), which we denote for brevity v 2
. In
both instances, this represents the elliptic flow value at a
specific momentum p. We see the 2-particle and 4-particle
cumulant as a function of other variables such as transverse
momentum p, number of produced particles N, and the
expected value of the square of transverse momentum
over the full phase space . We define
3.3 – Power Law Formulas
We continue by incorporating the power law
distribution of v 2
, given as:
For the Power-Law distribution, we have:
2.2 – General Distribution
We denote
We plot the three distributions under the condition that
= 0.05.
When we incorporate the probability distribution P(v 2
)
we integrate in terms of v 2
. Thus, for a general distribution,
we may express
Figure 1. Plotted above are sample probability
distributions where = 0.05.
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The probability distributions are plotted so that the
expected value of elliptic flow remains 0.05. We define w =
for the Bessel-Gaussian distribution. When w = 0,
the Bessel-Gaussian distribution reduces to the Gaussian
distribution. We see the Gaussian, Bessel-Gaussian with w
= 0, and Power Law curves are all very similar, while the
Bessel-Gaussian curve with w = 2 differs from the other
three curves.
3.4 – An Example of Numerical Comparisons
Our graphs take a reasonable value for as 0.05.
Additionally, we assume = 0.025 and = 0.25
(GeV/c) 2 . This allows us to solve for the unknown σ in the
Gaussian distribution, σ and in the Bessel-Gaussian
distribution, and α in the Power Law distribution. The
Gaussian σ value turns out to be around 0.0564, while α
≈ 313.
For this section, we tune the Bessel-Gaussian mean
and width to that of the Gaussian (i.e. we control both
and ). Our solutions are ( , σ) = (0, 5.64 × 10 −2 )
when we equate the variances of the Bessel-Gaussian and
Gaussian distributions, and ( , σ) = (1.57 × 10 −2 , 5.42 ×
10 −2 ) when we equate the variances of the Bessel-Gaussian
and Power Law distributions.
The Gaussian and Bessel-Gaussian with w=0
distributions are identical, and the power law distribution
is very similar to them. Thus, these three distributions
result in an upward shift of the 2-particle cumulant.
Because of the similarity between all three distibutions, all
three lead to essentially the same 2-particle cumulant (fig.
2).
The event-averaged 4-particle cumulant approaches
for large N. Specifically for the
Gaussian distribution, from section 3.1, the Gaussian
approaches 0 regardless of σ. Because we set the
variance of the Bessel-Gaussian distribution equal to
that of the Gaussian distribution, and is similar to that
of the power law distribution, the behaviors of all three
distributions are very similar. More general features of the
Bessel-Gaussian will be shown in section 3.5.
Figure 2. The event-averaged 2-particle cumulant
(top panel) and 4-particle cumulant
(bottom panel) for all three distributions (Gaussian,
Bessel-Gaussian, and Power Law distributions)
plotted as a function of event multiplicity N. The
results obtained without elliptic flow fluctuations
are shown in comparison in black. Additionally,
experimental results obtained from the ATLAS
collider are shown in green.
3.5 – Effects of Relative Fluctuation Size
The Bessel-Gaussian probability distribution, defined
in Section 3.2, may be rewritten in terms of two instead
of three variables. Denoting u = /σ and w = /σ, we
may rewrite the Bessel-Gaussian distribution in terms of
u and w as:
We define the relative fluctuation of v 2
as:
We can show that r(v 2
) = r(u) is a function of w only, and
so to manipulate the Bessel-Gaussian distribution, we only
need to manipulate w. Specifically, when w = 0, the relative
fluctuation of v 2
reaches a maximum of .
In the large event multiplicity limit, the 4-particle
Bessel-Gaussian cumulant is given by:
while the cumulant neglecting elliptic flow fluctuation is
86 | 2018-2019 | Broad Street Scientific PHYSICS

. Both these values depend on two parameters:
and σ. However, their ratio, which approaches
, is dependent only on w. The ratio of
these two values is shown as the dashed curve, and the
relative fluctuation of v 2
is shown as the solid curve (fig. 3).
When we equate the variance of the Bessel-Gaussian
distribution to that of the Gaussian distribution, we
obtain w = 0, and the maximum relative fluctuation (fig.
3). The corresponding large-N limit of for w = 0
is 0. On the other hand, for large w, relative fluctuations
are small (fig. 3). In that limit, the Bessel-Gaussian eventaveraged
4-particle cumulant will approach the results
obtained through TMC that neglected v 2
fluctuation, i.e.
at large N, and so the relative
fluctuation for small w approaches 1.
Because both curves (fig. 3) are solely functions of w,
the ratio
at large N may be expressed as a
function of the v 2
relative fluctuation only. The 4-particle
cumulant ratio against r(v 2
) is shown as the dashed curve
in Figure 4. As the relative fluctuation increases, we see
the ratio decrease from 1 to 0, i.e. the goes from
significantly negative to 0 for large N.
For the 2-particle cumulant, we observe its large event
multiplicity limit to be . Additionally, the 2-particle
cumulant neglecting elliptic flow fluctuation approaches
, so at large N, the ratio between the two may be
written as
Figure 4. The ratio between Bessel-Gaussian and
non-fluctuation cumulants at large N for both c 2
{2}
and c 2
{4}.
Therefore, we see as the relative fluctuation increases,
the ratio increases from 1 to 4/π.
To visualize our results, we plot in Figure 5 the Bessel-
Gaussian 2-particle and 4-particle cumulants for varying
relative fluctuations of v 2
under the condition that
= 0.05. These relative fluctuations were chosen so that
r(v 2
) = 0.523, 0.466, 0.319, and 0 correspond with w values
of 0, 1, 2, and ∞ respectively.
Figure 3. Relative fluctuation of v 2
for the Bessel-
Gaussian distribution (solid) and the ratio between
the large-N limits of the Bessel-Gaussian and nonfluctuation
cumulants (dashed) as functions of w.
Figure 5. The event-averaged (first) and
(second) for the Bessel-Gaussian distribution
as a function of event multiplicity N. Results with
various amounts of relative fluctuations of v 2
are
shown. Again, ATLAS results for the 4-particle
cumulant are shown in green.
PHYSICS
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4. Conclusions
When elliptic flow fluctuations are included in the
calculations of two and four-particle azimuthal cumulants,
there is a definite shift in the cumulant. For the two-particle
cumulant, there is an increase for the Gaussian, Bessel-
Gaussian, and power law distributions of v 2
fluctuations.
Meanwhile, for the four-particle cumulant, we observe a
large positive shift so that its value is close to 0 for large
event multiplicity when we incorporate Gaussian or
Power Law elliptic flow distributions. The Bessel-Gaussian
distribution allows for variation of the relative fluctuation
of v 2
. When the relative fluctuation is small, the 4-particle
cumulant tends towards a significantly negative value at
large event multiplicity, approaching results obtained
previously without including v 2
fluctuations. When the
relative fluctuation is large, the cumulant goes to zero
at large event multiplicity, approaching results from
the Gaussian and power law elliptic flow distributions.
Therefore, the c 2
{4} observable may be used to probe the
fluctuation of elliptic flow in both small and large systems.
5. Acknowledgements
Firstly, we would like to acknowledge Dr. G.L. Ma of
Fudan University for his patient, insightful mentorship.
We would like to gratefully thank Dr. Z.W. Lin for
valuable discussions and feedback. We also acknowledge
Dr. J. Bennett for engaging in weekly discussions and
offering advice as well as the NCSSM Foundation for
providing the necessary support and resources to carry out
his research.
6. References
Nagle, J. L., & Zajc, W. A. (2018). Small System Collectivity
in Relativistic Hadronic and Nuclear Collisions. Annual
Review of Nuclear and Particle Science, 68 (1), 211-235.
Snellings, R. (2011). Elliptic flow: A brief review. New Journal
of Physics, 13(5), 055008.
Jacak, B., & Steinberg, P. (2010). Creating the perfect liquid
in heavy-ion collisions. Physics Today, 63(5), 39-43.
Bzdak, A., & Ma, G. (2018). A remark on the sign change
of the four-particle azimuthal cumulant in small systems.
Physics Letters B, 781, 117-121.
Bilandzic, A., Snellings, R., & Voloshin, S. (2011). Flow
analysis with cumulants: Direct calculations. Physical Review
C, 83(4).
88 | 2018-2019 | Broad Street Scientific PHYSICS

AN INTERVIEW WITH DR. VALERIE ASHBY
From left, Navami Jain, BSS Editor-In-Chief; Emily Wang, BSS Editor-In-Chief; Dr. Jonathan Bennett, BSS Faculty
Advisor; Dr. Valerie Ashby, Dean of Trinity College of Arts & Sciences at Duke University; Kathleen Hablutzel, Publication
Editor-In-Chief; and Jackson Meade, BSS Essay Contest Winner
What drew you to chemistry?
That’s an easy answer. My dad was a math and science
teacher; he taught chemistry and various versions of math
in high school… so science was never scary to me. It just
seemed like what we did… The second thing is I had a great
high school chemistry teacher. I actually did something I
don’t recommend to my own Duke students, which is to
decide what you’re going to major in before you arrive.
Leaving high school, I said that I’m going to be a chemistry
major and I’m not going to change my major, because I had
heard these stories about how college students hit their
first hard course or their second hard course and they shift
their major. I decided I was not going to do that. The good
news was that I loved it, even at the college level… that’s
how I decided I was going to major in chemistry. Science
was always my thing.
So you’re in more of an administrative position now. Do
you ever wish you could go back to the lab?
Oh, you mean every 30 seconds? I wish for you that every
job you have is your favorite job. And I have led this crazy,
lovely life where every single job that I have held has been
my favorite job at that moment. When I was a faculty
member, it was my favorite job. Who I am and what I do
have overlapped my entire life. That’s a gift that I get to
be who I am in my job. I am a teacher, that's who I am.
Even though I’m out of the classroom, that’s still who I am.
The way that it presents itself now is through inspiring
other teachers, encouraging other faculty, and mentoring
students...I have office hours with students every Friday
even though I’m not teaching. They come and talk to me
about their lives and I get to do the thing that I love…
I also miss running my old research group. I kept my
research group at UNC when I took this job… I graduated
my last PhD students from UNC Chapel Hill last year.
For the first time in twenty years I haven’t had my own
research group. I’m so busy that I don’t have time, but
I miss training graduate students and I miss creating
knowledge. There’s something about waking up every
day trying to do something that nobody else has ever done
and answering a question that remains open, and then
teaching other people how to do that… it is so much fun.
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We were wondering how the scientific and problemsolving
skills you’ve gained as a chemist have translated
into other roles such as your current role?
It was absolutely great training. When you do scientific
research, it is team-based with vertically integrated teams;
so a professor, a postdoc, graduate students, undergrad
students, and then high school students who come in the
summer or during the academic year. That team-based
approach and learning how to work with every level of
that team are great training for what I do here.
I have an administrative team and it’s a vertically integrated
team… When you run a research group, you’re not just
doing science, you’re doing people - people who spend a
lot of time together in close proximity. Teaching graduate
students how to navigate being in a group that has a
personality and a culture… I had to manage all the finances
of the group, so I learned how to do big budgets for grants.
You learn how to write, you learn how to communicate
- so many different parts of running a research team. It’s
like a small business if you're doing science... So what
do I do in my present job? I run the finances - they’re
my responsibility. Human resources, the well-being of
students, faculty, and staff, making sure that we’re being
collaborative and collegial - all my responsibility. It’s
absolutely great training and I think I use all of that now.
My day-to-day life is really all of those skills that you learn
about being in a team and managing people.
And my job is to raise money. If you’re going to do science,
you better know how to raise money. You may know
who Joe DeSimone is - I was his first PhD student so we
have known each other for a very long time and one of
my favorite Joe quotes is “Val, a vision without funding
is just a hallucination.” And as a scientist, if that’s not
your mindset, you can’t actually do your science. This
enterprise doesn’t run without funding, so being a little bit
entrepreneurial is important... for this job.
While at UNC you worked with an NSF grant to
increase the number of underrepresented minority
students who receive doctoral degrees in STEM fields.
What were some of your more effective policies and
what challenges have you personally faced as a minority
woman in STEM?
Quite frankly, I never paid any attention to being a woman
or being underrepresented. Now, that’s a luxury. People
treated me so well it was never my experience. Now when
I advocate for women and underrepresented people I have
to say to them “I haven’t had a bad experience. My goal
is for you not to. And if you have, my goal is to help you
with it.” My PhD advisor was incredible - some people
have trouble with that. The reason I want to help so many
people is because I have had such a wonderful experience.
I always say to people if somebody tried to offend me at
some point or did something, I just didn’t take it in… it just
never affected me. So that’s my history with that.
I loved working in that program and it had a model that
worked already and my job was to not break it and to
try to expand it. It’s a cohort model of students and it’s
everything from making sure students are onboarded into
their departments. It’s very isolating to be a grad student.
Especially if you are an underrepresented student, you
could be the only one in the program. If you’re not in a
group that welcomes you and has a great culture, it can feel
even more isolating. We were the place where students
could come when they hit roadblocks...Sometimes we
were the place that would support them in going to talk
about their research... we would pay for travel for them
to go to conferences... we would help them engage with
faculty and collaborators... So many different ways. It
was quite successful and we were able to expand it into
the humanities, because all grad students need support for
different reasons.
What do you think is the future for women in STEM,
and what can we do to make sure that the STEM fields
are inclusive for all people?
That’s a great question. When you look at the number of
women faculty that we have in each one of our disciplines,
we are not very different from most universities... we have
more women who are humanists than social scientists
and scientists. I think 23-27% of our science faculty are
women. 50% of the graduate students are women... but
the numbers just don’t translate into the faculty for several
reasons... so we have a lot of work to do here for women
in science. Part of that is making sure that we have a
culture that is welcoming, but also that we are thinking
about how families and having children affects women
and men differently. It’s serious when you’re a scientist
because you have to be in the lab, right? There are several
family-friendly things that we can do… but making sure
that people have the mentorship that they need is really
important… [and] making sure the climate is such that we
are equally supportive of every single person. That’s not
trivial to pull off.
What can you do [referring to Navami, Emily, and
Kathleen]? Stay in. Don’t quit. If you love it, stay in. Even
if it gets hard just stay in there. Find some great mentors…
I have four mentors that I’ve had for more than twenty
years, including my PhD advisor. They keep me going.
When it got hard, I wanted to quit. And they kept me
going. Get good mentors. What can you do [referring to
Jackson]? What you do is more important than what they
do. All of my mentors are men. That actually is just what
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happened in my life. I’m not saying it’s a good or bad thing.
But you being equally as supportive is important… I’ve got
four of them [mentors] and they’ve been incredible. They
were just the right people for me…
If you love it, don’t let anything keep you from doing it.
Your part is to find what you love and don't give anybody
the power to take you out of doing what you are supposed
to be doing.
What advice do you have in general for STEM majors?
Get some sleep is what I tell my Duke students. Just relax.
It’s okay. It can be pretty intense. Have some fun. I’m
serious about that. I think the reason I love what I was
doing and what I have always done is because I have a
balanced life. The sooner you start taking care of your
whole self and form that habit, the better.
The problem with being an independent scientist is that
you’re independent, which is the same problem I have
with this job… nobody’s telling me when to come to work
every day and nobody’s telling me when to go home. The
problem is that if you are a crazy workaholic, you can do
this 24/7. As an independent scientist, you are actually
working for yourself because you’re running your own
small business. When do you not work because everything
you're doing is for you and your group? Start practicing
now being more balanced. The other recommendation I
would have, at least my experience with STEM majors, is
to make sure you really get a great liberal arts education.
You’re going to be smart enough; that’s not the question.
This navigating across culture, ethics, language… that’s
actually going to make you a more creative scientist. You
never know where you’re going to land in this world,
right? You might be doing your science on the other side of
the world. You need to feel an appreciation for differences
in culture and religion. Get a great liberal arts education
with depth in your science and I think it sets you up in a
beautiful way.
Can you tell us about a time that you failed and what
you’ve learned from that experience?
When I failed? Sure - you want to talk about last week or
yesterday or 20 minutes ago? [laughs]
So in graduate school at UNC, you can get a high pass, you
can get a pass, you can get a low pass. That’s the grading
scale. So I took a mechanistic organic chemistry class and
I got an L. And what that means is that if you’re in a PhD
program you get bumped out of the PhD program down
to the Master's program. Let me give some context to you.
We don’t admit Master's students typically into chemistry.
Because you can go from a B.A. or B.S. to a PhD and almost
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nobody gets a Master’s degree intentionally and stops.
So I got bumped down to the Master's and had to earn
my way back into the PhD program, meaning that I had
to pass. So having a good mentor is a good thing, because
right there I would have been gone and everything after
that would not have been possible had my PhD advisor
not said, “Val this is not a big deal. You weren’t prepared
because you didn’t know you were going to graduate
school.” And watching somebody else not flinch is really
good. He was so supportive. He said “This is not a problem.
We’re going to do what we need to do here. We’re gonna
pretend like this didn’t happen and we’re gonna keep you
moving as if you’re on the PhD track.” So I took my PhD
comps.
And I did all of the hourly exams - we took them on
Saturdays; you have to pass a certain number before you
qualify to take the actual oral exam. And then after I took
my comps I had to request in a letter to be readmitted. And
I did and there I was. And it was as if it didn’t happen…
Thank goodness for mentorship, because when your head
is not in the right place, your mentor can keep your feet
moving until your head catches back up…
The beauty for me of that failure is that when a student
comes in here and they have had an academic failure they
don’t think I’ve had one, right? Because they think you
can’t really do the Dean stuff, can you? What I get to say to
them is, it turns out, you can. You’re fine. You can recover.
And then I tell them my story.
I mentor students who think that their first failure is the
end of the road. Turns out you can get a C in physics and
still be the Dean. Perfection is not required.
For sports, Duke or UNC?
Oh - so I’m glad you asked me this. So Duke. I have to tell
you my story - this is so fun. So I hated Duke because I had
two UNC degrees and not only that I had an undergraduate
degree and when you have an undergraduate degree
from UNC the hate is deep. It’s like genetic. I was such a
Duke hater that I would root for anybody playing Duke
because I just wanted Duke to lose and badly, with shame.
[laughs] So when one of my mentors suggested that I
interview for this job, I said to him, “How am I going to
be able to do this?” And he said, “Val, get over yourself.”
And he is a UNC alum and he said this is a great job and
it’s a great place and you’re going to love the people,
you’re going to love the students. And all of that stuff
is going to go away the moment you show up and meet
people. And in my first interview, I walked out and I said
if they offer me this job I’m taking it. And I just found
my people sitting right there at the table and it was just
stunning to me… It’s a serious lesson for me on diversity.
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It’s easy to not like people from a distance. The moment
I know you, the game is over. Everything I told myself
about you is no longer true. You just become another
person, and that’s what I found. I sat at that table and I
thought “I love these students.” I love the ideals and
the values and I’m like, “These are my people.” I love
this place. I’m all in Duke. I’m fiercely competitive in
sports and I love great coaching. Duke 100%. On the
weekends, I’m in full Duke gear. It drives my friends
insane. [laughs] But it was surprisingly easy. The people
made all the difference and I love this place. I really do.
So this isn’t a newfound hatred for UNC, it’s a newfound
understanding?
It’s a newfound understanding and I never thought you
could love both of those places. I so appreciate what UNC
has done for me. I love how UNC grew me and supported
me and got me here. And I love that these guys have
accepted me but I also love what we do here - it’s pretty
doggone special and those students are incredible. I get to
love both.
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