Annual Report 2008.pdf - SAMSI

Jason Wilson (Duke) is involved in the interface working group. Jason Wilson is a graduate
student at Duke working toward his Ph.D. He was supported by SAMSI for the fall semester,
2007. He took the course in the fall on free boundaries and moving interfaces. He has attended
the Working Group and expects to give a talk in April. His thesis focuses on the construction of
overlapping coordinate grids with low distortion on a given, smooth, closed surface in three
dimensions. By “low distortion” we mean the metric tensor should be not far from the identity.
The surface could be given implicitly. His work will have application to boundary integral
methods and perhaps other methods where detailed information needs to be computed on the
surface. Generally methods for interfaces in two dimensions have matured, and methods in three
dimensions are developing rapidly; Wilson’s work could have use in this context. It was helpful
and inspiring for Jason to learn about the work of Shing-Yu Leung and Hongkai Zhao on their
recent method for moving an interface. Wilson’s work has some similarities, but he uses a more
detailed representation of the surface which may be of advantage depending on the application.
Martin Heller (NCSU) Over the last year I have worked on two projects in association with the
SAMSI stochastic partial differential equations group (SPDE). The first entails classification of
a random surfaces based on the random pattern. The second is investigation of limits for
interacting particle systems. Over the Spring 2008 semester, presentations were given for each
of these projects.
The motivation for the project to classify regions of a random surface comes from steel
fabrication. When a sheet of steel is fabricated, it is often far from perfect. In flawed regions,
the molecular arrangement may differ from the ideal steel regions. The molecular patterns of the
steel appear to have very little structure and a homogenous appearance similar to noise. After
viewing the random pattern present in the flawed steel, and the pattern present in the good steel,
it becomes apparent that these regions have a different random pattern. The flawed steel appears
to have a more heterogeneous mixing pattern than the good portions have. Leveraging this
insight, we have been focusing on discriminating between the two regions based on local
covariance statistics then classifying based on classification trees. Of particular interest in the
study are the vector autoregressive statistics and generalizations of Ising models.
The second project associated with the SAMSI SPDE group is in simulations of some
interacting particle systems. To begin with I simulated the Totally Asymmetric k-Exclusion
Process (TAKEP). The dual of the results of the simulations were then used to test the
theoretical upper and lower bounds in hopes of finding more precise bounds for the process.
Presentations outside SAMSI:
Joint Statistical Meetings in August 2008, “Molecular Patterns in Steel”
Relationship to Ph.D. Dissertation:
I am currently working on a rough draft of my work with Ito on the analysis of steel data, which
may be a part of my dissertation.
3. Environmental Sensor Networks
David Bell (Duke University) is the SAMSI Graduate Fellow associated with the Sensor
Network Dataset working group (Spring 2008) and also the Environmental Risk working group
(Fall 2007). He has been active in attending meetings as well as acquisition and exploration of
data. He has also been involved in modeling soil moisture data from a local wireless sensor
network in Duke Forest with James Clark, Paul Flikkema, Alan Gelfand, Yongku Kim, and