RECENT DEVELOPMENT IN COMPUTATIONAL SCIENCE

RECENT DEVELOPMENT 

IN COMPUTATIONAL SCIENCE 

Selected Papers 

from International Symposium 

on Computational Science 

International Symposium on Computational Science 

Kanazawa University, Japan 

February 2011 

Editors 

Rukman Hertadi 

Shinichi Miura 

Rinovia Simanjuntak 

Karel Svadlenka 

Volume 2

International Symposium on Computational Science 2011 

21-23 February 2011, Kanazawa University, Japan 

ISCS 2011 Organizing Committee 

M. A. Martoprawiro, S. Miura, H. Nagao, K. Nishikawa, S. Omata, M. Saito, R. Simanjuntak, 

Suprijadi, K. Svadlenka 

International Advisory Board 

E. T. Baskoro, M. A. Martoprawiro, S. Miura, H. Nagao, S. Omata, M. Saito, Suprijadi, 

K. Svadlenka 

Volume Editors 

� Rukman Hertadi 

_____________________________________________________ 

Faculty of Mathematics and Natural Sciences, Bandung Institute of Technology, Indonesia 

� Shinichi Miura 

Institute of Science and Engineering, Kanazawa University, Japan 

� Rinovia Simanjuntak 


� Karel Svadlenka (contact person) 

Institute of Science and Engineering, Kanazawa University, Japan 

E-mail: kareru@staff.kanazawa-u.ac.jp 

ISSN 2223-0785 

Published by Kanazawa e-Publishing Co., Ltd 

© Organizing Committee of ISCS 2011 

Printed in Japan 

Typesetting: Camera-ready by author. 

Printed on acid-free paper.

Group Photo February 17, 2011 �

Preface 

The Fourth International Symposium on Computational Science (ISCS 2011) was held in Kanazawa, 

Japan, February 15-17 and continued and extended the traditions of previous conferences in the series: 

ISCS 2007 in Bandung, West Java, Indonesia; ISCS 2008 in Kanazawa, Japan; and ISCS 2009 in Sanur, 

Bali, Indonesia. 

The tradition of ISCS springs from the fact that it was born from the cooperation between Bandung 

Institute of Technology, Indonesia, and Kanazawa University, Japan, on the enhancement of graduate 

students’ education in the field of computational science and numerical mathematics. The aim of the 

symposium is to provide an occasion to present and exchange results and ideas related to these research 

fields not only for young researchers worldwide but also for senior professors and scientists. 

This year’s symposium was successful in the sense that more than 40 participants from 6 countries 

including several researchers from Bandung Institute of Technology and Kanazawa University joined the 

program. Moreover, 10 students participating in the Double-degree program between Kanazawa University 

and Bandung Institute of Technology also had a short talk and poster presentation about their research. 

Topic areas of the symposium were very rich, ranging from applied and numerical mathematics and 

development of new algorithms in computational science, complex system modeling and simulation, 

computational chemistry, up to quantum and parallel computations. This highlighted the rapid development 

of computational science and the flourishing international cooperation. We would like to thank all the 

speakers for their inspiring talks. 

From the submissions that ISCS 2011 received, 8 full papers were selected for this proceedings. The 

selected papers cover a wide variety of topics in Computational Science, such as advanced molecular 

dynamics computations, particle methods for fluid dynamics or simulation of crystals. 

We would like to thank all symposium organizers and local organizing committee, including the staff 

and students of Department of Computational Science at Kanazawa University for the excellent work and 

support of ISCS 2011. We extend our thanks also to the main organizers of the symposium, namely the 

Department of Computational Science, Faculty of Science, Kanazawa University and the Faculty of 

Mathematics and Natural Sciences, Bandung Institute of Technology for their financial help and constant 

support in making ISCS 2011 a success. We owe special thanks to our sponsors: Fujitsu Limited and Japan 

Society for the Promotion of Science (Grant-in-Aid No. 21654013 represented by prof. S. Omata) for their 

generous support. 

We invite you to visit the ISCS website (http://iscs.cc) to recount the events of the conference and to 

view the technical program dedicated to the fostering of Computational Science. 

i 

October 2011 

Editors

Compression Stress Effect on Dislocations Movement and 

Crack propagation in Cubic Crystal 

Suprijadi a, Ely Aprilia a, Meiqorry Yusfi b 

aFaculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Jl. Ganesha 10, Bandung 40132 

Indonesia. Email: supri@fi.itb.ac.id, elyaprilia@yahoo.co.id 

bDepartment of Physics, Andalas University, Kampus Limau Manis, Padang 25163, Indonesia. 

Email: meiqorry@yahoo.com 

Abstract. Fracture material is seriously problem in daily life, and it has connection with mechanical properties itself. The 

mechanical properties is belief depend on dislocation movement and crack propagation in the crystal. Information about this 

is very important to characterize the material. In FCC crystal structure the competition between crack propagation and 

dislocation wake is very interesting, in a ductile material like copper (Cu) dislocation can be seen in room temperature, but 

in a brittle material like Si only cracks can be seen observed. Different techniques were applied to material to study the 

mechanical properties, in this study we did compression test in one direction. Combination of simulation and experimental 

on cubic material are reported in this paper. We found that the deflection of crack direction in Si caused by vacancy of lattice, 

while compression stress on Cu cause the atoms displacement in one direction. Some evidence of dislocation wake in Si 

crystal under compression stress at high temperature will reported. 

Keywords: crack, dislocation, FCC, Cu, Si 

1 Introduction 

Fracture material is seriously problem in daily life, in the past and present the accident by a crack propagation 

growth rapidly cause of material ages. Many problem in the past was initiate by a small crack which is growth 

and propagate to whole body, for example in airplane crash Boeing 747-146SR which flight from Tokyo 

(Haneda) to Osaka (Itami) on 1985, the aircraft was crash at Mt. Osutaka by fatigue metal and crack propagation 

only less from 1 hour after take-off from Haneda[1], sink of 12 US Ships including SS John P. Gaines which sank 

on 24 November 1943 [2] and other big damage as in dam break [3]. Base on this problems, many investigation 

with different techniques were done to study the phenomena. In principle, almost of investigation technique 

using stress or shear, for example stress were use in three point bending [4], hardness test [5] and thin plate 

buckling experiment [6]. 

Knowledge of material properties is useful in determining how the treatment is allowed in order not to 

damage the material. Loading which may result in damage to the materials is granted if the excessive load 

applied to them. If a material is given the excessive load will result in changes the properties of the materials. 

The ability of material in receiving excessive load that resulted in changes in shape or deformation makes the 

material can be classified into two parts, brittle and ductile [7]. In ductile material, dislocation wake is very easy 

to observe in room temperature, for example in steel [8] founded that dislocations more observed in unannealed 

steel crack propagation mechanism in Al thin film is reported [9], while in brittle material only crack were 

observed [10]. Increasing temperature on brittle material caused a dislocation wake, and a dislocation is believed 

can be occurred from a crack tip [11]. 

To increase the understanding of material properties, a computation on failure analysis were done by many 

researchers using molecular dynamic methods [12], or other methods [13]. In this paper we did combination of 

computation and experiment to understanding those phenomena, the propagation of cracks and dislocation 

wake will be reported. Possibility of crack propagation and its competition with dislocation wake will be 

discussed. 

2. Experimental 

Experiments on real materials were done to see the crystal damage in cubic crystal. A 500µm x 4mm x 15mm 

thin plate of cubic crystal was pressed under continuous force with speed less than 1mm/minute as schematic in 

Fig.1. The sample (in this figure the sample in Copper (Cu)) will bend in the fixture as can be seen in Fig.1.b, 

Different material were used, Si with (111) plane is used as represent of brittle material, while Cu used as 

1

ISCS 2011 Selected Papers Vol.2 SUPRIJADI, E. APRILIA, M.YUSFI 

represent of ductile material. To observe the crystal deformation on surface, combination of etch pitch and 

optical microscope were applied. 

3. Simulation 

(a) Schematic (b) sample in special fixture 

Figure 1.Experiment apparatus 

In generally, the crack front will propagate if any atom loss their cohesion force, the atomic decohesion can be 

happen if there is an energy which bigger than critical energy. Solving for the critical energy release rate of 

atomic decohesion can be done completely by assuming an infinitesimal distribution of opening displacement 

running along the crack front develops under applied loading. The applied stress solutions are now the vertical 

tensile components of the stress solutions. The opening stress vs. opening displacement relationship is given by 

[13] 

where γs is the surface energy and L is the opening displacement at the peak of the stress displacement 

relationship. This formula must also be expressed in terms of δ, the displacement occurring at the plane of the 

crack front in order to solve the integral equilibrium equation expression. Varying the crack length and crack tip 

root radius demonstrates the effect of the pre-crack geometry parameters on the critical energy release rate of 

atomic decohesion. 

(a) Face Center Cubic (FCC) of Cu (b) (111) Si 

Figure 2, FCC lattice and crystal plane model 

2

ISCS 2011 Selected Papers Vol.2 

Compression effect in cubic crystal 

Different methods for study of material damage were applied. To study of dislocation in cubic metal 

the molecular dynamic based on Wei [12] algorithm was used in cooper (Cu) with FCC structure (Fig.1.a), the 

results was analyzed using mathematical tools freeware Scilab 5.2.2 (www.scilab.org). While for study crack 

propagation in brittle material was simulated using finite element in two dimensions Si with orientation in [111], 

the planes model can be seen in Fig.1.b. The [111] geometry choose because of simple structure and has the same 

length between closer atoms. 

Simulation on crack follows the Griffith criteria, that crack will propagate if stress in a direction higher 

than stress maximum, the algorithm for the crack simulation as follows: 

Start subprogram 

Initiation ;define pre-crack, F_external, MaterialLength 

calculate VectorPosition, CriticalForce 

While (F_external > CriticalForce) 

discritization 

while (VectorPosition < MaterialLength) 

find DOF ;degree of freedom 

find stress distribution each node 

set new VectorPosition 

end while 

end while 

end subprogram 

In simulation of crack propagation in brittle material, the Si will be use (Fig.2.b). Silicon has Young’s 

modulus (E)=18.5 x 10 11 dyne/cm 2 , Surface energy(γ) is 1000 erg/cm 2; Poison ratio (ν) is 0.26, and 5.43 Ǻ of 

crystal dimension. 

4. Results and discussion 

4.1 Brittle material 

Figure 3 shows the crack front of Si under stressed. In Fig.a, the experiment was done in temperature lower than 

transition temperature. We observed that only crack propagated along stress axis while increasing temperature 

just above the temperature transition [11], the dislocation start growth up, in Fig.3.b, shows TEM image of 

dislocation wake around the crack and crack tip as reported in [17]. 

(a) cracks (b) dislocation wake 

Figure 3 Plastic deformations in Si under compression stress 

Simulation results that, the crack will propagate along stress direction, because of the (111) plane, we 

found that the crack propagated in zigzag pattern (Fig.4). To control the crack direction, at beginning, we setup 

3


the crack tip (Fig.2.b), different length of crack tip shows the crack easier deviated. Figure 4.a, shows the 

zigzagged crack by crack tip, deviated cracks more bigger in 100nm pre-crack (denote by (ii)) compare to 50nm 

denote by (i). All of the simulations did in perfect crystal, no vacancy as shown in shadow area in Fig.2.b. 

To find out effect of imperfect crystals, vacancy in some of node did in the middle of structure (Fig.2.b). 

The results show that increasing number of vacancy will make the crack easier to deviate. As reference, perfect 

crystal crack propagation (Fig. 4.a.) is used and in Fig.4.b, denoted by (i). Two atoms (ii) and four atoms (iii) was 

take out to give vacancy in the middle of structure (Fig.2.b). Increasing numbers of atom will bigger deflected as 

shown in Fig.4.b. The same problems were found in previous works as reported [7] as crack-step, the deflected 

crack were found in interface of Si3N4 and BN[14], the crack deflected cause of increasing energy during 

propagation in interface layer. 

(a) Crack tip effect (b) imperfect crystal effect 

Figure 4. Crack propagation in brittle material 

4.2 Ductile material 

Experiment on ductile material, we use the Cu, the sample was stressed in compression machine using continue 

stress with speed of 2 mm/minutes. The stress is stopped and release just after the sample buckle, it can be seen 

in stress-strain curve as below (Fig.5.a). In the center of buckling sample, we observed using optical microscope. 

Figure 5.b shows the image of dislocations in several places (see circles and denote by d1, d2, and d3), the 

dislocation occur in the same direction with stress direction (show by arrow). It is shown that the copper start 

deformation in room temperature under 1.938x10 8 N/m 2 (194 MPa). 

Figure 6, shows the result of molecular dynamic simulation in Cu under constant stress, different stress 

was applied start from 100 MPa to 4000 MPa. The figure shows the atoms configuration before pressed (a) and 

after pressed (b) the atoms were collected in the middle of cube, but it is not to easy to analyze, the atom 

displacement can be plot as Fig.4, it can be seen at higher stress, the atoms displacement increase rapidly. Atoms 

were distributed in one axis follow the compressing stress, the figure shows the dislocations start in area closed 

to surface and move to inner of cube. This phenomenon was reported in simulation of dislocation wake in bulk 

crystal [15]. 

4



(a) Stress-strain curve (b) optical microscope in Cu 

Figure 5 Experimental results of compressed copper 

(a) Before stressed (b) After stressed with 4000 MPa along z-axis 

Figure 6 Atoms distribution in cube metal 

The movement of the dislocation is made of a succession of motion of each straight segment, and the 

kinetics of motion of a straight segment depends upon the local effective stress and the line tension. The local 

effective stress is a sum of threshold stress, internal stress, external stress tensor, and image force tensor [15]. In 

this model, effect of external stress tensor is set to be main factor. Figure 5, shows the dislocation movement to 

central of the sample, it explained that the simulation give the same results as founded in other simulations 

method [15]. Figure 7.a, shows that if the stress applied not big enough, the dislocation only occur in small area 

close to surface where the stress concentrated. Different phenomenon were reported, the dislocation nucleated 

close to crack tip in Si at ductile brittle transition temperature (DBTT) [8] or in Cu [16], if there is a crack, the 

dislocation will starting occur just close to the tip, and spread in majority as stress direction applied. 

5


5. Conclusion 

(a) Stressed by 1000 MPa (b) Stressed by 4000 MPa 

Figure 5 Distributed of atoms displacement in Cu 

In brittle material, some vacancy atoms in a cubic crystal make the crack propagate in deviate direction along 

the compression direction. It can be shown that number of vacancies has tight relation with deviate angle of 

crack propagation, while the pre-crack play important role on crack propagation. In the ductile material, the 

dislocation wake starting from just beneath surfaces of material to middle of sample as found in [15], while the 

effect of compression direction has tight relation with dislocation wake. 

References 

[1] Kobayashi, H., Terada, H., (1985), Crash of Japan Airlines B-747 at Mt. Osutaka, Failure Knowledge 

Database, 1 - 10 

[2] Sawyer, L. A., Mitchell, W. H., (1970). The Liberty Ships: The history of the "emergency" type cargo ships 

constructed in the United States during World War II. Cambridge, Maryland: Cornell Maritime 

Press. ISBN 978-0-87033-152-7. 

[3] Biscarini,C., Di Francesco, S. ,Manciola,P., (2010), CFD modelling approach for dam break flow studies, Hydrol. 

Earth Syst. Sci., 14, 705–718 

[4] Chen, A-J, Cao J.J., (2010), Analysis of dynamic stress intensity factors of three-point bend specimen containing 

crack, Appl.Math.Mech.-Engl.Ed, 32 (2), 203 - 210 

[5] de la Fuente, O.R, Zimmerman, J.A., González, M. A., de la Figuera, J. , Hamilton, J. C., Pai, W.M, and 

Rojo, J. M., (2002), Dislocation Emission around Nanoindentations on a (001) fcc Metal Surface Studied by 

Scanning Tunneling Microscopy and Atomistic Simulations, Phys.Rev.Lett., 88, no.3, 

[6] Suprijadi, (2001), Transmission Electron Microscopy Study on Deformation and Fracture in Silicon Single 

Crystals, Nagoya University, Japan 

[7] Callister, Jr. William D.(2007), Material Science and Engineering . John Wiley & Sons, Inc. 

[8] Aguilar M.T.P., Correa, E.C.S, Monteiro, W.A., Cetlin, P.R., (2006), The effect of cyclic torsion on the 

dislocation structure of drawn mild steel, Materials Research, 9, 3 

[9] Suprijadi, Maula, R., Saka, H.,(2007), Observation of Micro Crack Propagation in a Thin Material, 

Indonesia Journal of Physics, 18 [2], 29 - 32 

[10] Saka,H, Nagaya, G., Sakuishi, T., Abe, S., (1999), Plan-view observation of crack tips in bulk materials by 

FIB/HVEM, Radiation Effects and Defects in Solids, 148 [1 & 4], 319 - 332 

[11] Suprijadi and H.Saka (1998), On the nature of a dislocation wake along a crack introduced in Si at the 

ductile-brittle transition temperature, Philosophy Magazine Letters., 78, 435 – 443 

[12] Wei,C., Bulatov, V.V., ( 2004), Mobility laws in dislocation dynamics simulations, Materials Science and 

Engineering A 387–389 , 277–281 

6



[13] Fischer, L.L. and Beltz, G.E., (1999), Effect of crack geometry on dislocation nucleation and cleavage 

thresholds, Material Research Society Symposium. 39, 57-62 

[14] Desiderio Kovar,M. D. Thouless, and John W. Halloran*, (1998), Crack Deflection and Propagation in 

Layered Silicon Nitride/Boron Nitride Ceramics, Journal of American Ceramics Society, 81 [4] 1004–12 

[15] Verdieryk, M,Fivelz, M. and Gromax,I., (1998), Mesoscopic scale simulation of dislocation dynamics in fcc 

metals: Principles and applications, Modelling Simul. Mater. Sci. Eng. 6 , 755–770. 

[16] Zhu, T., Li, J., and Yip, S., (2004), Atomistic Study of Dislocation Loop Emission from a Crack Tip, Phys. 

Rev. Lett, 93 [2], 

7

Self-Siphon Simulation Using Molecular Dynamics Method 

SPARISOMA VIRIDI a, SUPRIJADI b, SITI NURUL KHOTIMAH a, NOVITRIAN a, FANNIA MASTERIKA c 

aNuclear Physics and Biophysis Research Division, Faculty of Mathematics and Natural Sciences, 

Institut Teknologi Bandung, Jl. Ganesha 10, Bandung 40132 Indonesia, E-mail: dudung@fi.itb.ac.id, 

nurul@fi.itb.ac.id, novit@fi.itb.ac.id 

bTheoretical High Energy Physics and Instrumentation Research Division, Faculty of Mathematics 

and Natural Sciences, Institut Teknologi Bandung, Jl. Ganesha 10, Bandung 40132 Indonesia, E-mail: 

supri@fi.itb.ac.id 

cMagister in Physics Teaching Program, Faculty of Mathematics and Natural Sciences, Institut 

Teknologi Bandung, Jl. Ganesha 10, Bandung 40132 Indonesia, E-mail: fannia_masterika@yahoo.com 

Abstract. A self activated siphon, which is also known as self-siphon or self-priming siphon, is simulated using 

molecular dynamics (MD) method in order to study its behavior, especially why it has a critical height that 

prevents fluid from flowing through it. The trajectory of the fluid interface with air in front of the flow or the 

head is also fitted the trajectory modeled by parametric equations, which is derived from geometry construction 

of the self-siphon. Numerical equations solved using MD method is derived from equations of motion of the 

head which is obtained by introducing all considered forces influencing the movement of it. Time duration 

needed for fluid to pass the entire tube of the self-siphon, τ, obtained from the simulation is compared 

quantitatively to the observation data from the previous work and it shows inverse behavior. Length of the three 

vertical segments are varied independently using a parameter for each segment, which are N5, N3, and N1. 

Room parameters of N5, N3, and N1 are constructed and the dependency of τ to these parameters are discussed. 

Keywords: self-siphon, critical height, duration time, molecular dynamics, room parameter 


A self-siphon is a siphon that can be primed by itself. The oldest version of this apparatus could be 

the one that is invented by Leonardo da Vinci [1], a cow horn-like shape siphon, as illustrated in 

Codex Leicester [2]. It can be used in wide range of applications, such as unique siphon with 

hydraulic capillary and self-venting as microfluidic tehnologies for nuleic acid extraction [3], as large 

siphon system to convey water over a dam or retaining wall [4], as part of wastewater treatment [5] 

and Hydro-Jet Screen [6], and as apparatus in stabilizing wastewater ponds [7] and treating milking 

parlour wastewater in cold climate [8]. Some applications do need the advantage of a self-siphon, 

such for subcritical supercritical flows [9]. Seeing the uses of selfsiphon, many patents based on its 

feature has been reported, such as a self-priming siphon filled with hydrophilic material for irrigation 

[10] and self-priming siphon for removing liquid from a dead storoge of a elevated storage tank [11]. 

Many mechanisms have been used in inventing a self-siphon, which are where the flow is induced by 

creating a partial vacuum within priming chamber [12], where self-siphon is using one-way valve 

and must be inserted several times [13], where self-starting siphon has small bottle filled with air [14], 

or where self-siphon has several unequal length of bends [15, 16]. The last type of self-siphon will be 

discussed in this work. Experiments continuing previous work [17] have been conducted using 

segmented self-siphon and length variation for three vertical straight segments has been done [18]. 

Simulations are performed to explain the phenomenon using molecular dynamics method, which is 

simple than using two-fluid model that has already implemented for flow in a siphon [19]. 

9

ISCS 2011 Selected Papers Vol.2 S. VIRIDI, SUPRIJADI, S. N. KHOTIMAH, NOVITRIAN, F. MASTERIKA 

2 Simulations 

In order to make a model of the self-siphon, the real example in Figure 1 is mimiced also in several 

segments as illustrated in Figure 2. Three vertical straight segments, which are first, third, and fifth 

segment, have length that can be modified using several parameters: N1, N3, and N5. There are total 

seven segments, whose details are illustrated in Figure 2. Small segment in first, third, and fifth 

segment has lenght of w, which is chosen to be the same as in experiments, 2 cm. Other dimension 

parameters are R0 = R2 = R4 = 1 cm, L6 = 15 cm, θ0 = 0.75̟, θ2 = θ4 = ̟, and inner diameter of the tube d 

= 0.6 mm. 

Figure 1. Experimental configuration [17] of self-siphon indicated by numbers: 15 is zeroth and sixth 

segment, 11-14 is first segement, 10 is second segment, 6-9 is third segment, 5 is fourth segmen, and 1- 

4 is fifth segment. Notice that zeroth, second, and fourth segment already contribute one small 

segment to first, third, and fifth segment. 

As the self-siphon immersed into water, water will flow from inlet (fifth segment) to outlet 

(sixth segment). Time needed to accomplish all segments is defined as τ. Parameters N5, N3, and N1 

are varied and its influence on τ is observed. 

Equations of motion a head, the fluid interface with air in front of the flow, with mass m, 

cross section A, and thickness ∆h, is constructed, where forces applied on it is illustrated in Figure 3. 

There are two types of segment which have different equations of motion: straight segment and semicircular 

path. Fifth, third, first, and sixth segments are part of the first type of segment and zeroth, 

second, and fourth segments are part of the later type of segment. 

10


Self-siphon simulation using molecular dynamics method 

Figure 2. Model of self-siphon with length variation in fifth, third, and first segment indicates by set 

of number, N5, N3, and N1, which in this case N5 = 2, N3 = 3, and N1 = 4. 

Friction of the head with the tube is defined as f, which is 

f = −8 

πη∆hv 

, (1) 

as modified from Poiseuille equation in [20]. Equation (1) holds for both type of segments. For the 

vertical straight segments the force equations are 

0 = max 

(2) 

and 

− mg + ρ g y − y A − f = ma . (3) 

( w ) y 

And for the semi-circular segments 

− mg sin θR + ρg( 

yw 

− y) 

AR − fR = Iα 

, 

with 

(4) 

2 

I = mR , (5) 

v 

ω = , 

R 

(6) 

m = ∆hρA 

, 

Equation for time evolution of motion parameters are as follow 

(7) 

vi ( t + ∆t) 

= vi( 

t) 

+ ai∆t, 

i = x, 

y , (8) 

ri ( t + ∆t) 

= ri( 

t) 

+ vi∆t, 

i = x, 

y , (9) 

ω ( t + ∆t) 

= ω( 

t) 

+ α∆t 

, (10) 

θ ( t + ∆t) 

= θ( 

t) 

+ ω∆t 

, (11) 

Based on Equation (2) in the vertical segment the water does not flow in x-direction. In order to show 

whether the results in solving Equation (3) and (4) with MD simulation through Equation (8) – (11), 

there is a need to plot rx, ry, vx, vy, and t. It means that such relations 

0 cosθ 

R x x = + , (12) 

sinθ 

R y y = + , (13) 

0 

11


are needed, for the semi-circular segments. Parameters x0 and y0 are center of the semi-circular 

segments. 

Figure 3. Diagram of considered forces applied to water element with thickness ∆h: (a) in a vertical 

straight segment and (b) in circular segment. 

The simulations are performed until the flow reaches the outlet from the inlet or when there 

is no flow, it must be ended when the flow changes its direction in a current segment, where is 

flowing. 

3 Results and discussion 

Configuration of (N5, N3, N1) = (4, 1, 4) is chosen to see whether the flow can follow the trajectory of 

self-siphon as it proposed in [17] using parametric equations. The result of position of the head as 

function of time is shown in Figure 4 and also the trajectory of self-siphon. 

For this 414 configuration the fifth segment is passed between 0 s and 0.000928 s, the fourth 

segment is passed between 0.000928 s and 0.0010867 s, the third segment is passed between 0.0010867 

s and 0.0014116 s, the second segment is passed between 0.0014116 s and 0.0015913 s, the first 

segment is passed between 0.0015913 s and 0.0021186 s, the zeroth segment is passed between 

0.0021186 s and 0.0022143 s, and the sixth segment is passed between 0.0022143 s and 0.002792 s. It 

means the for 414 configuration τ = 0.002792 s. 

And for the velocity evolution in time, it is illustrated in Figure 5. In the chart of vy – vx, the 

direction of the head can be seen for every segment, more clearer as it seen in the chart of ry – rx. 

These results are obtained by using parameters value: ∆h = 0.01, ∆t = 10–7, η = 10 –8. Variation of N5, 

N3, N1 is conducted and 125 variations are noted, each from 0 to 4 for simulations as shown in Figure 

6. The influece of N1, N3, N5, independently to τ is also simulated and presented in Figure 7. It can be 

seen that as N3 increasing the value of τ is also increasing, but as N1 increasing value of τ is 

decreasing, this both trend do not match previously reported result [17]. Value of τ from simulations 

compared to previous result in [17] is 500 times lower as it should be. It means that the MD 

simulations need a scaling process or the implementation of Equation (1) needs more refinement 

since it depends on value of ∆h which is adjustable. Precise value of ∆h has not yet been investigated. 

A height of inlet measured from water surface can be defined as 

= y − ( N − N + N )w , (13) 

yinlet w 1 3 5 

12



and then from Figure 6 it can seen that, especially from Figure 6 (e) that the flow can occur when 

0. 5N 

1 + 1 − N3 

> 0, 

N5 

= 4 . (14) 

Current results [18] show other condition than it is suggested by Equation (14) for the flow to occur. 

Using Equation (14) into Equation (13) gives about 

yinlet < yw 

− 3w 

, (15) 

which is the condition that the self-siphon can flow the water. A critical height than can be defined 

from Equation (15) as 

y = yw 

− 3w 

. (16) 

critical 

Figure 4. Position of water element for configuration of (N5, N3, N1) = (4, 1, 4): r - t with symbols □ 

and ○ indicate x and y, respectively (left) and y - x (right). 

Figure 5. Velocity of water element (in m/s) for configuration of (N5, N3, N1) = (4, 1, 4): v – t with 

symbols □ and ○ indicate vx and vy, respectively (left) and (b) vy - vx (right). 

Equation (16) is a requirement for the self-siphon to be able to flow the water. Height of inlet 

measured from water surface must be lower than this value. 

13


(a) (b) (c) 

(d) (e) 

Figure 6. Variation parameter of N3 and N1 for different value of N5: (a) 0, (b) 1, (c) 2, (d) 3, and (e) 4. 

The symbols □ and ● indicate no flow and flow occurs, respectively, as predicted by MD 

simulations. 

14



Figure 7. Dependency of time needed for water to flow from inlet to outlet of the self-siphon, τ (in s), 

to number of element in certain straight segment: N1 (upper left), N3 (upper right), and N5 (lower 

center). 

4 Conclusions 

An model for simulating self-siphon flow using MD has been built. From the results it can be 

concluded that when water or fluid can flow, τ is increasing as N5 and N1 decreasing, but it is 

increasing as N3 increasing. The last two results, on which τ dependent is, shows inverse behavior as 

previously reported in experiment. A critical height is also defined as the maximum value of inlet 

height, where the self-siphon still can flow the water. 

Acknowledgment 

Authors would like to thank International Conference Grant IMHERE ITB and cooperation between 

Kanazawa University and Institut Teknologi Bandung in 2011 fur supporting presentation of this 

work, cooperation between Institut Teknologi Bandung and Ministerium of Religion Affair of 

Republic of Indonesia in 2009-2011 for supporting experiment part cited by this work, and Institut 

Teknologi Bandung Alumni Association Research Grant in 2010 for supporting simulation part of this 

work. 

15


References 

[1] E. Macagno (1991), Some remarkable experiments of Leonardo da Vinci, Issue La Houille 

Blanche 6, 463 - 471. 

[2] L. da Vinci (1991), Codex Leicester, Corbis, reproduced in multimedia form. 

[3] J. Siegrist, R. Gorkin, M. Bastien, G. Stewart, R. Peytavi, H. Kido, M. Bergeron, and M. Madou 

(2010), Validation of a centrifugal microfluidic sample lysis and homogenization platform for 

nucleic acid Extraction with clinical samples”, Lab on A Chip 10, 363-371. 

[4] C. W. Krusré and R. M. Lesaca (1955), Automatic siphon for the Control of Anopheles 

minimus var. flavirostris in the Philippines”, Am. J. Hygienise 61, 349-361 . 

[5] Michael G. Faram, Christopher A. Williams, and Keith G. Hutchings (2002), Storm overflow 

screening at wastewater treatment works, 2nd Biennial Conference on Management of Wastewaters 

(CIWEM/AETT), Edinburgh, Scotland, 14-17 April, 71 - 75. 

[6] Michael G. Faram, Robert Y. G. Andoh, and Bruce P. Smith (2001), Optimised CSO screening: 

a UK perspective, Novatech 2001: 4th International Conference on Innovative Technologies in Urban 

Drainage, Lyon, France, 25-27 June, 1031-1034. 

[7] Catherine Boutin, Alain Liénard, Nathalie Bilotte, and Jean-Pierre Naberac (2002), Association 

of wastewater stabilisation ponds and intermittent sand filters: the pilot results and the 

demonstration plant of Aurignac, 8th International Conference on Water Pollution Control, 

Arusha, Tanjanie, 16-19 September. 

[8] Kunihiko Kato, Tashinobu Koba, Hidehiro Ietsugu, Toshiya Saigusa, Takuhito Nozoe, Sohei 

Kobayashi, Katsuji Kitagawa, and Shuji Yanagiya (2006), Early performance of hybrid reed 

bed system to treat milking rarlour wastewater in cold climate in Japan, a poster, Lisbon, 

September. 

[9] H. A. Senturk, V. M. Basak, and T. Sahin (1978), New syphon for subcritical and supercritical 

flows”, J. Irrigation Drain. Div. 104, 442-446 

[10] Maurice Amsellem (2001), Self-priming siphon, in particular for irrigation, United States Patent 

6,178,984. 

[11] John N. Pirok an Joel H. Trammel (1962), Self-priming siphon drain, United States Patent 

3,019,806. 

[12] John H. Rice (1978), Self priming siphon, United States Patent 4,124,035. 

[13] Liu Songzeng (1991), Self-fill siphon pipes”, United States Patent 4,989,760. 

[14] R. M. Sutton (2003), Demonstration experiments in physics, American Association of Physics 

Teachers. 

[15] A. Adair (1945), Small-scale experiments for school classes, J. Chem. Edu. 22, 129. 

[16] M. Gadner and A. Ravielli (1981), Entertaining science experiments with everyday object, Courier 

Dover Publication. 

[17] Fannia Masterika, Novitrian, and Sparisoma Viridi (2010), Self-siphon experiments and its 

mathematical modeling using parametric equation, Proceeding of Conference on Mathematics and 

Natural Sciences 2010, 23-25 November, Bandung, Indonesia (in press). 

[18] Fannia Masterika, Novitrian, dan Sparisoma Viridi (2011), Eksperimen aliran fluida 

menggunakan self-siphon, Prosiding Seminar Nasional Inovasi Pembelajaran dan Sains 2011, 22-23 

Juni, Bandung, Indonesia (accepted). 

[19] Akihiko Minato, Takuji Nagayoshi, Kazuhide Takamori, Ichirou Harad, Masahiro Mase, and 

Kenji Otani, Numerical simulation of gas-fluid two-phase flow in siphon outlets of pumping 

plants”, a paper. 

[20] T. E. Faber (1995), Fluid dynamics for physicist, Cambridge University Press. 

16

Time benchmarks for the OpenMP and GPU parallelized calculation 

in the planewave pseudopotential density functional approach 

Junpei Gotou, a Shinya Haraguchi, a Masahito Tsujikawa, a Tatsuki Oda b 

a Graduate School of Natural Science and Technology, Kanazawa University, Kanazawa 920-1192, 

Japan, E-mail: gotou@cphys.s.kanazawa-u.ac.jp 

b Institute of Science and Engineering, Kanazawa University, Kanazawa 920-1192, Japan, 

E-mail: oda@cphys.s.kanazawa-u.ac.jp 

Abstract. We have investigated the computational performance of the first principles molecular 

dynamics code which employs planewave basis set and pseudopotential of electron-ion interaction. 

The efficiency of task has been measured in terms of matrix multiplication (MM), fast Fourier 

transformation (FFT). For the implementations of the OpenMP and GP-GPU utilities, the MM 

was found to mark the considerable high score, whereas the FFT a fairly good one. Analyzing the 

resulting whole performance, efficiency of the task other than the MM and FFT has to be improved 

for a higher performance. 

Keywords: Car-Parrinello molecular dynamics, first-principles electronic structure calculation, 

parallelization, OpenMP, GP-GPU 


Electronic properties in the realistic system with a nano-size scale have been becoming a target 

in the computational material science which explicitly includes effects on the quantum mechanics. 

Such a calculation needs a large amount of computational source. This is why the higher computational 

efficiency is required. The density functional approach has been playing an important 

role in material science. Indeed, the target extends to many topics associated with the increase 

of performance in both of hardware and software. The extension has been supported by parallel 

computations, which are performed in many levels of computer wares. 

It is important to use the parallel calculation code which is matched with its architecture. 

Even when we develop the computational code for the density functional calculation, some tests 

for new architectures are required for grasping a future efficiency in the computation. Following 

the message passing interface (MPI), the OpenMP has been one of the central issues for the 

improvement in the current computational code. Recently, the general purpose graphic processing 

unit (GP-GPU) is also a choice for getting a higher performance. The test of hybrid calculations 

could also be meaningful. 

In this work, we have investigated the performance about computational time in the pseudopotential 

planewave code for DFT calculation. The results on the matrix multiplication (MM) and 

fast Fourier transformation (FFT) are reported individually in detail in the implementations of 

the OpenMP and GP-GPU. 

2 Computational circumstances 

2.1 Properties of computer archtechture 

We have used three kinds of machines for the performance investigation. Their properties are 

summarized in Table 1. The names of machines are referred in the text. 

17

ISCS 2011 Selected Papers Vol.2 J. Gotou, S. Haraguchi, M. Tsujikawa, T. Oda 

Table 1: Properties of the computers for investigation. The machine names are used in the text. 

Machine Name CPU GPU CUDA 

M1 Quad-Core,AMD,2.3GHz no device no install 

M2 Intel Xeon X5590,3.33GHz Tesla C1060 CUDA Toolkit 2.3 

M3 Intel Xeon X5680,3.33GHz Tesla M2050 CUDA Toolkit 3.1 and 3.2 

The OpenMP is a parallel programming language by which the memory is shared in a node of 

the machine. The message communication like MPI is unnecessary in the OpenMP calculation. 

It is also unnecessary to make a major correction when rewriting the single processing code to a 

parallelized one. However, the execution may not be secure even when there is no error. When 

using two or more threads in the OpenMP calculation, the correspondence between a temporal 

thread memory and real memory may not be secured. Therefore, it is required to make attension 

to the synchronization between them. The speed-up factor is used for presenting parallelization 

performances. This factor is estimated from the inversed ratio of the time by n’s processors with 

respect to that by single one. Originally, GPU is a special set of many processors for graphical 

processes. The CUDA Toolkit developed by NVIDIA has become available to the computation for 

general purpose. 

2.2 Properties of the target code 

The calculation code used in the investigation is for the Car-Parrinello molecular dynamics (CPMD), 

which is based on the density functional theory (DFT). Details of the scheme can be found in the 

reference [1, 2]. The wave functions of dynamical variables are transformed by FFT between real 

and inverse spaces. In the ultrasoft pseudopotential scheme, the MM can be a considerable part for 

the time-consuming. In such a scheme of the DFT, the task of calculation is categorized to MM, 

FFT and the others. The code used can employ a scheme of noncollinear magnetism, affording to 

treat vector type spin density. Such scheme requires twice of memory for wave functions due to 

the two component spinor [3]. The starting code is parallelized in k points (sampling wave vectors 

in wave functions) with using MPI. 

2.3 Sample systems 

For investigating the computational time, the two sample systems have been considered. Both 

of them are slab systems; one is non-magnetic and the other magnetic with noncollinear scheme 

[3, 4]. Results of the former can be used for comparison with other codes and those of the latter 

may provide us the perspective to the application to the magnetic system with the spin-orbit 

interactions [5, 6]. The non-magnetic system, as shown in Fig. 1, consists of 13 monolayers (MLs) 

in BaTiO3 with the inplane lattice constant (a = 3.94˚A); 7 BaO MLs and 6 TiO2 MLs (32 atoms 

in unit cell). In both sides of the slab, the vacuum layer with dv = 5.29˚A is included. The 

periodic boundary condition is taken into account due to the planewave basis in which the energy 

cut-offs of 30Ry and 300Ry were used for the wavefunction and the density, respectively. The 

6 special k points are used for MPI parallel computations. The magnetic system is a thin film 

Fe(5MLs)/MgO(6MLs)/Fe(5MLs) like a magnetic tunnel junction (22 atoms in unit cell, a = 4.20˚A, 

the vacuum layer of dv = 5.29˚A, the energy cut-offs of 30Ry and 300Ry, and 4 special k points). 

18

ISCS 2011 Selected Papers Vol.2 Time Benchmarks for the OpenMP and GPU 

dv 

dv 

Figure 1: Non-magnetic and magnetic slab systems for 

the performance invesitigation; 13 monolayers (MLs) 

of BaTiO3 (left) and the magnetic tunnel junction of 

Fe(5MLs)/MgO(6MLs)/Fe(5MLs) (right). The dv indicates 

the vacuum layer. 

The parameters used in this work are reported in Table 2. 

In these systems, the main parts for time consuming are MMs and FFTs. In the magnetic 

system, the MM and FFT needs the 70% and 20% of the total cpu time in the single processing 

calculation (without using MPI, OpenMP, and GPU). In this paper, we report the result in 

computational performance for OpenMP parallelization and GP-GPU computation. 

3 Testings for the elements 

3.1 Matrix multiplication (MM) 

For the OpenMP parallelization, the MM is performed as shown in Fig. 2. Figure 3 shows 

parallelization efficiency for matrix multiplication. Using 8 cores, we obtain a high parallelization 

efficiency of 94%. It was confirmed that the MM can be parallelized with a high efficiency. 

The MM can be performed using the routines of xGEMM (x =S,D,C,Z) for the typical matrices 

in the BLAS library. The CUDA Toolkit provides the library for the GPU. Figure 4 shows the 

FLOPS (floating point number operations per second) in the MM for the various matrix sizes 

[7]. The times of data transfer from the host computer to the device (GPU) and vice versa were 

included for the estimation. For the architecture of Tesla C1060, the performance is not high 

except for the single real matrices (SGEMM and CGEMM), whereas the performance becomes to 

a much higher one in Tesla M2050 even for DGEMM and ZGEMM. The performance has become 

to a high value in archiecture of Tesla M2050. The comparison with the performance of OpenMP 

(see the data of ”8 thread” in Fig. 4) implies that the performance of CPMD becomes higher in 

the GPU of Tesla M2050 instead of the OpenMP. 

19 

dv 

dv


Table 2: Characters and Parameters in sample systems. 

Sample BaTiO3 Fe/MgO/Fe 

lattice tetragonal lattice tetragonal lattice 

lattice constants a=3.94˚A, c=34.5˚A a=2.98˚A, c=37.1˚A 

number of k point 6 special points 4 special points 

number of atoms 32 (Ba:7, Ti:6, O:19) 22 (Fe:10, Mg:6, O:6) 

number of Kohn-Sham orbitals 148 264 

Energy Cutoff for wave function 25Ry 25Ry 

Energy Cutoff for density 300Ry 300Ry 

Fourier mesh for wave function 24×24×216 18×18×240 

Fourier mesh for density 48×48×360 32×32×400 

number of plane waves 7697 4731 

Figure 2: Parallelization schemes of matrix multiplication 

(MM) in the OpenMP parallelization. 

speedup factor 

8 

7 

6 

5 

4 

3 

2 

1 

0 

0 1 2 3 4 5 6 7 8 

Num.of Processors 

Figure 3: The parallelization efficiency (speed-up factor) 

of the matrix multiplication (MM) in the OpenMP 

of M1 for the size of 5000×5000. 

In the GPU calculation, the data transfer (host to device and vice versa) is time-consuming. 

The typical ratios are presented in Fig. 5. In the larger sizes of matrix, the ratios of data transfer 

become suppressed. This implies the efficiency of GPU in the application of larger systems. It 

is interesting to see that the transfer from the host (CPU) to the device (GPU) needs more time 

compared with that from the device to the host. Such feature of results is attributed to the amount 

of data transfer and the bandwidth for up- and down-loading between the host and device. 

3.2 Fast Fourier transformation (FFT) 

In the target code, the physical value (wave functions and densities) is efficiently calculated by using 

one of real and reciprocal spaces [2]. Requiring the conversion between them, three dimensional 

FFT (3D-FFT) is used. The parallelization scheme of OpenMP for 3D-FFT is shown in Fig. 6. In 

this, the 3D-FFT is divided to three times of 1D-FFTs so that the number of calculation tasks is 

increased and we obtain the good load balance among the threads associated with the OpenMP. 

This sometimes works well because in the application systems of typical size of CPMD calculation, 

the size of FFT is not enough large. Such sizes are only several times or several score times of the 

20


GFLOPS 

GFLOPS 

350 

300 

250 

200 

150 

100 

50 

0 

300 

250 

200 

150 

100 

50 

0 

(a) real number (M2) 

DGEMM(8 Threads) 

DGEMM(Tesla C1060) 

SGEMM(Tesla C1060) 

Ratio(Single/Double) 

256 

512 

1024 2048 

Matrix size 

4096 

(c) real number (M3) 

Tesla C1060 

Tesla M2050 with cuda3.1 


256 

512 

1024 2048 

Matrix size 

4096 

5120 

5120 

7 

6 

5 

4 

3 

2 

1 

0 

RATIO 

GFLOPS 

GFLOPS 

350 

300 

250 

200 

150 

100 

50 

0 

300 

250 

200 

150 

100 

50 

0 

(b) complex number (M2) 

ZGEMM(8 Threads) 

ZGEMM(Tesla C1060) 

CGEMM(Tesla C1060) 

Ratio(Single/Double) 

256 

512 

1024 2048 

Matrix size 

4096 

5120 

(d) complex number (M3) 

Tesla C1060 



256 

512 1024 

Matrix size 

2048 

Figure 4: Effective FLOPS values of the MM for various matrix sizes (256 ∼ 5120) by SGEMM, CGEMM, DGEMM 

and ZGEMM routines in Tesla GPUs (Tesla C1060 and Tesla M2050). The upper and lower two panels are obtained 

in the machines of M2 (a)(b) and M3 (c)(d) (see Table 1), respectively. The times for memory transfer are included 

in the estimation. 

Memory Transfer Rate [%] 

100 

80 

60 

40 

20 

0 

MM 

DtoH 

HtoD 

37.5% 

14.6% 

47.8% 

128 

51.8% 

11.3% 

36.8% 

256 

56.9% 

20.1% 

22.9% 

1024 

79.2% 

8.6% 

12.2% 

4096 

Figure 5: Data transfer ratio in DGEMM calculation for 

various matrix sizes in M3. 

21 

4096 

6 

4 

2 

0 

RATIO


Figure 6: Parallelization scheme for three dimensional 

fast Fourier transformation (3D-FFT) in the OpenMP. 

speedup factor 

8 

7 

6 

5 

4 

3 

2 

1 

0 

0 1 2 3 4 5 6 7 8 


Figure 7: The parallelization efficiency (speed-up factor) 

of 3D-FFT in the OpenMP. The size of 48 × 48 × 

216 is used. 

number of available threads in OpenMP. 

The parallelization efficiency in OpenMP is presented in Fig. 7. Using 8 cores, we obtain 

the efficiency of 65%. The parallelization efficiency has decreased compared with the MM (see 

Fig. 3). This may be because in the scheme the temporal memory for 1D-FFT, as the overhead 

of calculation, is stored discontinuously from the original memory area of 3D-FFT. As another 

investigation for 3D-FFT, the automatic parallelized version of FFTW [8] in OpenMP are tested 

(not reported here), resulting the parallelization efficiency of 25% for using 8 cores. 

In this work, we have carried out the test of CUFFT for 3D-FFT. The computational times are 

presented in Fig. 8. The efficiency is found to depend on the size of FFT (spiky structure in the 

figure). There are many sizes where the efficiency is worse than that of FFTW [8]. This implies 

the 3D-FFT by CUFFT is not appropriate for the CPMD code in which the size of FFT depends 

on the input parameters. 

4 Results on CPMD code 

4.1 MPI+OpenMP (Hybrid) 

The hybrid version of code is organized with k point parallelization on MPI, the OpenMP calculation 

both in MM and FFT, and other minor parallelizations. The efficiencies are presented 

with those of the MPI version in Fig. 9. Using 16 cores (2 MPI+ 8 OpenMP), the performance 

amounts to 37%. This value is still fearly well, but the additional improvement must be required 

for an more efficient calculation. 

4.2 MPI+GPU 

The MPI+GPU version of CPMD code has been checked mainly in M2, which has 8 cores and 3 

GPUs. The BaTiO3 system is used for the computation. The time report is presented in Figs. 10 

and 11. In the latter, the times for MM, FFT are included. In these figures, the labels of BLAS 

and FFTW indicate the single processing calculation for the MM and the FFT, respectively. The 

22


Elapsed time (sec) 

5 

4 

3 

2 

1 

FFTW 

CUFFT(DOUBLE) 

CUFFT(SINGLE) 

0.02 

0.01 

0 

0 50 100 

0 

0 100 200 300 400 

Transform Size (N^3) 

Figure 8: The computational times with respect to the 

various sizes for the CUFFT routine of 3D-FFT (GPU) 

in M2. 


70 

60 

50 

40 

30 

20 

10 

MPI + GPU 

MPI(BLAS+FFTW) 

MPI(CUBLAS+CUFFT) 

MPI(CUBLAS+FFTW) 

0 

0 1 2 3 4 5 6 


Figure 10: Conputational times (single CPMD iteration 

in second) with respect to the number of MPI 

threads for MPI+GPU (Tesla C1060) version. The 

single MPI thread can access to a single GPU in M2. 

Speed Up Factor 

16 

14 

12 

10 

8 

6 

4 

2 

6 

4 

2 

MPI + OpenMP 

MPI 

0 

0 2 4 6 

0 

0 2 4 6 8 10 12 14 16 


Figure 9: Parallelization efficiency for the MPI and 

Hybrid versions for BaTiO3 system. 


35 

30 

25 

20 

15 

10 

5 

0 

6.30 

5.09 

20.0 

33.9 

2.35 

16.6 

2.08 

21.0 

Other 

FFT 

Matrix 

8.70 

2.02 

4.45 

2.23 

FFTW+BLAS CUFFT+CUBLAS FFTW+CUBLAS 

Figure 11: Conputational times (single CPMD iteration 

in second) of MM, FFT, and others for BaTiO3 

by MPI+ GPU (Tesla C1060) version (3MPI+3GPU). 

GPU calculation for the MM (CUBLAS) is improved considerably, whereas the FFT by CUFFT 

is more time-consuming than the FFTW, as expected from the result in Fig. 8. 

4.3 MPI+OpenMP+GPU 

In the experience which is encountered in the previous sections, the FFT by GPU cannot be carried 

out so high performance. Taking into account this, the MPI+OpenMP+GPU (hybrid+GPU) 

version is organized with the MPI (k point parallelization), the MM by GPU, the FFT by OpenMP 

(6 threads in OpenMP), and other minor parallelization. This is tested in the magnetic system 

(Fe/MgO/Fe) with M3 (4 threads in the MPI and 2 GPUs). The result with the CUDA Toolkit 

23



25 

20 

15 

10 

5 

0 

4.98 

4.44 

13.9 

23.3 

MPI 

4.87 

1.41 

2.75 

9.03 

Hybrid 

5.87 

4.09 

1.79 

Other 

FFT 

Matrix 

12.08 

4.71 

1.63 

1.93 

7.97 

MPI+GPU Hybrid+GPU 

Figure 12: Computation times (single CPMD iteration in 

second) for the slab of Fe(5MLs)/MgO(6MLs)/Fe(5MLs) 

in M3. 

3.1 is represented in Fig. 12. In the MPI+GPU calculation, the FFTW is used in the 3D-FFT for 

each k point sampling. The hybrid+GPU calculation marks the highest score among the versions 

investigated. By introducing OpenMP and GPU, the time ratio of MM has become to 24% from 

70% in the single processing calculation and from 60% in the calculation. If preparing one GPU per 

MPI thread, instead of one GPU per two MPI threads, the MM can be accelarated. Introducing 

the MPI, OpenMP, and GPU to the CPMD code, the computation other than the MM and FFT 

becomes to the major part of time-consuming. It should be improved in future. 

5 Conclusions 

We have investigated computational performance of the CPMD code for the OpenMP parallelization 

and the GPU architecture in addition to the MPI parallelization. Our test has succeeded to 

reduce the computing time considerably, compared with the MPI version for the magnetic slab 

system which is an accesible model for typical magnetic tunnel junction. Based on such development 

of the code which accords with the new architectures, we may approach electronic structures 

and molecular dynamics for larger realistic systems with the high performance computation. 

Acknowledgment 

One of authors (T.O.) would like to thank the Japan Society for the Promotion of Science (JSPS) for 

financial supports (Grant 22104012, 22360014, and 22340106). One of authors (M.T.) acknowledges 

the JSPS Research Fellowships (Grant No.20-6647) for Young Scientists. 

References 

[1] D. Vanderbilt (1990). Soft self-consistent pseudopotentials in a generalized eigenvalue formalism, 

Phys. Rev. B, 41, 7892-7895. 

24


[2] K. Laasonen, A. Pasquarello, R. Car, C. Lee, and D. Vanderbilt (1990). Car-Parrinello molecular 

dynamics with Vanderbilt ultrasoft pseudopotentials, Phys. Rev. B, 47, 10142-10153. 

[3] T. Oda, A. Pasquarello, and R. Car (1998). Fully Unconstrained Approach to Noncollinear 

Magnetism: Application to Small Fe Clusters, Phys. Rev. Lett., 80, 3622-3625. 

[4] T. Oda and A. Hosokawa (2005), Fully relativistic two-component-spinor approach in the 

ultrasoft-pseudopotential plane-wave method, Phys. Rev. B, 72, 224428(1-4). 

[5] K. Sakamoto, T. Oda, A. Kimura, K. Miyamoto, M. Tsujikawa, A. Imai, N. Ueno, H. Namatame, 

M. Taniguchi, P. E. J. Eriksson, R. I. G. Uhrberg (1997). Abrupt Rotation of the 

Rashba Spin to the Direction Perpendicular to the Surface, Phys. Rev. Lett., 102, 096805(1-4). 

[6] M. Tsujikawa and T. Oda (2009). Finite Electric Field Effects in the Large Perpendicular 

Magnetic Anisotropy Surface Pt/Fe/Pt(001): A First-Principles Study, Phys. Rev. Lett., 102, 

247203(1-4). 

[7] http://www.softek.co.jp/SPG/Pgi/TIPS/public/accel/cublas-matmul.html 

[8] Matteo Frigo and Steven G. Johnson, ”manual for FFTW 3.2.2” July 2009, 

http://www.fftw.org/. 

25

Simulation Of Fluid-Solid Interaction 

Using Moving Particle Semi-Implicit 

And Mass Spring System 

Mourice Woran a,b , Seiro Omata b 

a Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Jl. Ganesha 10, 

Bandung 40132 Indonesia. 

b Institute of Science and Engineering, Kanazawa University, Kakuma, Kanazawa 920-1192 Japan, 

E-mail: moris 3gun@polaris.s.kanazawa-u.ac.jp 

Abstract. Interactions between fluids and deformable solid objects are very important in practical 

applications and it is an essential task to be able to simulate them correctly. A model for this kind 

of simulation is presented. The fluid is handled by use of a particle method, the so-called moving 

particle semi-implicit (MPS), whereas the solid is modeled by a spring-mass system which maintains 

its volume throughout the simulation. The interaction relies on the coupling force between 

the solid and the fluid, through which the movements of both parts influence each other. 

Keywords: Fluid-solid interaction, particle method, MPS, mass spring system, volume preservation, 

weak coupling. 


Fluid-deformable solid interaction is the interaction of some movable or deformable solid with an 

internal or surrounding fluid flow [1]. The consideration of fluid-deformable solid interactions is 

crucial not only in the design of many engineering systems but also in the medical science, where 

as examples we can name the treatment of aneurysms in large arteries or artificial heart valves. 

Animation of fluids is a particularly difficult task due to the underlying laws that govern fluid’s 

motion. These laws, known as the Navier-Stokes equations, are highly unstable partial differential 

equations that are quite difficult to solve in an efficient way. Recently, particle methods have 

been developed to handle fluid motion. Particle methods draw attention for their advantages 

of Lagrangian and meshless formulation. Large motion of free surfaces can be tracked without 

numerical diffusion while fluid disintegration and merging can be analyzed without mesh tangling. 

Moreover particle methods are also fitted to large deformation and fracture of solid materials [10]. 

Moving Particle Semi-implicit (MPS) is one of the particle methods that was developed by 

Koshizuka and coworkers for incompressible flow [7] [8] [9]. Incompressibility is achieved by keeping 

the density of particles constant during the computation. MPS is based on Taylor series expansion 

that employs an original form of the weight function to approximate spatial derivatives of the 

Lagrangian Navier-Stokes system by a deterministic particle interaction model [6]. 

Although fluid is simulated through a rather complex process, solids are much easier to handle. 

While solids can be represented as rigid bodies delineated by a surface made of triangles, they can 

also be represented as a set of linked point masses [12]. This model, for which a simple example is 

given in Figure 3, is especially well suited to animation. It is used in the presented method because 

of its flexibility to handle both rigid and non-rigid bodies, its easy manipulation, and the way it 

fits in the interaction model. 

27

ISCS 2011 Selected Papers Vol.2 M. Woran, S. Omata 

The purpose of this paper is to make a simple fluid-solid interaction with volume preservation 

for the solid, by using MPS and mass spring model. Several models have been proposed to handle 

this kind of interaction [5] [3], including those using MPS and mass-spring system [13]. However, 

our model is different in the way we handle the mass-spring system. Through this model we 

simulate the motion of a membrane with external force applied from above (see Figure 1a) and 

the deformation and motion of a box inside parallel flow (Figure 1b). 

(a) Test model 1 (b) Test model 2 

Figure 1: Test models. 

2 MPS in Computational Fluid Dynamics (CFD) 

Finite difference method (FDM), finite volume method (FVM) and finite element method FEM are 

very powerful, popular and widely used methods in CFD. In these methods, continuum domain is 

discretized into a fixed discrete grid or mesh. The strategy with fixed grids assures both robustness 

and accuracy when obtaining the solution of a differential equation using the discrete system. However, 

this strategy also gives several limitations in analyzing complex geometries and multiphysics 

problems, which consequently limits the application of these methods to practical problems. The 

limitations of the fixed grid and mesh-based methods have triggered the development of a mesh 

free method which uses only a set of distributed nodes to express the mechanical system in a 

discretized form. The particle method developed for incompressible flow is called moving particle 

semi-implicit (MPS). In the MPS method, fluids are represented by a set of moving particles and 

governing equations are discretized by particle interaction models, hence grids are not necessary. 

2.1 Governing Equations 

Governing equations express the conservation laws of mass and momentum, 

1 ∂ρ 

+ ∇ · u = 0, (1) 

ρ ∂t 

Du 1 

= − 

Dt ρ ∇P + v∇2u + f, (2) 

while incompressible fluids must satisfy 

∂ρ 

= 0. 

∂t 

28

ISCS 2011 Selected Papers Vol.2 Simulation of fluid-solid interaction by MPS and mass-spring system 

Here ρ denotes density, P pressure, v viscosity, u velocity and f external force. The left-hand 

side of Eq.(2) is the Lagrangian time differentiation involving advection terms. In MPS methods 

advection terms are directly incorporated into the calculation of moving particles. In this study, 

we solve two-dimensional problems and the only outer force considered is the gravity [9]. The 

Navier-Stokes solution process by MPS is a semi-implicit prediction-correction process. Namely, 

the basic Eq.(2) is divided into two parts, 

and 

( ) explicit 

Du 

= υ∇ 

Dt 

2 u + f (3) 

( ) implicit 

Du 

Dt 

= − 1 

∇P. (4) 

ρ 

We solve Eq.(3) first to predict the velocity and position of fluid particles. Therefore, in the first 

part the accelerations of the particles taking into account all the terms except for pressure are 

evaluated, and the temporal velocities and positions are calculated by 

u ∗ = u k + ∆t 

r ∗ = r k + ∆tu ∗ . 

( ) explicit 

Du 

Dt 

The pressure term Eq.(4) is included by solving Poisson equation for pressure in the second part 

of the algorithm. The velocities and positions of each particle are modified as 

u k+1 = u ∗ + ∆t 

r k+1 = r ∗ + ∆t 2 

2.2 Particle Interaction Model 

( ) implicit 

Du 

Dt 

( ) implicit 

Du 

. 

Dt 

A particle interacts with its neighboring particles within the support of weight function w(r), where 

r is a distance between two particles. The weight function employed in this study has the following 

form 

{ re 

w(r) = r − 1 0 ≤ r < re 

0 re ≤ r. 

Hence, a particle interacts with only a finite number of particles located within the distance of 

re. The cutoff radius re limits the number of the neighboring particles and allows to reduce the 

computational cost. The accuracy may be deteriorated with few neighbor particles when we adopt 

an excessively small radius. On the other hand, a larger radius will make the spatial resolution 

lower [6]. 

To calculate the weighted average, a normalization factor called particle number density between 

particle i and its neighbors j located at positions ri and rj is used: 

〈n〉i = ∑ 

w(|rj − ri|). (5) 

j�=1 

29


Figure 2: Particle interaction given by weight function. 

This value is assumed to be proportional to the density. As the density is almost constant in 

incompressibility calculation, we use the constant n 0 instead of 〈n〉i in the formulation of weighted 

average. 

The gradient operator is modeled using the weight function. A gradient vector between two 

neighboring particles i and j is evaluated as (φj - φi)(rj − ri) / |rj − ri| 2 , where φ is a physical 

quantity. The gradient vector at ri is then a weighted average of these vectors : 

〈∇φ〉 i = d 

n0 ∑ (φj − φ 

j�=i 

′ 

i ) 

|rj − ri| 2 (rj − ri)w(|rj − ri|), (6) 

where d is the number of space dimensions and n 0 is the reference value of the particle number 

density. In Eq.(6) a different value φ ′ 

i is used in place of φi because of stability reasons. If the 

configuration of neighboring particles is isotropic, Eq.(6) is not sensitive to absolute value and any 

value can be used for φ ′ 

i . However, the configuration is not isotropic in general. In that case, the 

in this study is calculated by 

value of φ ′ 

i 

φ ′ 

i = min φj for {j | w(|rj − ri|) �= 0}. 

This means that the minimum value is selected among the neighboring particles within the distance 

of re. Using Eq.(6), forces between particles are always repulsive because φj − φ ′ 

i is positive. As 

noted in [6], this contributes to numerical stability. 

Laplacian operator is modeled by the following identity: 

∑ 

(φj − φi)w(|rj − ri|). 

〈∇ 2 φ〉 i = 2d 

λn 0 

j�=i 

Here, the parameter λ is introduced so that the variance increase is equal to the analytical solution, 

which yields 

∑ 

j�=i 

λ = 

|rj − ri| 2w(|rj − ri|) 

∑ 

j�=i w(|rj 

. 

− ri|) 

30


3 Mass Spring Model 

The mass-spring model is an array of masses linked by springs. Each mass connects to its adjacent 

masses as in the figure below. The movement of each mass is determined by the spring force and 

damp force between the masses. 

Figure 3: Basic mass-spring model. 

The spring force complies with the Hooke’s law. Supposed there are springs connecting the mass 

i with its neighbors denoted by Ω. According to Hooke’s law, the spring force is written as 

and the damp force has the form 

Fint = − ∑ 

j∈Ω 

ki,j(|li,j| − l 0 i,j) li,j 

|li,j| , 

Fdamp = − ∑ 

bi,j(vi − vj), 

j∈Ω 

where kij is the stiffness of the spring, l 0 ij is the rest length of the spring, bij is the coefficient of 

elasticity of the spring between the masses i and j , li,j is the vector connecting neighboring masses 

and vi is the speed of the mass i. 

According to Newton’s second law of motion, the total force on each node (mass) is 

Fi = Fint + Fdamp + Fext, 

where Fext is the external force that also influences the movement of nodes. 

To solve this equation the Verlet method is used. Beginning at a time step n and given position 

rn, velocity vn and force Fn acting on each node, the following equations are used to obtain values 

for the next step [11]. 

v n+ 1 

2 = vn + ∆t 

2 m−1 Fn 

rn+1 = rn + v n+ 1 

2 ∆t 

Fn+1 = F (rn+1) + Fdamp + Fext 

∆t 

vn+1 = v 1 n+ + 

2 2 m−1Fn+1. 31


4 Volume Preservation 

During deformable solid object simulation we need to keep its volume constant to maintain reliability 

of our model. Here we adopt the method of [4]. The idea is to use the divergence theorem 

to transform the expression for the volume of the solid body to an integral over the surface of the 

body. This integral is then evaluated using a triangular mesh for the surface and there is no need 

to analyze the structure of the whole object. 

The condition of total volume preservation is cast into a constrained dynamic system. The 

constrained formulation using Lagrange multipliers results in a mixed system of ordinary differential 

equations and algebraic expressions. The system of equations is represented using dn generalized 

coordinates q, where n is the number of discrete masses. The generalized coordinates which are 

simply the Cartesian coordinates of the discrete masses are defined in our 2D setting as 

q = [x1, y1, x2, y2, . . . , xn, yn] T . 

The difference between V0 (original volume) and V (current volume) should be 0 for each 

iteration process, which is written using the constraint function Φ(q, t) as follows: 

Φ(q, t) = V − V0 = 0. 

To maintain the volume at a constant value, implicit method is applied. The equation of motion 

and kinematic relationship between q and ˙q are discretized in the following way: 

˙q(t + ∆t) = ˙q(t) − ∆tM −1 ∇Φ(q, t)λ + ∆tM −1 F A (q, t), (7) 

q(t + ∆t) = q(t) + ∆t ˙q(t + ∆t). (8) 

Here F A are spring forces acting on the discrete masses, M is a dn×dn diagonal matrix containing 

discrete nodal masses, λ is a Lagrange multiplier, and ∇Φ = ∇qV . We treat the constrained 

equations at new time implicitly, 

Φ(q(t + ∆t), t + ∆t) = 0. (9) 

Eq. (9) is now approximated using a truncated first-order Taylor series: 

Φ(q, t) + ∇Φ T (q, t)(q(t + ∆t) − q(t)) + Φt(q, t)∆t = 0. (10) 

Substituting ˙q(t + ∆t) from Eq. (7) into Eq. (8) we obtain 

q(t + ∆t) = q(t) + ∆t ˙q(t) + (∆t) 2 {M −1 F A (q, t) − M −1 ∇Φ(q, t)λ}. (11) 

Substituting this result into Eq. (10) results in the following identity, which yields the Lagrange 

multiplier by a simple division: 

∇Φ T (q, t)M −1 ∇Φ(q, t)λ = 1 

1 

2 Φ(q, t) + 

∆t ∆t Φt(q, t) + ∇Φ T (q, t)( 1 

∆t ˙q(t) + M −1 F A (q, t)). (12) 

5 Weak Coupling of Fluid and Solid 

In this simulation the interaction between the fluid and the solid is carried out in the manner of 

weak coupling, where the effect of the fluid on the solid is calculated after one iteration of the fluid 

[13]. Steps of the interaction between the fluid and the solid are described as follows. 

32


1. Determine the motion of fluid particles for one calculation step using the MPS method with 

time step ∆t fluid . 

2. Calculate the fluid force F fluid 

i , consisting of pressure and viscous force acting on each solid 

particle i that interacts with fluid: 

where F viscosity 

i 

mi( Du 

Dt )implicit . 

F fluid 

i 

= F pressure 

i 

+ F viscosity 

i , 

= mi( Du 

Dt )explicit (without considering external force f), and F pressure 

i 

3. Determine the motion of the solid particles using the spring network model for time ∆t fluid . 

This amounts to solving the set of equations of motion with respect to the solid particles, 

mi¨ri + bi,j( ˙ri − ˙rj) = Fi + F fluid 

i 

with the Verlet method. Here, the dot denotes the time derivative, j is a neighbor of the 

solid particle i and Fi includes the spring forces and volume constraint. Since the time step 

∆t solid used in mass spring calculation is different from the time step ∆t fluid , the motion of 

solid was calculated for ∆t fluid /∆t solid iterative steps. 

4. Return to step 1 and repeat procedures 1. - 4. until the final time is reached. 

6 Results and Discussion 

First, we tested the mass spring and volume preservation model using a 7 × 7 mass spring system 

with the configuration of springs as in Figure 3. The response of the object was compared for the 

cases with and without volume constraint after applying an external force from above for a period 

of time and then releasing it. The difference is shown in Figure 4 and Figure 5 shows the evolution 

of the relative volume error computed by the formula 

V − V0 

ε = . 

Next, we tested the fluid-solid interaction model using two problems (Figure 6). In the first 

computation, the upper part of a two-dimensional tube corresponds to a deformable solid wall and 

acts like a membrane, while the the bottom part is considered as a rigid wall. External force is 

applied on the upper wall from above for a period of time. Solid deformations due to the external 

force cause oscillations of the membrane. This vibration triggers an interaction between fluid and 

solid and a flow is observed inside the tube. In order to preserve tube’s volume, we connected the 

bottom and upper part with a spring. In this way, the whole domain is included in the mass-spring 

system and the volume is thus preserved. For the upper membrane, 3 × 39 nodes are used. 

In the second test problem, both upper and lower part of the tube are rigid walls, while we 

insert a deformable solid object inside the tube. The boundary condition on the inlet is selected as 

uniform velocity U0 in the negative x-direction Here we use 9 × 5 nodes to approximate the box, 

which deforms into a parachute-like shape, while being transported by the fluid flow. 

33 

V0 

= 

(13)


7 Conclusion 

Figure 4: Mass spring model without and with volume preservation. 

Figure 5: Relative error of volume during the simulation. 

We have succeeded in simulating a simple fluid-solid interaction by use of the Moving Particle 

Semi-implicit method for fluid flow and mass-spring system for solid deformation keeping the 

volume constant throughout the simulation process. The key of the model is a weak coupling 

34


Figure 6: Results of test problems. 

interaction between the fluid and the solid, where the effect of viscosity and pressure count as the 

external forces for mass-spring system after one fluid iteration. We use a smaller time steps for 

solid calculations then for fluid calculations. To be able to simulate a real part of a human body 

like in [13] or [5], parameter tuning and increase in resolution are indispensable. 

References 

[1] H.-J. Bungartz, M. Schäfer (2006). Fluid-structure Interaction: Modelling, Simulation, Optimization, 

Springer-Verlag. 

[2] D. Bourguignon, M.-P. Cani. Controlling anisotropy in mass-spring systems, Eurographics 

Workshop on Computer Animation and Simulation (EGCAS), 113–123. 

[3] O. Genevaux, A. Habibi, J.H. Dischler. Simulating fluid-solid interacion, LSIIT UMR CNRS- 

ULP 7005. 

[4] M. Hong, S. Jung, M.H. Choi, S.W.J. Welch (2006). Fast Volume Preservation for a Mass- 

Spring System, IEEE Computer Graphics and Applications 26(5), 83–91. 

[5] M. Kazama, S. Omata (2009). Modeling and computation of fluid-membrane interaction, Nonlinear 

Analysis 71, e1553-e1559. 

35


[6] M. Kondo, S. Koshizuka (2011). Improvement of stability in moving particle semi-implicit 

method, Int. J. Numer. Meth. Fluids 65, 638?-654. 

[7] S. Koshizuka, Y. Oka (1995). A particle method for incompressible viscous flow with fluid 

fragmentation, Comput. Fluid Dyn. J. 4 (1), 29-46. 

[8] S. Koshizuka, Y. Oka (1996). Moving particle semi-implicit method for fragmentation of incompressible 

fluid, Nucl. Sci. Eng. 123 (3), 421-434. 

[9] S. Koshizuka, A. Nobe , Y. Oka (1998). Numerical Analysis of Breaking Waves Using The 

Moving Particle Semi-Implicit Method, International Journal for Numerical Methods in Fluids 

26, 751-769. 

[10] S. Koshizuka (2005). Moving Particle Semi-Implicit (MPS) Method : A Particle Method for 

Fluid and Solid Dynamics, in IACM expressions. Bulletin for The International Association 

for Computational Mechanics, 4–9. 

[11] J. Li, D. Zhang, G. Lu, Y. Peng, X. Wen, Y. Sakaguti (2005). Flattening Triangulated Surfaces 

Using a Mass-Spring Model, Int. J. Adv. Manuf. Technol. 25, 108–117. 

[12] G.S.P.Miller (1988). The motion dynamics of snakes and worms, SIGGRAPH 88 Confrence 

Proceedings, 198 – 178. 

[13] K. Tsubota, S. Wada, T. Yamaguchi (2006). Particle method for computer simulation of red 

blood cell motion in blood flow, Computer Methods and Programs in Biomedicine 83, 139–146. 

36

High-Pressure Crystal Structure Prediction 

Using Evolutionary Algorithm Simulation 

Athiya M. Hanna 1,2 , Toru Yoshizaki 1 , Muhamad A. Martoprawiro 2 , Tatsuki Oda 1 

1 Institute of Science and Engineering, Kanazawa University, Kakuma, Kanazawa 920-1192 Japan, 


2 Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Jl. Ganesha 10, 

Bandung 40132 Indonesia, E-mail: athiya.mh@students.itb.ac.id, muhamad@chem.itb.ac.id 

Abstract. We implemented a high-pressure crystal structure prediction using evolutionary algorithm 

method, one of successful method to deal with this kind of problems. This method employs 

three evolution operators to generate a new offspring from its parents; heredity operator, permutation 

operator, and mutation operator. We run two simulation tests to this method and found 

results having a good agreement with experimental results. We also found some metastable structures 

produced by this method. 

Keywords: high-pressure, evolutionary algorithm, ab-initio, crystal structure prediction. 


Crystal structure prediction at particular conditions are of the important challenge declared by 

John Maddox more than twenty years ago in his article [1]. The underlying problem of this challenge 

is searching the global minimum among the very high diversity of crystal structures even for the 

simple chemical compositions. Trimarchi et al. classify the optimization problem into three type 

of problems [2]. The type-I problems are structural relaxation problem of given crystal structures, 

which are the search of visible local minimum of given structure. The type-II problems are the 

search of correct chemical arrangement among the possible ones of given chemical composition and 

lattice type crystal. The type-III problems are to find the stablest structure where the lattice type 

and atomic arrangement are unknown. Maddox’s challenges are all about the type-III problem 

and the crystal structures at high-pressure now become one of his challenges to be solved. 

There are also other reasons why crystal structure prediction at certain condition, especially 

high-pressure, is important. The article written by McMillan [3] summarizes the current progress 

on high-pressure materials and there are some of these reasons in it. High-pressure condition is 

leading us to new physical behavior of materials; superhard materials synthesized in high-pressure 

condition to replace diamond, new optoelectronics properties of materials, and expansion region 

of superconductivity phenomena over all elements and increasing Tc of superconductivity. The 

crystal structures at high-pressure now become a challenge to be solved. 

To overcome this problem, many scientists have developed several powerful method to predict 

crystal structure at particular condition. Among these methods, one of the successful ones was 

evolutionary algorithm method [4]. From biological inspiration, the evolutionary algorithm method 

can be derived into two schemes; Lamarckian and Darwinian ones. Lamarckian scheme within 

evolutionary algorithm incorporates structure optimization procedure while evaluating fitness value 

and takes the fitness value of the optimized structure. While the Darwinian scheme skips this 

optimization procedure and goes directly to evaluating the fitness value. Woodley et al. proves 

that the Lamarckian scheme is more efficient and successful rather than the Darwinian one [5]. 

In this research, we used the Lamarckian scheme of evolutionary algorithm method adopted 

from the one developed by Oganov and his research group [4, 6, 7]. 

37

ISCS 2011 Selected Papers Vol.2 A. M. Hanna, T. Yoshizaki, M. A. Martoprawiro, T. Oda 

2 Evolutionary Algorithm 

In this method, we treat lattice parameters and atomic coordinates of a crystal structure as a set of 

variables. For each crystal structure, there must be an evaluation parameter which is a function of 

the set of variables, namely, fitness value. This fitness value is taken from thermodynamics potential 

calculated by the optimizer code. In this research, we use enthalpy as the fitness value. As the 

enthalphy becomes lower, the fitness value represents the better structure. A set of crystal structure 

and its fitness value is an entity called individual. Some individuals produced in a generation cycle 

are called population or generation depending on the context. The above concepts are illustrated 

in Figure 1 (a) and (b). 

(a) (b) 

Figure 1: (a) A set of crystal structure and its fitness value is fused in an individual, (b) some individuals are 

grouped to be a population or generation. 

START 

Previous 

Population 

Structure 

Generator 

No 

Volume 

Rescalation 

Initial 

Selection 

Stage, pass? 

Yes 

Ab-Initio 

Computation 

Figure 2: Flowchart of single generation in the method. 

Elite 

Selection 

Flowchart of single generation of our evolutionary algorithm method is described in Figure 

2. This flowchart can be partitioned into two parts; structure generation part and selection and 

adaptation part. 

2.1 Structure Generation 

Structure generation plays a keyrole in the evolutionary algorithm method. Structure generation 

generate a new crystal structure randomly if the cycle is initial generation or from previous generation 

if it is not initial generation. There are three evolution operators used in this method: 

heredity operator, permutation operator, and mutation operator. 

38 

Stage 

END

ISCS 2011 Selected Papers Vol.2 Crystal Structure Prediction Using Evolutionary Algorithm 

Heredity Operator 

Heredity operator needs two parents to generate an offspring. As described in the previous work 

[2, 4, 6, 7] and illustrated in Figure 3, first all the parents are transformed arbitrarily. Then the 

heredity operator chooses a random number between 0.0 to 1.0 to slice one of lattice vectors of 

the two parents randomly. The plane of this cut is parallel to two other lattice vectors. Then the 

offspring is constructed by combining atomic position of the two parents delimited by the cut on 

crystal slab. Lattice parameters of the offspring are weighted average of the two parent’s whose 

weight is also determined randomly. If the number of atoms in a unit cell is not equal to the 

parents, the corresponding atom is added or drawn stochastically, so that the number of atoms of 

the offspring is equal to its parents. 

Permutation Operator 

Figure 3: Heredity operator. 

Permutation operator is a one-parent operator. It needs only one parent to generate an offspring. 

As illustrated in Figure 4, it chooses two lattice points of different atomic species and then swap 

their atomic identity. This procedure is repeated as many as parameter given by the user. 

Figure 4: Permutation operator. 

The permutation operator explores correct chemical arrangement of the crystal structure in 

the configurational space [7]. It works only for crystal structure which consists of more than one 

atomic species. It is completely useless in single species crystals. 

Mutation Operator 

Mutation operator is also a one-parent operator. It distorts lattice vectors of the parent (Figure 

5), while atomic coordinates remain unchanged relative to the lattice vectors. This transformation 

is done using random symmetric matrix [2, 4]. A new lattice vector of the offspring is produced 

by this following formula: 

a ′ = (I + ɛ)a , (1) 

39


where a ′ , a are lattice vectors before and after mutation operation respectively. The (I + ɛ) is the 

symmetric matrix defined as 

⎛ 

⎞ 

ɛ12 ɛ13 

1 + ɛ11 2 

2 

(I + ɛ) = ⎝ ɛ12 

ɛ23 

2 1 + ɛ22 ⎠ 

2 , (2) 

1 + ɛ33 

ɛ13 

2 

where ɛij are generated randomly by 0-mean gaussian random distribution between 0.0 and 1.0. 

2.2 Selection and Adaptation 

ɛ23 

2 

Figure 5: Mutation operator. 

Each new structure produced by one of the three operators raised above is set to certain volume 

which is of the best crystal structure of previous generation [7]. This rescalation compensates the 

pre-condition of the crystal structure generated by the evolution operator which may not be a 

good initial structure before the crystal structure is relaxed to enhance the structure relaxation in 

ab-initio computation stage. The volume of initial generation is approximated by atomic radii. 

To enhance the structure relaxation more effectively before it is performed, each generated 

structure must be passed through an initial selection stage. There are three criteria in this selection 

[2, 4, 6, 7]; minimum interatomic distance, minimum lattice vector length, and minimum and 

maximum angle of lattice parameters. The structure which violates these criteria is rejected and a 

new structure is generated again by structure generation using the same operator. This procedure 

is repeated until it matches to the criteria. 

Fitness value of each individual as a function of crystal structure set of varibles is computed 

in ab-initio computation using first-principle method. Details of the ab-initio method will be 

described in Section 3. 

Elite selection stage plays a role as nature selection of the Lamarckian evolution theory. In this 

stage, a few worst individuals are discarded and other remaining elite structures are passed to the 

next cycle of generation and also ranked based on their fitness values. The ranking by the fitness 

value is useful for procreation or parent selection to generate a new population. 

3 Ab-Initio and Simulation Methods 

We used density functional theory (DFT) scheme of ab-initio computation [8] . Within the scheme, 

we employed planewave basis function and ultrasoft pseudopotential [9], and used generalized 

gradient approximation (GGA) for exchange-correlation term [10]. We also used two kinds of kpoint 

meshes used for ab-initio calculation: low k-point mesh for generating all possible individuals 

throughout the generations, and high k-point mesh for reoptimization of the last stablest structure 

of the generations. Our simulation test was carried out on two cases: single phase simulation and 

phase transition simulation. 

40


3.1 Single Phase Simulation 

Single phase simulation was run on silicon (Si) and phosphorus (P). Some details of ab-initio and 

evolutionary parameters are presented in Table 1. 

Table 1: Ab-initio and evolutionary parameters used in single phase simulation. 

Parameter Silicon (Si) Phosphorus (P) 

Pressure 20 GPa 190 GPa 

Energy cut-off wave-function 15 Ry 20 Ry 

Energy cut-off density 150 Ry 240 Ry 

k-point mesh 4 x 4 x 4 8 x 8 x 8 

Number of indiv. per generation 10 10 

Probability heredity 0.6 0.7 

Probability mutation 0.4 0.3 

3.2 Phase Transition Simulation 

Phase transition simulation was run on phosphorus (P) to see phase transition behavior in highpressure 

range using this method. We used several pressure, 95, 100, 110, 120, 130, 140, 150, 

160, 170, and 190 GPa. Cut-off energy for wave function and electron density used in this case 

are 20 Ry and 240 Ry respectively. For generating part of simulation, we used 4 x 4 x 4 k-point 

mesh. The evolutionary parameters used in this simulation are showed in Table 2. At the end of 

Table 2: Evolutionary parameters used in phase transition simulation on phosphorus. 

Pressure Number of indiv. per gen. Prob. heredity Prob. mutation 

95 GPa 10 0.6 0.4 

100 GPa 10 0.6 0.4 

110 GPa 10 0.6 0.4 

120 GPa 8 0.625 0.375 

130 GPa 8 0.625 0.375 

140 GPa 8 0.625 0.375 

150 GPa 10 0.6 0.4 

160 GPa 8 0.625 0.375 

170 GPa 8 0.625 0.375 

180 GPa 8 0.625 0.375 

190 GPa 10 0.7 0.3 

simulation, for each different pressure, we then reoptimized the last stablest individual using 16 x 

16 x 16 k-point mesh to enhance the accuracy of our calculations. 

41


4 Result and Discussion 

4.1 Single Phase Simulation 

Profiles of silicon and phosphorus in the series of generation are shown in Figure 6. In the profile of 

silicon, there is a divergent behavior along the fitness value (enthalpy), whereas in phosphorus the 

enthalpies are converged in the narrow range. Such convergence in the profile may be controlled by 

the probability of evolution operators. Indeed, in the comparison between two figures, the higher 

probability of heredity results in the convergence profile on generation series. This convergence is 

an advantage if one can prevent the same structure to be generated again. However, if one cannot 

prevent such kind of procedure, this convergence become a disadvantage. It may be effective to 

prevent redundancy of same structures as Oganov et al. did [6, 11]. 

(a) (b) 

Figure 6: (a) Flow of generation series of silicon at 20 GPa and (b) phosphorus at 190 GPa. 

The reoptimized results of the last stablest individual shown in Table 3 give a good agreement 

with experimental result of the similar materials [12, 13]. Although there is some redundancy of 

same structures, these resutls show the prediction power of evolutionary algorithm method. 

Table 3: Comparison of our result with experimental data. 

Lattice Parameters a (˚A) b (˚A) c (˚A) α β γ Vol. (˚A 3 ) 

Si last generation (20 GPa) 2.471 2.471 2.362 89.978 89.932 115.014 13.071 

Si re-optimized (20 GPa) 2.512 2.512 2.380 89.998 89.997 118.293 13.229 

Si Experiment [12] (∼ 16 GPa) 2.551 2.551 2.387 90 90 120 13.45 

P last generation (190 GPa) 2.119 2.132 2.047 89.788 90.660 118.955 8.088 

P re-optimized (190 GPa) 2.122 2.126 2.045 89.848 90.463 118.986 8.066 

P Experiment [13] (151 GPa) 2.175 2.175 2.0628 90 90 120 8.452 

42


4.2 Phase Transition Simulation 

Result of generation series for each pressure is similar to single phase simulation. The reoptimized 

last stablest generation for all pressures are summarized in Table 4, and we also found metastable 

structures for some pressures. 

Table 4: Summary of the reoptimized last generation of all pressures in phase transition simulation. 

Press.(GPa) Struct.[S] Vol.(˚A 3 )[S] H(eV)[S] Struct.[M] Vol.(˚A 3 )[M] H(eV)[M] 

95 SC 10.1469 -237.29666 

100 SC 10.0380 -236.98075 

110 SC 9.8366 -236.35717 SH 9.2032 -236.28198 

120 SC 9.6456 -235.74231 SH 9.0181 -235.71340 

130 SC 9.4509 -235.15132 SH 8.8409 -235.15565 

140 SC 9.2821 -234.56238 d-SC 8.9916 -234.55954 

150 SH 8.5704 -234.04512 SC 9.1134 -233.99563 

160 SH 8.4116 -233.53843 SC 8.9842 -233.42351 

170 SH 8.2897 -233.01649 SC 8.8512 -232.86837 

180 SH 8.1739 -232.50200 SC 8.7302 -232.31919 

190 SH 8.0660 -232.00137 

SC = Simple Cubic; SH = simple Hexagonal; d-SC = Distorted Simple Cubic 

(a) (b) 

Figure 7: Profiles of (a) volume versus pressure and (b) enthalpy versus pressure. 

From Table 4, we ploted a graph of volume versus pressure and enthalpy versus pressure, as 

depicted in Figure 7, with the curve of Murnaghan equation of state in which its parameters are 

taken from the works of Akahama et al. [13, 14]. It is shown in Figure 7 that the transition 

pressure obtained from our simulation occurs at around 140 GPa. It is overestimated, compared 

to the experimental result (137 GPa) of Akahama et al. [13]. Our prediction volumes at the 

pressures above 150 GPa are also lower than the one predicted by the experiment (Murnaghan 

state of equation). This underestimation is probably due to the k-point mesh which should be finer 

43


at high-pressure condition or the typical accuracy of GGA approach. The pressure dependences of 

the volume and enthalpy are consistent with a typical behavior at the first-order phase transition. 

Around the transition point, the lattice type is switched over between simple cubic and simple 

hexagonal structures for both of the ground state structure and the metastable one. 

5 Conclusion 

We have performed simulations of crystal structure prediction using the evolutionary algorithm 

method in combination with ab-initio calculation. Results of our simulation have a good agreement 

with the previous experimental works. We found that this implementation of evolutionary 

algorithm method on crystal structure prediction formed a good new path to answer Maddox’s 

challenge of the crystal structure prediction. We also found the metastable structure was switched 

in accordance with the transition pressure. The evolutionary algorithm simulation experienced in 

this work strongly supports us to the research of crystal structure predictions. 

References 

[1] J. Maddox. (1988). Crystal from first principles. Nature, 335(6187), 210. 

[2] G. Trimarchi and A. Zunger. (2007). Global space-group optimization problem: Finding the 

stablest crystal structure without constraints. Phys. Rev. B, 75, 104113-1–104113-8. 

[3] P.F. McMillan. (2002). New materials from high-pressure experiments. Nat. Mater., 1(1), 

19-25. 

[4] A. R. Oganov and C. W. Glass. (2006). Crystal structure prediction using ab initio evolutionary 

techniques J. Chem. Phys., 124(24), 244704. 

[5] S.M. Woodley, and C.R.A. Catlow. (2009). Structure prediction of titania phases. Computational 

Materials Science, 45(1), 84–95. 

[6] A. R. Oganov, Y. Ma, A. O. Lyakhov, M. Valle, and C. Gatti. (2010). Evolutionary crystal 

structure prediction as a method for the discovery of minerals and materials Reviews in 

Mineralogy and Geochemistry, 71(1), 271–298. 

[7] C. W. Glass, A. R. Oganov and N. Hansen. (2006). USPEX-evolutionary crystal structure 

prediction Computer Physics Communications, 175(11-12), 713–720. 

[8] P. Hohenberg and W. Kohn. (1964). Inhomogeneous electron gas Phys. Rev. 136, B864-B871.; 

W. Kohn and L. J. Sham. (1965). Self-consistent equations including exchange and correlation 

effects Phys. Rev. 140, A1133–A1138. 

[9] D. Vanderbilt (1990). Soft self-consistent pseudopotentials in a generalized eigenvalue formalism 

Phys. Rev. B, 41, 7892-7895. 

[10] J. P. Perdew, J. A. Chevary, M. R. Pederson, D. J. Singh, and C. Fiolhais. (1992). Atoms, 

molecules, solids, and surfaces: Applications of the generalized gradient approximation for 

exchange and correlation, Phys. Rev. B, 46, 6671-6687. 

[11] A.R. Oganov and M. Valle. (2009). How to quantify energy landscapes of solids. J. Chem. 

Phys., 130(10), 104504. 

44


[12] J. Z. Hu, L. D. Merkle, C. S. Menoni, and I. L. Spain. (1986). Crystal data for high-pressure 

phases of silicon Phys. Rev. B, 34(7), 4679. 

[13] Y. Akahama, M. Kobayashi, and H. Kawamura. (1999). Simple-cubic-simple-hexagonal transition 

in phosphorus under pressure. Phys. Rev. B, 59(13), 8520–8525. 

[14] Y. Akahama, H. Kawamura, S. Carlson, T. L. Bihan, and D. Häusermann. (2000). Structural 

stability and equation of state of simple-hexagonal phosphorus to 280 GPa: Phase transition 

at 262 GPa. Phys. Rev. B, 61(5), 3139–3142. 

45

Quantum control of high harmonic generation in anharmonic potential 

Muhamad Koyimatu a,b , Kiyoshi Nishikawa b 


Bandung 40132 Indonesia, E-mail: s105koyimatu@mail.chem.itb.ac.id 

b Institute of Science and Engineering, Kanazawa University, Kakuma, Kanazawa 920-1192 Japan, 

E-mail: kiyoshi@wriron1.s.kanazawa-u.ac.jp 

Abstract. 

In this work, we first aim to realize the high harmonic generation(HHG) spectrum in a classical 

and quantum treatment, and then to achieve the quantum control of the HHG spectrum. Here, we 

consider the HHG from the Duffing oscillator well-known as a typical anharmonic system. The 

HHG induced by the intense laser is a nonlinear optical process, where a molecular system absorbs 

n photons with energy �ω and emits one high energy photon with energy n�ω. The light generated 

by HHG is a promising light source with an attosecond ultrashort pulse, which could be used to 

analyze the electronic structure and motion in molecule. 

First, we perform a classical simulation to explain the structure of the HHG spectrum. Then, we 

investigate quantum-mechanically the mechanism of HHG, and compare the classical and quantum 

result. In quantum treatment, we apply the Fourier Grid Method (FGM) to obtain the eigenvalues 

and wavefuntion of the Duffing oscillator and use the Split Operator Method (SOM) to solve the 

time-dependent Schrödinger equation. Here we study the laser intensity dependence of the HHG 

with a single laser pulse, and then from the interference point of view, we focus on the role of 

the relative phase of two laser pulses and simulate to find out the phase dependence of the HHG. 

Finally we investigate the laser control of the HHG by changing the initial quantum state, which 

is a kind of a wave packet due to the superimposition of few eigenstates. 

Keywords: HHG, SOM, anharmonic oscillator, quantum control 


Nonlinear optics process (NLOP) describes the response of the molecular system to the strong 

electromagnetic wave, and is usually induced only by a strong light such as a laser with high 

intensity. If the induced dipole moment of the material respond instantaneously to an applied 

electric field E(t), the induced polarization P (t) can be expressed in terms of the power of the 

electric field E(t), 

P (t) = χ (1) E(t) + χ (2) E 2 (t) + χ (3) E 3 (t) + · · · . (1) 

Above perturbation treatment of the nonlinear optics could describe accurately the characteristics 

of the ordinary nonlinear optical phenomenon. With sufficiently intense laser field, the higher order 

terms play an very important role, and give rise to Fourier components of the polarization with high 

harmonics of the laser frequency, emitting the electromagnetic wave with the same frequency as the 

polarization. The harmonic generation is an interesting phenomenon, which describe a nonlinear 

process of light matter interaction, and a typical example of the process is a second-order harmonic 

generation. 

47

ISCS 2011 Selected Papers Vol.2 M. Koyimatu, K. Nishikawa 

Due to the great progress of the laser technique, an intense laser with the intensity 10 8 < 

I < 10 12 W/cm 2 have become available, and we have discovered the noble interesting multiphoton 

processes in molecule [1], such as multi-photon absorption (MPA), multi-photon ionization 

(ATI), multi-photon dissociation (MPD), above threshold dissociation (ATD), the high harmonic 

generation (HHG), and so on, which are nonlinear optical processes arising from the higher-order 

effect of the external laser field. 

Here we focus on the HHG, where a molecule absorbs n photons (with energy �ω ) and emits 

one high photon with energy n�ω. HHG is experimentally observed by irradiating a noble gas 

with a near-IR laser pulse with a ultra high intensity 10 14 W/cm 2 , and the energy of the radiating 

electromagnetic wave is in the region of the extreme-ultraviolet (XUV) [2]. It have been known 

that the emitted photon energy is found to be the odd harmonics of the laser frequency (2m+1)�ω, 

and in some cases, the harmonic order n = 2m + 1 becomes larger than 100. The HHG spectrum 

has a characteristic structure, namely in a low energy region of HHG spectrum, the intensity of 

HHG rapidly decreases as the harmonic order increases, and then the typical harmonic shows a 

plateau, followed by a sharp cut-off. Thus the HHG provides an attractive light source of ultrashort 

coherent radiation in the XUV and soft-X-ray range, and it is expected that using the attosecond 

laser pulses by HHG, we could observe the electronic structure in molecule and control directly 

the motion of electron in molecule. 

On the other hand, several theoretical methods have been developed to understand the basic 

mechanism of the HHG. Most familiar model is the sp-called three-step model by P.B.Corkum 

to explain semiclassically the basic generation mechanism of higher-order harmonics. Usually the 

potential induced by the ultrahigh intensity of the external oscillating field is comparable with the 

Coulomb potential due to the nucleus, so that electron moves in the deformed oscillating Coulomb 

potential, being a superposition of the Coloumb potential and the time dependent potential due 

to the laser field. When the intensity of the external field becomes close to the maximum, the 

electron go through the potential barrier by the tunneling ionization. Then the ionized electron is 

accelerated by the strong laser electric field, and acquire a lot of energy form the external field. 

Finally this accelerated ionized electron return back to the nucleus to recombine with it, emitting 

the high energy photon. Namely an electron emits the electromagnetic wave by three steps, i.e., 

(1) field induced tunnel ionization, (2) acceleration in the laser field, and (3) recombination and 

photoemission. Thus the energy of the emitted photon depends on the ionization potential of the 

atom and on the kinetic energy of the electron upon its return to its parent ion. 

The paper is organized in the following way. In section 2,we develop the theoretical treatment, 

where we introduce the split operator method (SOM) to solve the time-dependent Scrödinger equation, 

and the Fourier grid Hamiltonian (FGH) method to solve the time-independent Scrödinger 

equation. In SOM, the time development operator U(t) to generate the wavefunction |Ψ(t)〉 from 

the initial state |Ψ(0〉) is an unitary transformation so that the norm of the wavefunction is always 

kept constant. Furthermore it uses the fast Fourier transformation (FFT), so that it solves the 

dynamics of the system in a very efficient way. On the other hand, FGH method is a effective 

way to solve the eigenvalue problem of the Hamiltonian matrix, and yields the eigenvalues and 

eigenvectors, which is required to construct the initial wavepacket for the quantum control of HHG. 

In section 3, we describe the details of the target Duffing oscillator, which is a typical anharmonic 

oscillator. The anharmonic term plays an fundamental role to generate the HHG. In section 4, 

we perform the classical simulation of the HHG, From the numerical solution of the Newton’s 

equation, we estimate the dependence of the HHG spectra on the field intensity. In section 5, 

we develop the quantum mechanical treatment of the HHG, and calculate the HHG spectrum by 

changing the field intensity, and moreover investigate the relative phase dependence in the case of 

48

ISCS 2011 Selected Papers Vol.2 Quantum control of high harmonic generation in anharmonic potential 

the two color lase pulse. Finally we study the initial state dependence on HHG spectrum, where 

we adopt some initial wavepackets as a initial state. Last section treat the summary of this work. 

2 Theoretical Treatments and Numerical Methods 

2.1 Time-dependent Schrödinger Equation and Split Operator Method 

Now we develop the semiclassical theory of the light-molecule interaction, where the molecular 

system is treated quantum-mechanically, but the electromagnetic filed is described by the timedependent 

external field. Then the time-dependent Schrödinger equation is given by 

i� d 

dt |Ψ(t)〉 = [H0 + V (t)]|Ψ(t)〉, (2) 

where H0 and V (t)is the unperturbed molecular Hamiltonian and the perturbation Hamiltonian, 

respectively. In our simulation of the light-molecule interaction, the interaction Hamiltonian between 

the classical electronic field E(t) and the dipole moment operator µ(r) is given by 

V (t) = −µ(r) · E(t) (3) 

where the applied electric field E(t) is assumed as E(t) = E0g(t) sin(ωt), where E0 and ω mean 

the amplitude vector and the frequency of the external electric field, and the shape function g(t) 

of the laser pulse is assumed to be Gaussian function g(t) = e−(t−T0)2 /σ 2 

, where T0 and σ are the 

temporal center and the pulse width of the Gaussian pulse, respectively. 

The time-dependent Schrödinger equation is generally solved by expanding the state ket |Φ(t)〉 

in terms of the eigenstate |n〉 of the molecular Hamiltonian H0 for the set {|n〉|n = 0, 1, 2, · · ·} is 

a complete orthonormal set, namely |Φ(t)〉 = � 

n Cn(t)|n〉. 

However, we here introduce the time-development operator U(∆t) for the infinitesimal time 

increment ∆t in order to analyze the dynamics of the time-dependent system. Then the formal 

solution of time dependent Schrödinger equation is given by 

|Ψ(∆t)〉 = U(∆t)|Ψ(0)〉, (4) 

where the infinitesimal time-development operator is given in terms of the total Hamiltonian H 

by U(∆t) = e −iH∆t/� . 

Here we divide the Hamiltonian operator into two parts i.e., H ≡ H0 + V (t) = T + W (t). Note 

that the kinetic operator T = p 2 /2m and the potential term W (t) = V0 + V (t) does not commute. 

Now we employ the split operator method [3, 4] to solve the TDSE of the system numerically. The 

infinitesimal time-development operator is approximated by 

−i(T +W )∆t/� 

U(∆t) ≡ e 

≈ e −iW ∆t/2� e −iT ∆t/� e −iW ∆t/2� + O(∆t 3 ). (6) 

This approximation is correct up to the order ∆t 3 . Moreover, this approximated operator is unitary, 

so that the norm of the wavefunction obtained by applying this operator is kept constant while 

the numerical simulation. In order to get a state vector |Ψ(t)〉 at finite time t, we just apply this 

infinitesimal time-development operator to the initial state n-times, namely |Ψ(t)〉 = U(∆t) n |Ψ(0)〉, 

where n is the number of the simulation step, so the arbitrary time is given by t = n∆t. 

In general, the wavefunction and the potential terms are diagonal in the coordinate space, 

and the kinetic operator is diagonal in the momentum space, Therefore we adopt the fast Fourier 

49 

(5)


transformation(FFT) in our numerical simulation, then we could effectively calculate the timedependent 

wavefunction as follows; 

Ψ(r, t0 + ∆t) ≡ 〈r|e −iW ∆t/2� e −iT ∆t/� e −iW ∆t/2� |Ψ(t0)〉 (7) 

= e −iW (r,t0)∆t/2� FFT −1 p2 

−i 

[e 2m ∆t/� FFT[e −iW (r,t0)∆t/2� Ψ(r, t0)]], (8) 

where the last line shows schematically the procedure of the programing, and FFT stand for the 

fast Fourier transform from the coordinate space to the momentum space, while FFT −1 represents 

the inverse FFT from the momentum space to the coordinate space. 

2.2 Time-independent Schrödinger Equation and Fourier Grid Hamiltonian 

Method 

In quantum simulation of the HHG, we need the wavefunction and the corresponding energy of 

the molecular system. In order to calculate correctly the eigenfunction and its energy in one and 

two dimensional systems, we here develop the Fourier Grid Hamiltonian(FGH) Method. 

Now let us consider the general Hamiltonian H with a kinetic energy T and a local potential 

V (x). In actual numerical simulation, we adopt the discrete variable representation, namely, we 

discretize the coordinate variable to construct the Hamiltonian matrix, where every spatial point 

is described by the set {xi = x0 + (i − 1)∆x | i = 1, 2, 3, · · ·, n} and ∆x is an spatial increment. We 

apply the second order differencing(SOD) to the 2nd-order spatial differenciation, then the explicit 

form of the matrix element for the kinetic and potential operator is given by, in the discretized 

coordination representation 〈〈x〉〉, 

Ti,j ≡ 〈xi| p2 

2m |xj〉 = 

�2 

2m∆x2 {2δi,j − δi,j+1 − δi,j+1a}, (9) 

Vi,j ≡ 〈xi|V |xj〉 = V (xi)δi,j. (10) 

By means of the diagonalization of the Hamiltonian matirix Hi,j, we could obtain the eigenfunctions 

and eigenvalues of the system described by the Hamiltonian operator H. However, the 

accuracy of this method is mainly due to the evaluation of the kinetic operator, so we need a larger 

basis set to get a accurate results. 

Now we develop the more efficient and accurate method called the Fourier Grid Hamiltonian(FGH) 

method. First we note that the kinetic operator is diagonal in the 〈〈p〉〉 representation. 

Using the wavefunction of the momentum eigenstate 〈x|p〉 = eipx / √ 2π, then the matrix element 

of the kinetic operator T is given by, in 〈〈x〉〉 representation, 

� 

〈x|T |y〉 = 

dp 〈x|T |p〉〈p|y〉 = 1 

2π 

� 

dp e −ip(x−y) �2 p 2 

. (11) 

2m 

This final expression means that this matrix element is given in terms of the Fourier transformation 

of the kinetic energy (�p) 2 /2m. Speaking exactly, p and q in above equation mean the wave vector, 

and we use this notation in the following. 

Next we turn to the discrete variable representation, namely we introduce the discretized 

momentum basis set {|pi〉 | i = 1, 2, 3, · · ·, N} in addition to the discretize coordinate basis set 

{|xi〉 | i = 1, 2, 3, · · ·, N}, where N means the dimension of the basis set, and usually is taken 

to be odd integer N = 2n + 1. Let the interval L of the coordinate under consideration be 

50


xmin ≤ x ≤ xmax, so that x1 = xmin and xN = xmax. Now we set L = xmax − xmin, then the 

spatial increment is ∆x = L/(N − 1). 

On the other hand, in the discretized momentum space, we could take the domain of the 

momentum as 0 ≤ p ≤ pmax, where p1 = 0 and pN = pmax. Taking into account the periodicity in 

both spaces i.e., x1 = xN+1 and p1 = pN+1 in the discrete Fourier transformation, the momentum 

increment ∆p and maximum momentum pmax are given by in terms of ∆x and N as ∆p = 

2π/(N∆x). Each basis point of two spaces is given by pi = (i − 1)∆p and xi = x0 + (i − 1)∆x, 

however we could shift the domain of the momentum space due to the periodicity, namely we 

change the domain of the momentum point such as −pmax/2 ≤ pi ≤ pmax/2. 

Now we calculate the matrix element of kinetic operator in the discretized basis set, 

〈xi|T |yj〉 = 1 

2π 

= 

1 

∆x 

n� 

∆p e −ipl(xi−xj) 

Tl, (12) 

l=−n 

n� 

l=1 

2Cos(2πl(i − j)/N) 

N 

Tl, (13) 

where, for integer l, we define Tl = (�∆p) 2 /(2m) × l 2 . Thus we obtain the explicit form of the 

Hamiltonian matrix as 

Hi,j = 1 2 

{ 

∆x N 

n� 

Cos(2πl(i − j)/N) Tl + V (xi)δi,j}. (14) 

l=1 

In this case, the Hamiltonian matrix Hi,j∆x include more element than in the second-order 

differencing method, but a diagonalization of this Hamiltonian yield numerically more accurate 

result of the eigenvalues and eigenvectors. 

3 Duffing Oscillator 

The purpose of the paper is to present a detailed analysis of HHG by an anharmonic oscillator. 

Since HHG by noble gas atoms irradiated with intense laser pulses has been observed, the theory 

of the highly nonlinear optical processes has been developed to investigate the characteristic 

features of HHG spectrum, which consists of a first decrease, a long plateau, and a sharp cutoff. 

Many model atoms are studied to explain the characteristic response. Here we adopt the typical 

anharmonic oscillator with a quartic anharmonicity, so-called Duffing oscillator. The anharmonic 

oscillator generally presents several appealing properties to investigate the nonlinear dynamics of 

one dimensional systems, especially this allow us to make a comparison between the classical and 

quantum-mechanical treatments [5]. Thus we will show that we can be able to understand the 

some important aspects of HHG just by this very simple model. 

The Duffing potential is written as 

V (x) = 1 

2 ω2 0 x 2 + 1 

4 v x4 , (15) 

where the first term represents the ordinary harmonic oscillator with the fundamental frequency 

ω0, and the second one corresponds to the quartic anharmonicity with the anharmonic coefficient 

v. In this work, we restrict the motion of the electron to the bound state, namely we consider only 

the confining case v > 0. 

51


Next, we turn to the quantum mechanical treatment of the Duffing oscillator. We calculate 

the wavefunction and the corresponding energy of the Duffing oscillator using the FGH method 

mentioned in the previous section. Here we used the parameter set {ω0 = 1, v = 5}. The resultant 

wavefunctions are used to construct the initial wavepacket of the HHG simulation in order to study 

the initial state dependence on the HHG spectrum, namely to investigate the quantum control of 

the HHG. Figure 1 shows the Duffing potential and five lowest wavefunctions. 

Figure 1: Plot of Duffing potential and wavefunction 

In tis figure, the narrow quadratic curve means the Duffing potential, and the other one is 

the harmonic potential. The Duffing potential confines the electronic motion in the more narrow 

region. The behavior of the wavefunction of the Duffing oscillator is similar to the harmonic 

oscillator. 

4 Classical Simulation 

Here we develop the classical treatment of the HHG by the Duffing potential, so we investigate the 

classical motion of the electron in the quartic confining anharmonic oscillator under the intense 

electric field of the laser, E(t) = E0 sin(ω1t), where E0 and ω1 are the intensity and the frequency 

of the applied electric field, respectively. Then the total time-dependent potential of this system 

is given by 

V (x, t) = 1 

2 ω2 0 x 2 + 1 

4 v x4 − ex E0 sin(ω1t), (16) 

where the last term means the interaction of the electric field E(t) and the electric dipole moment 

ex, and e is the charge of the electron. The harmonic frequency ω0 is greater than the one of the 

external field ω1, namely ω0 > ω1. This physically means that the electron doing fast motion due 

to the Duffing potential moves under the slowly oscillating potential. 

In this model, we study not only the details of the HHG spectrum, but also the damping effect 

to the HHG spectrum. The quantum theory does not treat this damping effect, because there is 

no Hamiltonian to describe correctly the damping effect. Namely, the system with the damping 

term is dissipative and do not conserve the energy, but practically this effect is very important. 

Now consider the Newton’s equation of motion with damping effect given by 

¨x + Γ ˙x + ω 2 0 x + v x 3 = E0 sin(ω1t), (17) 

52


where Γ is a damping coefficient. In order to analyze the oscillator dynamics given by the potential 

of Eq.16, we numerically integrate Eq.17. We assumed that the electron is rest at the origin at an 

initial time, namely we set the initial condition of the trajectory x(t) as {x(0) = 0 and ˙x(0) = 0} 

to solve the second order differential equation. 

As mentioned in the previous section, the power spectrum I(ω) is proportional to the absolute 

square of the Fourier transform of the acceleration α(t), i.e., I(ω) ∝ |α(ω)| 2 . Thus in the following, 

we calculate α(ω) to discuss the HHG spectrum. In the following, we will show the results of the 

HHG simulation in order to investigate the damping effect, the field intensity dependence, and the 

anharmonicity dependence to the HHG. 

1. The damping effect on the HHG spectrum: 

Here we show the typical example of the trajectory x(t) and the related HHG spectrum, where 

the x-axis is the harmonic order n = ω/ω1 In the following simulation we set the harmonic frequency 

ω0 = 1, namely we adopt this scaled unit. Here we used the parameters {v = 1, E0 = 5, and ω1 = 

0.1}. In figure 2, two trajctories x(t) corresponding to the weak and strong damping cases and the 

harmonic oscillator without the damping (v = 0 and Γ = 0) are shown, and the corresponding HHG 

spectrum are shown in figure 3 The spectrum of the harmonic oscillator (without anharmonicity 

Figure 2: Time variation of trajectory x(t) with respect 

to { Γ = 10(Green), 0.01(Blue), and harmonic oscillator 

(Red) } 

Figure 3: The corresponding HHG spectrum 

and damping) shown by red peak in Fig.3 has only two peaks corresponding to the external 

frequency ω1 = 0.1 and the harmonic frequency ω0 = 1. The harmonic oscillator does not show 

any interesting optical response, while Duffing oscillator with the interaction of the electron and 

the field shows several peaks of the HHG, but for large damping suppress the HHG spectrum, i.e., 

there are small peaks (green) for Γ = 10. Therefore we are sure that the anharmonicity plays an 

very important role in the nonlinear optical response. 

The amplitude of all trajectories if Fig.?? have two frequency components of the periodic motion 

corresponding to ω0 and ω1. As the damping becomes large, the high frequency component 

of the x(t) decrease, so that the largest damping Γ = 10 gives a smooth curve (green) and this 

behavior of the trajectory makes the HHG spectra disappear drastically. On the other hand,for 

small damping, several sharp spectrum peaks of the high harmonic order with 13 ≤ n ≤ 31 appear. 

2. Field intensity dependence: 

53


In order study the intensity dependence, we set parameters {v = 5, Γ = 0.01, and ω1 = 0.1}, 

and we perform the simulation by changing the field intensity such as E0 = 1, 5, and 10. As shown 

from Fig.4, as the field intensity increase, the amplitude of the trajectory also become large. For 

large field intensity, there appear the large ripple with the large amplitude corresponding to the 

high frequency component shown by blue curve in Fig.4. From the HHG spectrum shown in Fig.5, 

Figure 4: Time variation of trajectory x(t) with respect 

to {E0 = 1(red), 5(green), and 10(Blue)} 


we easily find out that as the intensity become large, both the intensity and the harmonic order 

of the HHG spectrum also become large. For strong field E0 = 10 case, two peak groups appear 

around the harmonic order 15 < n < 40 and 50 < n < 70. 

3. Anharmonicity dependence: 

As we mentioned before, anharmonicity is very important to induce the HHG. In order to 

study the anharmonicity dependence, we set parameters {E0 = 5, Γ = 0.01, and ω1 = 0.1}, and we 

perform the simulation by changing the anharmonicity coefficient such as v = 0.1, 1, and 10. Here 

we use the time variation of the acceleration α(t) instead of the trajectory x(t). From the Fig.6, the 

behavior of the acceleration apparently looks like one of the trajectory, and as the anharmonicity 

becomes large, the high frequency component corresponding to the HHG shows the oscillation with 

more high frequency. While the low frequency component shows quite different behavior, namely 

the envelop of the large anharmonicity oscillate alternately with large and small amplitude. Fig.7 

clearly shows that the global pattern of the HHG spectrum is similar for three cases, but its peaks 

shift to the high frequency (i.e., high harmonic order). 

5 Quantum Simulation 

Here, we develop the quantum mechanical treatment of the HHG. The time-dependent Schr—”odinger 

equation determines how a given initial wavefunction will change with time. It differs from Newton’s 

law in two important ways: it involves a first time derivative instead of a second, and the 

square root of -1 appears explicitly in it. A wavefunction in an infinite square well is similar in 

some respects to a classical string clamped at both ends. In this section, we especially focus on 

the initial state dependence, the relative phase dependence in two color external field, and the 

interference effect on the HHG spectrum. 

54


Figure 6: Time variation of acceleration α(t) with respect 

to {v = 0.1(red), 1(green), and 10(Blue)} 

1. Initial state dependence: 


Initial wave function is calculated numerically by Fourier Grid Hamiltonian method, and we 

consider the lowest three states of the Duffing system, {Ψ0, Ψ1 and Ψ2}. By changing these initial 

wave functions, we make some quantum simulation and get the information about initial state 

dependence to HHG spectrum. Figure 8 show that we could see clearly some groups in the HHG 

Figure 8: Initial state dependence on the HHG spectrum, where Ψ0 (red), Ψ1(green) and Ψ2(blue) 

spectrum peak, and in generally as the energy of the initial wave function becomes higher, the 

intensity of the give more intense HHG spectrum. But in the lowest region of the harmonic order, 

spectrum peaks from Ψ0 and Ψ1 is more intense, and the higher harmonic order region, the HHG 

pek groups from Ψ2 look like more intense than Ψ0 and Ψ1. 

2. Relative phase dependence of two-color laser pulses: 

55


Next we performed the HHG simulation with a two-color laser, and examined the effect of the 

relative phase difference between two laser pulses. We here consider the following external field 

with two-color {ω1, 3ω1}, 

E(t) = E0g(t) (sin(ω1t) + sin(3ω1t + δ)) , (18) 

where, δ is a relative phase of two laser pulses. The reason assuming the frequency of second 

pulse with three times the original pulse is that we expected the interference effect of two pathway 

by the two pulses in the HHG spectrum may occur. We observed the small difference in some 

peaks of the HHG spectrum, however we did not find out the drastic change of the some ports of 

the HHG spectrum due to the change of the relative phase of two pulses. 

3. Analysis of interference effect: 

Finally we have tried to control the HHG spectrum by using the wavepacket, which is a superposition 

of the three lowest states, {Ψ0, Ψ1 and Ψ2}. where we In this simulation we adopted 

the three states, {ψ0, (ψ0 + ψ1)/ √ 2 and (ψ0 + ψ1 + ψ2)/ √ 3}, as the initial state. If we consider 

the wavepacket made from three stationary states, then we could consider three pathway from 

three initial states to induce the HHG spectrum, and the HHG spectrum induced by three initial 

states could have a interference effect. Thus we have expected that the HHG spectrum from each 

component wavefunction constituting the wavepacket could make a interference, so that the HHG 

spectrum have a different structure from one of the each component wavefunction. The resultant 

HHG spectrum is shown Fig.9. The superposed initial state with higher energy gives stronger 

Figure 9: HHG spectrum from the superposed initial state, where Ψ0(red),(Ψ0 + Ψ1)/ √ 2(green) and (Ψ0 + Ψ1 + 

Ψ2)/ √ 3(blue) 

HHG spectrum in almost all region except the lowest high harmonic order region. 

Next we investigate the details of the difference due to the interference effect. In Figs.10 and 

11, we show the averaged HHG spectrum (red curve) from two independent states and the HHG 

spectrum (blue curve) form the superposed state with interference effect. IN Fig.10, the red curve 

56


show the averaged HHG spectrum with the initial state Ψ0 and Ψ1, and the blue curve is the 

spectrum of the superposed state (Ψ0 + Ψ1)/ √ 2, while Fig.11 show the same spectrum related to 

the three initial states, Ψ0, Ψ1, and Ψ2. We find clearly out that, in both cases, the intensity of 

the HHG spectrum from the wavepacket is larger than one of the averaged spectrum. However 

we could not realize the increase or decrease of spectrum peaks only with respect to the specified 

region. Namely it seems difficult to control only the specified peaks of the HHG spectrum. 

Figure 10: The averaged HHG spectrum from two states Figure 11: The interference effect for three-state case : the 

(res) and the HHG spectrum from the superposed state averaged HHG spectrum (red) and the HHG spectrum of 

(blue) 

the superposed state (blue) 

6 Summary 

The purpose of this work is to investigate the mechanism and spectrum of the high harmonic 

generation(HHG) in a classical and quantum-mechanical point of view, and finally we have made 

an simulation to achieve the quantum control of the HHG spectrum. Here, we considered the 

HHG from the Duffing oscillator well-known as a typical anharmonic system. HHG spectrum is 

calculated in terms of the Fourier transform of the acceleration (α(ω)). 

In classical simulation, we have studied the damping effect, the intensity dependence, and 

the anharmonicity dependence on the HHG spectrum. In first simulation, we have found that 

the harmonic oscillator does not give rise to the nonlinear optical response, and then the large 

damping generates the weak HHG spectrum. Thus we understand that the anharmonicity is the 

fundamental quantity to induce the nonlinear optical response including HHG. Next by changing 

the field intensity and analyzing the time variation of the trajectory, we have clearly found that 

there are two oscillating components, corresponding to the harmonic (high) frequency ω0 and the 

(low) frequency of external field ω1. The HHG comes from the high frequency component, and 

the intense field yields the HHG with higher harmonic order. Then we have investigated the role 

of the anharmonicity. We have reconfirmed that as the anharmonic coefficient becomes large, the 

HHG spectrum with high harmonic order appears and the cut off energy increases. 

In quantum simulation, we have studied the initial state dependence, the relative phase dependence 

in two color external field, and the interference effect on the HHG spectrum. First we 

have took the lowest three states of Duffing oscillator {|Ψ0〉, |Ψ1〉, and |Ψ2〉} as an initial state 

57


|Ψ(0)〉, where we calculated the eigenfunctions and eigenvalues of Duffing oscillator by means of 

the FGH method. The initial state with more higher energy gives rise to the HHG spectrum 

with the more higher harmonic order. Next we performed the HHG simulation with a two-color 

laser, and examined the effect of the relative phase difference. However the change of the relative 

phase of two pulses does not show the clear difference on the HHG spectrum. Finally we have 

tried to control the HHG spectrum by using the wavepacket, where we adopted the three states 

{|Ψ0〉, (|Ψ0〉 + |Ψ1〉)/ √ 2, and (|Ψ0〉 + |Ψ1〉 + |Ψ2〉)/ √ 3} as the initial state |Ψ(0)〉. It is expected 

that the superposed state has many channel corresponding to each state to generate the HHG, and 

the HHG from some channel could give rise to the interference among some channels. From the 

resultant HHG spectrum, in almost all region, the superposed initial state with the higher energy 

state shows the stronger HHG spectrum, however, we could not find out clearly the interference 

effect. Namely three spectrum has almost the same shape, but we just found some peaks have a 

little difference in some region of the HHG spectrum. 

Last I would like to comment on the mechanism of the HHG. In order to explain the HHG from 

the rare gas by the intense laser, P.B. Corkum proposed the three-step model, where the ionization 

and tunneling of the electron due to the deformation of the Coulomb attractive potential by the 

strong electric field of laser pulse plays an very fundamental role. However in the Duffing model 

only with the bound states, we could observe the HHG spectrum. From these simulation, it seems 

that the anharmonicity is the fundamental quantity to induce the nonlinear optical response. 

References 

[1] P. B. Corkum (1993). Plasma perpective on strong field multiphoton ionization. J. Phys. Rev. 

A, 71, 1994 – 1997 

[2] C. Winderfeld, Ch. Spielmann, and G. Gerber (2008). Optimal control of high-harmonic generation. 

Rev. Mod. Phys., 80, 117 – 140 

[3] M.D. Feit, J.A. Fleck Jr. and A. Steiger (1982). Solution of the Schrödinger equation by a 

spectral method. J. Comp. Phys., 47, 412 – 433 

[4] M. D. Feit and J. A. Fleck (1983). Solution of the Schrödinger equation by a spectral method 

II: Vibrational energy levels of triatomic molecules a) . J. CHem. Phys., 78, 301 – 308 

[5] Ph. Balcou, Anne L’Huillier, and D. Escande (1996). High-order harmonic generation processes 

in classical and quantum anharmonic oscillators. J. Phys. Rev. A , 53, 3456 – 3468 

58

Molecular Dynamics Studies on Structure and Dynamics of Spherical Micelles 

Micke Rusmerryani a,b , Gia Septiana Wulandari a,b , Shuhei Kawamoto b , Hiroaki 

Saito b , Kiyoshi Nishikawa b ,Hidemi Nagao b 


Bandung 40132 Indonesia 

b Institute of Science and Engineering, Kanazawa University, Kakuma, Kanazawa 920-1192 Japan 

E-mail: micke@wriron1.s.kanazawa-u.ac.jp 

Abstract. Due to the soft and flexible structure, lipid molecule forms various shapes such as 

micelle, bilayer and vesicle. In these systems, since the spherical micelle can be applied to the 

application of drag delivery system, the analysis of detailed structure and dynamics of the micelle 

is important. In this study, we carried out molecular dynamics (MD) simulations of the spherical 

micelles dimer in water solvent to investigate the dynamical structure and correlated motion of 

the micelle dimer. The MD simulations were run under the constant NPT and NVT conditions 

with periodic boundary. We adopted the ASIC analysis, which is based on the aperture, symmetry, 

isotropy, and compactness of the micelle structure to analyze the shape fluctuations for each 

micelle. From this analysis, we show the stability and correlated motion of spherical micelle and 

investigate the patterns of synchronization motions between micelle dimer. The mutual fluctuations 

were periodically shown in the constant NVT simulation, implying that the existence of synchronization 

phenomena between micelle dimer. 

Keywords: spherical micelles, molecular dynamics, dynamics, synchronization 


Biological phospholipids show a self-assembly processes to form a certain aggregate such as micelles, 

vesicles, and membranes. In these systems, the micelle is an aggregate of surfactant molecules in 

aqueous solution. The micelle is formed by the competition between the hydrophobic and the 

electrostatic interactions of lipid molecule. The shape of micelle also depends on the molar density 

of lipid in aqueous solution. In the high lipid density condition, the lipid molecule aggregates so 

as to direct the head group of lipid to each other and forms the inverse micelle. 

Because of the soft and flexible structure, the structure (shape and size) of micelle fluctuates 

in aqueous solution and depends on both the component of the surfactant molecule and solution 

conditions such as the temperature and presence of impurities [1]. Also, it forms various structures 

such as the spherical, cylindrical, and rod-like structure. In these structures, because the spherical 

micelle structure is relatively stable in aqueous solution, the spherical micelle is expected to apply 

to drag delivery system. 

In the previous research [2], four structural parameters, aperture A, symmetry S, isotropy I, 

and compactness C (ASIC), were introduced to investigate the shape uctuation of micelle system. 

From the analysis of ASIC parameters at each time step, the structural fluctuation and correlated 

motion of the micelle were shown in detail. This analysis clearly showed the correlation between 

the isotropy I and compactness C. This technique could be expanded for other cases in biological 

dynamics. Other valuable informations can be shown by combining with the other parameters. In 

other research [3], the synchronization motion in mutual micelle clusters were implied in aqueous 

solution. Based on the previous research, it should be interesting to investigate the dynamical 

59

ISCS 2011 Selected Papers Vol.2 Micke Rusmerryani et al. 

(a) Chemical Structure of POPC (b) POPC Spherical Micelle 

(c) Spherical Micelles in Boxwater 

Figure 1: Initial Condition 

structure and the synchronization motion in mutual clusters such as two spherical micelles. Thermodynamic 

conditions will also be studied to figure out the effects on lipids dynamics. Our goal 

is to find out whether the dynamics of both micelle have any correlation. In this study, we thus 

carried out molecular dynamics (MD) simulations of the spherical micelle dimer in water solvent 

to reveal the dynamical structure and correlated motion of the micelle dimer system. We analyze 

the fluctuation of the spherical micelle by the ASIC analysis and investigate the synchronization 

motion between micelle dimer by the time correlation analysis. 

2 Computational Methods 

2.1 Initial Structure 

In this study, we used 8 POPC (1-palmitoyl-2-oleoyl-phosphatidycholine) lipids for each micelle. 

Figure 1 (a) shows the structure of POPC lipid. The POPC lipid has two hydrocarbon chains 

and one phosphatidylcholine (PC) head group [4]. The initial coordinates of the micelle dimer and 

water molecule were placed in the MD box by Packmol program [5]. The 11,326 TIP3P water were 

filled in the MD box (8.2 × 15.8 × 8.2 nm). Figure 1(c) shows the snapshot of initial structure of 

micelle dimer in the MD box. 

2.2 Molecular Dynamics Simulation 

In this study, two molecular dynamics simulations under the constant NPT and NVT conditions 

were carried out by NAMD 2.7b3 program package. We used the CHARMm36 force field [6] and 

TIP3P model for the POPC and water molecule, respectively. The periodic boundary condition 

60

ISCS 2011 Selected Papers Vol.2 Molecular Dynamics Studies on Spherical Micelles 

(a) After 10 ns NPT simulation 

(b) After 10 ns NVT simulation 

Figure 2: Final Snapshot 

was applied to the MD box, and the particle mesh Ewald (PME) method was adopted for the 

electrostatic interaction. The cutoff length for nonbond interaction in real space was 12 ˚A [7]. 

The constant NPT simulation is used for the system equilibrium. The MD box decreased until 

5.85 × 11.11 × 5.84 nm after 10 ns. The length of MD box fluctuated 0.36% during the simulation. 

We conformed the micelle dimer sufficiently equilibrated in 10 ns. After 10 ns, the MD simulation 

was continued to the constant NVT simulation for 10 ns. The effects due to the difference of the 

MD conditions on structural and dynamical behavior of micelle dimer are also investigated in this 

study. Both MD simulations were run under the constant temperature (T=300 K). Figure 2 shows 

the last snapshots of micelle dimer for each simulation at 10 ns. 

3 Analysis 

3.1 ASIC analysis 

In this study, the ASIC analysis was adopted to investigate the dynamical structure and correlated 

motion of the POPC spherical micelle dimer [2]. The ASIC analysis gives four structural 

parameters, aperture A, symmetry S, isotropy I, and compactness C of the micelle system. Each 

parameter can be calculated by using the defined vectors �r1(t), �r2(t) and � R(t) in the POPC lipid. 

The vector �r1(t) is applied for the unsaturated acyl chain, the vector �r2(t) is applied for the saturated 

acyl chain, and the vector � R(t) is given by averaging the vectors �r1(t) and �r2(t). The 

61


time-dependent ASIC parameters are expressed as following equations; 

A(t) = 1 

� 

� 

� 

� 

N 

N � 

|�r1i(t) × �r2i(t)|, (1) 

i=1 

S(t) = 1 

N | 

N� 

�Ri(t)|, (2) 

i=1 

I(t) = 1 

� 

� 

� 

N� N� 

� 

| 

N 

� Rj(t) × � Rk(t)|, (3) 

j=1 k=2,(k>j) 

C(t) = 1 

N 

N� 

| � Ri(t)|, (4) 

where, N is the total number of lipids in a micelles. We analyze the flexibility of micelle by 

assessing these ASIC parameters at each MD time steps. The detailed dynamics information 

about the dynamics of spherical micelles can be obtained by these four parameters. 

3.2 Time correlation and delayed time analysis 

The time correlation analysis was performed to investigate the correlated motion between micelle 

dimer in water solvent. The relaxation properties of micelle structure were evaluated by using 

time correlation function (TCF). The TCF is one of the most common tools to analyze the timedependent 

properties of physical variable and is useful to investigate the dynamics of micelle 

structure. The relaxation of structural parameter is estimated by the sufficient statistical average 

of the time series of structural parameter. The time-correlation function (TCF) of variable A(t) is 

defined as following equation; 

CAA(dτ) = 1 

T − τ 

i=1 

� T −τ 

0 

A(t) · A(t + τ)dt, (5) 

where τ is lag time[8]. This equation is the same as the form of auto-correlation function, when 

the A(t) and A(t + τ) are the same variable, whereas the cross-correlation function correlation is 

defined by the two different variables. For example, the time correlation of dynamical properties 

A(t) and B(t) is expressed as 

CAB(dτ) = 1 

T − τ 

� T −τ 

0 

A(t) · B(t + τ)dt. (6) 

Delayed time analysis was evaluated by calculating the direction correlation between the micelle 

dimer [3]. From the Eq.2, we dene symmetry vector � S(t), by using the vector � R(t). The direction 

correlation (DC) is expressed by following equation; 

Dc ij (t, t ′ ) = � Si(t) · � Sj(t ′ ) 

| � Si(t)|| � Sj(t ′ . (7) 

)| 

This analysis gives the degree of parallel between the i th and j th micelle. When the DC equals 

to 1, the micelle dimer should have parallel orientation. Conversely, when the DC equals to -1, 

the micelle dimer are in antiparallel condition. This analysis can be applied to investigate the 

synchronization motion between micelle dimer. 

62



Figure 3: Time (ns) vs RMSD (nm 2 ) 

Figure 4: Time (ns) vs Distance (nm) 

From each MD simulation, we obtained trajectories of micelle dimer in water solvent. Here, we 

simply call those micelles as the micelle 1 and micelle 2. We first calculated the root mean square 

displacement (RMSD) of each micelle to assess the equilibrium of the system during the simulations. 

The observed RMSD in the constant NPT and NVT simulation is shown in Figure 3. The results 

showed that the structures of both micelles in the constant NPT condition were equilibrated after 

5 ns. However in NVT simulation, the RMSD of micelle 1 increased after 5 ns, showing the large 

displacement of micelle 1 in the system. 

Figure 4 shows the distance between the center of mass of each micelle. We found that the 

micelles were getting closer to each other, and then went back to the initial distance in the constant 

NPT MD simulation. In NVT simulation, the observed micelle distance was found to be flctuated 

around the 5.5 nm. This difference could be cased by the difference of simulation conditions; the 

fluctuation of MD box possibly affects the dynamics of micelle. The distance between micelle dimer 

in NVT simulation was found to be larger than that in NPT simulation. 

63


Figure 5: Time (ns) vs ASIC-NPT plotted every 20 ps 

Figure 5 and 6 shows the observed ASIC parameters as a function of MD time steps. We found 

that the structural parameter of micelle A, I and C were high values whereas S showed low value 

in both constant NPT and NVT condition. In the constant NVT condition, the ASIC parameters 

were found to fluctuate around average values. In NPT simulation, the motion of lipid chain tail 

are more exible than in NVT simulation, because it has wider range of A-uctuation. However, the 

constant NVT simulation shows a higher A value. In the symmetry parameter S, the micelle 2 

was more symmetric than micelle 1 in NPT simulation, whereas the opposite symmetry character 

was shown in NVT simulation. We also found that the most symmetric structure was micelle 2 in 

NPT ensemble. Figure 5 shows that the micelle 2 reached nearly zero at some points, indicating 

that the micelle 2 has sufficient symmetry at these time steps. 

Some interesting results were shown in the parameters of isotropy I and compactness C. In 

NPT simulation, the highest (or the lowest) I was exactly shown at the same time when the 

parameter C showed the highest (or the lowest) value. This implies that there is a correlation 

between the isotropy I and compactness C. We also found that both micelles have quite similar 

distribution of C fluctuation in NPT simulation. 

To reveal the correlation between micelle dimer and the correlation in themself, the time correlation 

were calculated by using Eq. (5) and (6). The observed TCF are shown in Figure 7. The 

observed TCF of micelle 1 in the constant NPT simulation monotonically decrease value in first 3 

64


Figure 6: Time (ns) vs ASIC-NVT plotted every 20 ps 

ns, implying the relaxation of TCF of each micelle in this time. However, further statistic average 

should be taken for the clear this relaxation property. On the other hand, in the constant NVT 

simulation, we did not see the usual relaxation in each micelle in this time range. This implies the 

there is no correlation in each micelle. The larger correlation time or sufficient statistic average 

should be used for the observation of relaxation of the TCF. 

The direction correlation was estimated by Eq. 7. The calculated DC in the constant NPT 

and NVT condition are shown in Figure 8. We found that the observed correlation values sometimes 

show parallel direction. The probability distribution of DC in the constant NPT simulation 

shows that the peak of distribution appears around zero. However, in NVT simulation, mutual 

fluctuations were shown at many times, suggesting that two micelles have the similar orientation 

during the simulation. 

Figure 9 shows the calculated direction correlation with delayed time of 1 ns. In this figure, 

the direction correlation was plotted with gray scaled color; DC = 1 was represented as white 

color, and DC = 1 was represented as black color. Mutual fluctuations periodically occur in NVT 

simulation. On the other hand, there are unsmooth patterns at several times. This result shows 

that the dynamics of each micelle are correctively oscillated in this period of time, indicating the 

synchronization motion of micelle dimer. 

65


5 Summary 

Figure 7: Autocorrelation of Symmetry 

Figure 8: Direction correlation at the same time 

We have carried out the molecular dynamics (MD) simulation of the micelle dimer in water solvent 

to investigate the dynamical structure and correlation motion of the micelle system. We found 

that the structure of micelle was randomly fluctuated during MD time steps. The simulation also 

showed the sufficient correlation between the isotropy and compactness of micelle structure. We 

analyzed the time correlation function of each micelle in both constant NPT and NVT simulations 

and showed the difference of relaxation of symmetry fluctuation of micelle. We however found that 

further statistic average should be taken for the clear this relaxation property. In the analysis of 

direction correlation between micelle dimer, the dynamics of each micelle were found to be oscillated 

correctively in the period of time, indicating the synchronization motion of micelle dimer. In 

the future, it is interesting to investigate another method to reveal the existence of synchronization. 

Furthermore, the concepts of limit cycle and synchronization might help us to analyze the 

phenomena of synchronization. 

66


References 

Figure 9: Color-mapped of DC with delayed time 1 ns 

[1] P. S. Goyal, V. K. Aswal (2001). Micellar structure and inter-micelle interactions in micellar 

solutions: Results of small angle neutron scattering studies. Current Science. 

[2] A. Purqon, A. Sugiyama, H. Nagao, K. Nishikawa (2007). Aperture, symmetry, isotropy, and 

compactness analysis and their correlation in spaghetti-like nanostructure dynamics. Chem. 

Phys. Lett., 443, 356 - 363. 

[3] A. Purqon, H. Nagao, K. Nishikawa (2008). Synchronization Patterns in Spaghetti-Like Nanoclusters. 

Int. Journal of Quantum Chem., 108, 2870 -2880. 

[4] Hanahan, Donald J. (1997). A Guide to Phospholipid Chemistry, Oxford University Press, 

New York. 

[5] L. Martinez, R. Andrade, E. G. Birgin, J. M. Martinez (2008). Packmol: A Package for 

Building Initial Configurations for Molecular Dynamics Simulations. Journal of Comp. Chem., 

30, 2157 - 2164. 

[6] J. B. Klauda, et all (2010). Update of the CHARMM All-Atom Additive Force Field for Lipids: 

Validation on Six Lipid Types. J. Phys. Chem., 114, 7830 - 7843. 

67


[7] D. Frenkel, B. Smith (2002). Understanding Molecular Simulation: From Algorithms to Applications, 

Academic Press, USA. 

[8] J. Ramirez, S. K. Sukumaran, B. Vorselaars, A. E. Likhtman (2010). Efficient on the fly 

calculation of time correlation functions in computer simulations. The Journal of Chem. Phys., 

133, 154103. 

68

Temperature Effects on Dynamics of Spherical Micelles : 

A Molecular Dynamics Study 

Gia Septiana Wulandari 1,2 , Micke Rusmerryani 1,2 , Shuhei Kawamoto 1 , 

Hiroaki Saito 1 , Kiyoshi Nishikawa 1 , Hidemi Nagao 1 

1 Computational Science, Graduate School of Natural Science and Technology, Kanazawa 

University, Japan 

2 Computational Science, Graduate School of Mathematics and Natural Science, Bandung 

Institute of Technology, Indonesia 

E-mail: gia@wriron1.s.kanazawa-u.ac.jp 

Abstract. We studied the temperature effect on the dynamics of spherical micelle dimer in water 

solvent by using molecular dynamics (MD) simulation. For this purpose, we carried out the 

MD simulations of 8-8 spherical POPC micelle dimer in 11,326 TIP3P water molecules under 

the constant NPT condition for 10 ns and continued the MD simulation under the constant NVT 

condition for 10 ns. We ran the MD simulations of this system at two different temperatures, 340 

K and 370 K. The dynamical behavior of the micelle was analyzed by calculating ASIC parameters. 

We found that the effects of temperature on stuctures and dynamics of micelle were different for 

the constant NPT and NVT condition. 

Keywords: Molecular Dynamics, lipid, POPC, temperature effects 


Biological phospholipids show self-assembly processes to form certain clusters such as micelle, 

vesicle, and membrane[1, 6]. Micelle is an aggregate of surfactant molecules in aqueous solutions[9]. 

The self-assembly is a term used to describe processes in which a disordered system of pre-existing 

components forms an organized structure or pattern as a consequence of specific local interactions 

among the components themselves without external direction. 

In the computational study of micelle systems, several groups have studied the temperature 

effects on dynamics of micelle so far. Acep Purqon in his doctoral thesis gave an interesting 

inspiration to this study. He studied seven issues on bionanocluster fluctuations[1]. One of the 

issues is to identify solvent effects on the micelle. He analyzed the effects of salty water and 

temperature on the phospholipids of micelle. In this study, four parameters, aperture A, symmetry 

S, isotropy I, and compactness C (ASIC) of the micelle system were introduced to investigate the 

structural character of the micelle in water solvent. From these structural parameter analysis, he 

found that the symmetry S and aperture A parameters increase as the temperature rises, showing 

the irregular structure and rapid tail fluctuation of the micelle system. The effects of salt and 

temperature consequently contribute to shape fluctuations as well. In contrast, the micelle system 

shows wider fluctuation in pure water. 

However, the temperature effects on the self-aggregation of micelle and structural stability of 

the lipid of the micelle in water solvent are still not clear. In this study, we therefore analyze the 

structures and dynamics of small spherical micelle dimer consisting of phospholipids molecules by 

molecular dynamics (MD) simulations. We also study the stability of spherical micelles at two 

temperatures and describe the temperature effects on the dynamics of the spherical micelles. 

69

ISCS 2011 Selected Papers Vol.2 Gia et al. 

2 Computational Details 

In this study, we used 16 palmitoyloleoyl-phosphatidylcholine (POPC) lipids, which is a diacylglycerol 

and phospholipid found in human or animal, for the micelle dimer simulation. To construct 

the initial condition for the system, we used Packmol program [4]. We divided those lipids into 

two spherical initial conditions, 8 lipids for each spherical system as in Figure 1(a). Then we put 

those lipids into the MD box (82 × 158 × 82 ˚ A) filed with 11,326 TIP3P water molecules (Figure 

1(b)). 

2.1 Molecular Dynamics Simulation 

(a) lipids (b) initial condition (c) POPC 

Figure 1: POPC. (a) shows 8-8 spherical POPC lipid we used as initial condition for this system. (b) shows initial 

condition for this system. (c) shows how did we define two vectors to calculate ASIC parameter 

We carried out the MD simulations by using NAMD2.7.b3 [7] program with CHARMM36 force 

field [10, 5] with 12 ˚ A cutoff radii for nonbond interactions. We ran the MD simulations of the 

system at 340 K and 370 K under the constant pressure condition (NPT ensemble) for 10 ns then 

continued the simulation under the constant volume condition (NVT ensemble) for 10 ns. By using 

NPT ensemble, the water and MD box size should be equilibrated in a few ns. The constant NPT 

simulation was adopted to prevent the effect of the fluctuation of MD box on the dynamics of 

micelle dimer. We then continued the MD simulation under the constant NVT conditions, without 

change the volume of MD box. We used the last coordinate of micelle dimer in the constant 

NPT simulation as the initial condition for the constant NVT simulation. The effects due to 

the difference of the MD conditions on structural and dynamical behavior of micelle dimer were 

investigated in this study. We carried out the MD simulations of micelle dimer system at 340 K 

and 370 K to investigate the effect of temperature difference on this system. 

2.2 Analysis Method 

After the MD simulations, we analyzed the structural and dynamical behavior of the micelle dimer. 

First, we calculated the root mean square displacement (RMSD) to assess the system equilibrium. 

The RMSD is frequently used to measure the displacement of the system at time t form the initial 

70

ISCS 2011 Selected Papers Vol.2 Temperature Effects on Dynamics of Spherical Micelle 

coordinate. The RMSD ise calculated by following equation; 

� 

� 

� 

RMSD(t) = � 1 

N� 

(R(i, t) − R(i, 0)) 

N 

2 

i=1 

where N is the number of lipid molecule, t is the MD time step, and R(i, t) is the coordintes of lipid 

molecules pf micelle. We also calculated symmetry parameter S, which is one of four structural 

parameters given by Acep et al. [1]. Although there are four parameters, aperture A, symmetry 

S, isotropy I, and compactness C for analysis of micelle system, we only investigate the symmetry 

parameter S of micelle in this study. To calculate symmetry S, we defined three vectors −→ R1(t), 

−→ 

R2(t), and −→ r (t) in each POPC lipid as shown in Figure 1(c). These vectors are defined by the two 

atoms, which are a phosphate atom in the head group and the hydrocarbon atom of lipid chain 

tail. The vector −→ R1(t) is applied for the unsaturated acyl chain, the vector −→ R2(t) is applied for the 

saturated acyl chain, and the vector −→ r (t) is given by averaging the vectors −→ R1(t) and −→ R2(t). The 

symmetry parameter S(t) at each time steps is estimated by following equation; 

S(t) = 1 

N 

� � 

� N� � 

� 

� 

−→ � 

ri (t) � 

� � . 

By this calculation, we can assess a symmetry property of the micelle. The low S value means 

that the system has high symmetry. From the time series of the calculated symmetry value S(t), 

we analyze the dynamics of spherical micelle. We also calculated time correlation function (TCF) 

and direction correlation (DC) to investigate the correlation between micelle dimer in system. The 

time correlation function is defined as 

C(t) = 1 

T 

�T 

0 

i=1 

S1(t ′ )S2(t ′ + t)dt ′ , 

where Si is a symmetry value of micelle i. The time correlation between S1(t) and S2(t ′ +t) should 

be evaluated by ensemble average of these values. We can also estimate autocorrelation function 

of symmetry parameter of each micelle when we take Si of the same micelle in this equation. We 

compare the calculated TCF between S1 and S2, and the autocorrelation function of symmetry Si 

of each micelle. 

We also calculated direction correlation (DC) to see the correlation between micelle dimer in 

direction. This calculation shows the degree parallel of micelle dimer. We evaluated this correlation 

by following equation; 

D ij 

C (t, t′ −→ 

Si(t) 

) = 

−→ Sj(t ′ ) 

| −→ Si(t)|| −→ Sj(t ′ )| , 

where −→ S (t) means the average of lipid vector in the micelle, −→ S (t) = 1 

N 

DC value equals to zero, they have anti-parallel direction. 


N� −→ 

ri (t). If the calculated 

From each MD simulation, we obtained trajectories of two micelles in water solvent. Here, we 

simply call those micelles as the micelle 1 and micelle 2. Figure 2 shows the distance between the 

71 

i=1


(a) NPT at 340 K (b) NPT at 370 K 

(c) NVT at 340 K (d) NVT at 370 K 

Figure 2: Distance between the center of micelle 1 and the center of micelle 2. At higher temperature di distance 

is getting closer. 

center of mass of micelle 1 and the center of micelle 2. We found that the micelle 1 and micelle 

2 were getting closer at higher temperature (T = 370K) as the MD time step increases in the 

constant NVT condition. In order to assess the system equilibrium, we calculated RMSD of the 

micelles. 

Figure 3 shows the calculated RMSD of each micelle in several conditions. We found that the all 

RMSD were roughly equilibrated in 10 ns MD time. We then analyzed the fluctuation of symmetry 

parameter S(t) as a function of time. The results in both constant NVT and NPT simulations at 

two temperatures are shown in Figure 4. The results show that the system is randomly fluctuate 

during the simulation time. 

Table 1 shows standard deviation of symmetry parameter S. The small standard deviation indicates 

that the data points tend to be very close to the average value, whereas the large standard 

deviation indicates that the data spread out in wide range. We found that the standard deviation 

obtained from the constant NPT simulation shows a larger value than that in the constant 

NVT simulation, indicating that the structure of micelle in the NPT simulation should be largely 

fluctuated. 

For further analysis, we calculated the TCF of micelle in each MD condition. The calculated 

results are shown in Figure 5. The dotted line shows the time correlation function as a function 

72




Figure 3: RMSD calculation. At lower temperature, system seems more equilibrium than at higher temperature. 

Ensemble T Micelle SD Symmetry 

NPT 

340 K 

370 K 

1 

2 

1 

2 

2.62 

1.99 

6.48 

3.13 

NVT 

340 K 

370 K 

1 

2 

1 

2 

4.58 

4.37 

2.16 

4.32 

Table 1: Standard Deviation of Symmetry 

of time steps between the micelle 1 and micelle 2. We did not see the usual relaxation between 

the symmetry of micelle dimer in this time range. This imply the there is no correlation between 

micelle 1 and 2. The larger correlation time or sufficient statistic average should be used for the 

observation of relaxation of the TCF. The other lines, which indicate the autocorrelation function 

of each micelle, show different result with the dotted line. The observed TCF monotonically 

decrease value, implying the relaxation of TCF of each micelle in this time. However, further 

statistic average should be taken for the clear this relaxation property. 

73


(a) NPT at 340 K 

(b) NPT at 370 K 

(c) NVT at 340 K 

(d) NVT at 370 K 

Figure 4: Symmetry. It shows that system are fluctuative. 

Besides analyzing correlation in time, we investigate the correlation of micelles in direction. As 

shown in Figure 6, the direction of micelle 1 and micelle 2 were shown to be randomly changed 

during the MD time steps in all simulation conditions. Figure 7 shows that, the micelle 1 and micelle 

2 are more anti-parallel under the constant NPT condition at higher temperature (T = 370K), 

while they are more parallel under constant NVT condition at the same temperature. 

4 Conclusion 

We have carried out the molecular dynamics simulations of spherical micelle dimer in water solvent 

at two different temperatures under the constant NPT and NVT condition to investigate the 

temperature effects on this system. We evaluated the symmetry parameter S of the micelle dimer 

system at each MD time steps and showed that the micelle largely uctuates at higher temperature 

under the constant NPT condition, while the large fluctuation was shown at lower temperature 

in the constant NVT condition. In the calculation of the time correlation function of micelle 

74




Figure 5: Time Correlation Function 



Figure 6: Direction Correlation 

75




Figure 7: Distribution of Direction Correlation 

system, we found that there is not any correlation between micelle 1 and micelle 2, whereas the 

micelles have sufficient correlation with themselves. Also at constant NPT condition, the micelle 1 

and micelle 2 are more anti-parallel at higher temperature, while they are more parallel at higher 

temperature in the constant NVT condition. 

References 

[1] A. Purqon (2008). Shape Fluctuation Modes and Synchronization Patterns in Self-Assembly 

Aggregate Bionanocluster, Kanazawa University, Japan. 

[2] C. J. Högberg; A. M. Nikitin; A. P. Lyubartsev. (2008). Modification of the CHARMM Force 

Field for DMPC Lipid Bilayer. J. Comput. Chem., 29, 2359-2369. 

[3] C. Moitzi; I. Portnaya; O. Glatter; O. Ramon; D. Danino. (2008). Effect of Temperature 

on Self-Assembly of Bovine -Casein above and below Isoelectric pH. Structural Analysis by 

Cryogenic-Transmission Electron Microscopy and Small-Angle X-ray Scattering. Langmuir, 

24, 3020-3029. 

[4] L. Martinez, R. Andrade, E. G. Birgin, J. M. Martinez (2008). Packmol: A Package for 

Building Initial Configurations for Molecular Dynamics Simulations. Journal of Comp. Chem., 

30, 2157 - 2164. 

76


[5] J. B. Klauda, et al. (2010). Update of the CHARMM All-Atom Additive Force Field for Lipids: 

Validation on Six Lipid Types. J. Phys. Chem., 114, 7830 - 7843. 

[6] John, K. and Bar, M. (2005). Alternative Mechanisms of Structuring Biomembranes: Self- 

Assembly versus Self-Organization. Phys. Rev. Lett., 95, 198101. 

[7] M T Nelson, et al. (1996). NAMD: a Parallel, Object-Oriented Molecular Dynamics Program. 

International Journal of High Performance Computing Applications, 10, 251-268. 

[8] O. Domenech; S. M. Montero; J. H. Borell. (2006). Colloids and Surface, 47, 102. 

[9] S. Pal; S. Balasubramanian; B. Bagchi. (2002). Temperature Dependece of Water Dynamics 

at an Aquoeous Micellar Surface : Atomistic Molecular Dynamics Simulation Studies of a 

Complex System. J. Chem. Phys., 117, 2852. 

[10] X. Toxvaerd. (1993). Molecular Dynamics at Constant Temperature and Pressure. Phys. Rev. 

E, 47, 343-350. 

77

International Symposium on Computational Science 2011 

Date: February 15 – 17, 2011 

Venue: Kanazawa University, Kakuma Campus, Kanazawa, Japan 

Organized by: 

Building of Natural Science and Technology, 

Lecture rooms n.103 and n.104 (Feb. 15-16), 

Lecture room n.301 (Feb. 17) 

Organizing Committee: 

Department of Computational Science, 

Faculty of Science, Kanazawa University 

Faculty of Mathematics and Natural Sciences, 

Bandung Institute of Technology 

K. Svadlenka (Kanazawa University) 

M. Saito (Kanazawa University) 

K. Nishikawa (Kanazawa University) 

S. Omata (Kanazawa University) 

H. Nagao (Kanazawa University) 

S. Miura (Kanazawa University) 

M. A. Martoprawiro (Bandung Institute of Technology) 

S. Haryono (Bandung Institute of Technology) 

R. Simanjuntak (Bandung Institute of Technology) 

R. Hertadi (Bandung Institute of Technology) 

Sponsored by: 

Fujitsu Limited 

JSPS Grant-in-Aid (No. 21654013, S. Omata) 

v

February 15 (Tuesday): 1 st day 

10:00-10:30 Registration 

10:30-10:40 Opening address 

Symposium Program 

Morning session (room 103, chairperson: Mineo Saito) 

10:40-11:20 Laksana Tri Handoko (Indonesian Institute of Sciences) 

Modeling nano particle dynamics using statistical mechanics approach 

11:20-12:00 Suprijadi Haryono (Bandung Institute of Technology) 

Uniaxial stress effect on crystal dislocations movement and crack propagation in cubic crystal 

Lunch break 

Afternoon session 1 (room 103, chairperson: Kiyoshi Nishikawa) 

14:00-14:40 Harno Pranowo (Universitas Gadjah Mada) 

Microsolvation conformation of crown ether-transition metal cation complexes by ab initio 

method 

14:40-15:20 Muhamad A. Martoprawiro (Bandung Institute of Technology) 

Computational study of iron(II)-based spin transition complex 

Afternoon session 2 (room 104, chairperson: Karel Svadlenka) 

14:00-14:40 Shinya Okabe (Iwate University) 

The existence of shortening-straightening flow for non-closed planar curves with infinite length 

14:40-15:20 Hideki Murakawa (University of Toyama) 

Numerical simulations of nonlinear cross-diffusion systems using a linear scheme 

Coffee & Poster break 

Evening session (room 103, chairperson: Shinichi Miura) 

16:00-16:40 Makoto Iima (Hokkaido University) 

Numerical simulation and mathematical analysis of flapping flight problem 

16:40-16:55 Muhamad Koyimatu (Kanazawa University & Bandung Institute of Technology) 

Quantum control of high harmonic generation in anharmonic potential 

16:55-17:10 Athiya M. Hanna (Kanazawa University & Bandung Institute of Technology) 

High-pressure crystal structure prediction using evolutionary algorithm simulation 

17:10-17:25 Nyayu Siti Nurainun (Kanazawa University & Bandung Institute of Technology) 

Hydrogen impurities in graphene: first principles study 

17:25-17:40 Micke Rusmerryani (Kanazawa University & Bandung Institute of Technology) 

Molecular dynamics studies on structure and dynamics of spherical micelles 

17:40-17:55 Gia Septiana Wulandari (Kanazawa University & Bandung 

Institute of Technology): 

Temperature effects on dynamics of spherical micelles: a molecular dynamics study 

vi

February 16 (Wednesday): 2 nd day 

Morning session (room 103, chairperson: Shinichi Miura) 

10:00-10:40 Hitoshi Imai (University of Tokushima) 

Numerical simulation on non-existence and non-uniqueness of solutions for the Tricomi 

equation 

10:40-11:20 Sparisoma Viridi (Bandung Institute of Technology) 

Self-siphon simulation using molecular dynamics method: a preliminary study 

11:20-12:00 Zaki Su’ud (Bandung Institute of Technology) 

Unprotected loss of flow simulation in fast reactor safety analysis 

Lunch break 

Afternoon session 1 (room 103, chairperson: Fumiyuki Ishii) 

14:00-14:25 Hiroaki Saito (Kanazawa University) 

Hydration property of globular proteins: a molecular dynamics study 

14:25-14:50 Kazutomo Kawaguchi (Kanazawa University) 

The molecular dynamics simulation of protein complexes 

14:50-15:15 Tatsuki Oda (Kanazawa University) 

Toward a computer modeling in magnetic anisotropy and its electric-field-control for 

nano-structures 

15:15-15:40 Shinichi Miura (Kanazawa University) 

Variational path integral molecular dynamics method applied to molecular vibrational 

fluctuations 

Afternoon session 2 (room 104, chairperson: Hideki Murakawa) 

14:00-14:40 Katsuyuki Ishii (Kobe University) 

Mathematical analysis for an approximation scheme to mean curvature flow 

14:40-15:20 Takeshi Fukao (Kyoto University of Education) 

Variational inequality for the Navier-Stokes equations with time dependent constraint 

15:20-15:40 Elliott Ginder (Kanazawa University) 

A variational method for volume-controlled membrane motions 


Evening session 1 (room 103, chairperson: Tatsuki Oda) 

16:20-16:50 Phung Thi Viet Bac (AIST) 

Theoretical investigations of hydrogen diffusion into metallic nanoparticles 

16:50-17:15 Fumiyuki Ishii (Kanazawa University) 

First-principles study of ferroelectricity in hydrogen-bonded molecular systems 

17:15-17:40 Mineo Saito (Kanazawa University) 

First-principles calculations of defects in graphenes 

17:40-17:55 Shuhei Kawamoto (Kanazawa University) 

Free energy of peptide to permeate lipid bilayer membrane -- coarse-grained simulation 

17:55-18:10 Muhammad Ilyas (Kanazawa University & Bandung Institute of Technology) 

Generalized extended Hamming codes over Galois ring of characteristic 2 n 

vii

Evening session 2 (room 104, chairperson: Takeshi Fukao) 

16:20-17:00 Naoto Nakano (Hokkaido University) 

On steady simple shear flows of a continuum model with density gradient-dependent stress 

17:00-17:25 Hiroshi Iwasaki (Kanazawa University) 

Numerical simulation of Biot's consolidation problem 

17:25-17:40 Triati Dewi Kencana Wungu (Osaka University) 

Study of lithium montmorillonite by ab initio calculation 

February 17 (Thursday): 3 rd day 

Morning session (room 301, chairperson: Hiroaki Saito) 

9:20-9:35 Putu Harry Gunawan (Kanazawa University & Bandung Institute of Technology) 

Simulation of surface detection and surface tension with smoothed particle hydrodynamics 

9:35-9:50 Mourice C. K. Woran (Kanazawa University & Bandung Institute of Technology) 

Simulation of fluid-solid interaction using moving particle semi-implicit and spring-mass 

system 

9:50-10:05 Ruddy Kurnia (Kanazawa University & Bandung Institute of Technology) 

A novel scheme smoothed particle hydrodynamics to overcome energy loss 

10:05-10:20 Christian Fredy Naa (Kanazawa University & Bandung Institute of Technology) 

Explicit step improvement on moving particle semi-implicit and its analysis by using surface 

detection algorithm 


10:50-11:30 Akhmaloka (Bandung Institute of Technology) 

Thermophilic microorganisms and thermostable enzyme from Indonesia hot springs 

11:30-12:00 Hidemi Nagao (Kanazawa University) 

Reduction potential of blue copper proteins 

viii

List of Participants 

Akhmaloka Rector of Bandung Institute of Technology, Indonesia 

Phung Thi Viet Bac 

Takeshi Fukao 

Elliott Ginder 

Putu Harry Gunawan 

Laksana Tri 

Handoko 

Athiya Mahmud 

Hanna 

Suprijadi Haryono 

Nanosystem Research Institute, National Institute of Advanced Industrial Science 

and Technology (AIST), Japan, E-mail: phung.bac@aist.go.jp 

Department of Mathematics, Faculty of Education, Kyoto University of Education, 

Japan, E-mail: fukao@kyokyo-u.ac.jp 

Graduate School of Natural Science and Technology, Kanazawa University, Japan, 

E-mail: eginder@polaris.s.kanazawa-u.ac.jp (PhD student) 

KU-ITB Double-Degree Program* Master Student, 

E-mail: erik_mathboy@yahoo.com 

Group for Theoretical and Computational Physics Research Center for Physics, 

Indonesian Institute of Sciences, Indonesia, E-mail: handoko@teori.fisika.lipi.go.id 


E-mail: athiya_mh@yahoo.com 

Faculty of Mathematics and Natural Sciences, Bandung Institute of Technology, 

Indonesia, E-mail: supri@fi.itb.ac.id 

Yasuaki Hiwatari Toyota Physical and Chemical Research Institute, Japan 

Makoto Iima 

Department of Mathematics, Hokkaido University, Japan, 

E-mail: makoto@nsc.es.hokudai.ac.jp 

Muhammad Ilyas KU-ITB Double-Degree Program* Master Student, E-mail: reiken7@gmail.com 

Hitoshi Imai 

Fumiyuki Ishii 

Katsuyuki Ishii 

Hiroshi Iwasaki 

Kazutomo 

Kawaguchi 

Shuhei Kawamoto 

Masaki Kazama 

Muhamad Koyimatu 

Ruddy Kurnia 

Wicharn 

Lewkeeratiyutkul 

Department of Applied Physics and Mathematics, Faculty of Engineering, 

University of Tokushima, Japan, E-mail: imai@pm.tokushima-u.ac.jp 

Institute of Science and Engineering, Kanazawa University, Japan, 

E-mail: fumiyuki@kanazawa-u.ac.jp 

Faculty of Maritime Sciences, Kobe University, Japan, 

E-mail: ishii@maritime.kobe-u.ac.jp 


E-mail: iwasaki@cs.s.kanazawa-u.ac.jp 


E-mail: kkawa@wriron1.s.kanazawa-u.ac.jp 

Graduate School of Natural Science and Technology, Kanazawa University, Japan, 

E-mail: kawamoto@wriron1.s.kanazawa-u.ac.jp (PhD student) 

Fujitsu Limited Next Generation Technical Computing Unit, 

E-mail: kazama.masaki@jp.fujitsu.com 


E-mail: koyimatu@wriron1.s.kanazawa-u.ac.jp 


E-mail: ruddy.kurnia@gmail.com 

Department of Mathematics, Faculty of Science, Chulalongkorn University, 

E-mail: Wicharn.L@chula.ac.th 

ix

Muhamad 

Abdulkadir 

Martoprawiro 

Khamron Mekchay 

Shinichi Miura 

Hideki Murakawa 

Christian Fredy Naa 

Hidemi Nagao 

Faculty of Mathematics and Natural Sciences, Bandung Institute of Technology, 

Indonesia, E-mail: muhamad@chem.itb.ac.id 

Department of Mathematics, Faculty of Science, Chulalongkorn University, 

Email: k.mekchay@gmail.com 


E-mail: smiura@mail.kanazawa-u.ac.jp 

Graduate School of Science and Engineering for Research, University of Toyama, 

Japan, E-mail: murakawa@sci.u-toyama.ac.jp 


E-mail: chris_mail@yahoo.com 


E-mail: nagao@wriron1.s.kanazawa-u.ac.jp 

Naoto Nakano Hokkaido University, Japan, E-mail: nakano.naoto@gmail.com 

Kiyoshi Nishikawa 

Nyayu Siti Nurainun 

Tatsuki Oda 

Shinya Okabe 

Seiro Omata 

Harno Dwi Pranowo 

Micke Rusmerryani 

Hiroaki Saito 

Mineo Saito 

Zaki Su'ud 

Karel Svadlenka 


E-mail: kiyoshi@wriron1.s.kanazawa-u.ac.jp 


E-mail: nyayu@cphys.s.kanazawa-u.ac.jp 



Faculty of Humanities and Social Sciences, Environmental Sciences, Iwate 

University, Japan, E-mail: okabes@iwate-u.ac.jp 


E-mail: omata@kenroku.kanazawa-u.ac.jp 

Austrian-Indonesian Center for Computational Chemistry, Chemistry Department, 

Faculty of Mathematics and Natural Sciences, Universitas Gadjah Mada, 

Yogyakarta, Indonesia, E-mail: harnodp@ugm.ac.id 


E-mail: micke@wriron1.s.kanazawa-u.ac.jp 


E-mail: saito@wriron1.s.kanazawa-u.ac.jp 


E-mail: m-saito@cphys.s.kanazawa-u.ac.jp 

Department of Physics, Bandung Institute of Technology, Indonesia, 

E-mail: szaki@fi.itb.ac.id 


E-mail: kareru@staff.kanazawa-u.ac.jp 

Masako Takasu Tokyo University of Pharmacy and Life Sciences, E-mail: takasu@toyaku.ac.jp, 

Nuclear Physics and Biophysics Research Division, Faculty of Mathematics and 

Sparisoma Viridi Natural Sciences, Bandung Institute of Technology, Indonesia, 

E-mail: dudung@fi.itb.ac.id 

Mourice Ceisper 

Kevin Woran 


E-mail: moris_3gun@polaris.s.kanazawa-u.ac.jp 

x

Gia Septiana 

Wulandari 

Triati Dewi 

Kencana Wungu 

Mieko Yamada 


E-mail: gia@wriron1.s.kanazawa-u.ac.jp 

Department of Precision Science & Technology and Applied Physics, Graduate 

School of Engineering, Osaka University, Japan, 

E-mail: triati@dyn.ap.eng.osaka-u.ac.jp 


E-mail: myamada@kenroku.kanazawa-u.ac.jp 

* This Double-Degree Program is an educational program based on the agreement of cooperation 

between Kanazawa University and Bandung Institute of Technology. Therefore, the affiliation of 

students participating in this program is as follows: 

Graduate School of Natural Science and Technology, Kanazawa University, Japan & 


xi

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