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```					      Transport phenomena and structure
formation at micro/nanometerscale in
biomedicine and material science
   Daniel Vizman, West University of Timisoara, Faculty of Physics
   Victor Sofonea, Center for Fundamental and Advanced Technical
Research, Romanian Academy – Timisoara Branch
   Titus Beu, Babes-Bolyai University, Faculty of Physics, Cluj- Napoca
   Adrian Neagu, “Victor Babes” University of Medicine and Pharmacy,
Timisoara

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Challenge: Multiscale simulation

Continuum media mechanics
Particle
Distribution function     mass, momentum, energy
Position momentum,
Boltzmann Equation              equations
interaction forces

MOLECULAR                         MESOSCALE                 MACROSCALE
LEVEL (~10-9m)                      (10-6m)                   (>10-3m)

•Monte Carlo                     •Lattice Boltzmann         •Finite Element
•Molecular Dynamics              •Phase Field               •Finite Volume

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UNIVERSITATEA DE MEDICINĂ ŞI FARMACIE
“VICTOR BABEŞ” TIMIŞOARA,
CENTRUL DE MODELARE A SISTEMELOR
BIOLOGICE ŞI ANALIZA DATELOR

MONTE CARLO SIMULATIONS

 The biological tissue is represented on a cubic lattice.

 Cell rearrangements are obtained by random sampling.

P 1                   if E  0
 Probability of acceptance
P  exp(  E ET )     otherwise

ET = effective measure of cell motility.
Monte Carlo simulations yield energetically favourable tissue
conformations by minimizing the total energy of adhesion.
3
20 000 MCS            100 000 MCS
EXAMPLE
 Spontaneous
emergence of tubular
structures:                                     Type 0
Aggregate:
•200 m diameter
•Rint/Rext = 0.8                              Type1

•2060 cells
•2109 nodes occupied by gel
Type 2
 01  0.7 ET
 02  1.5 ET
 12  0.3 ET

Neagu A. et al. Phys. Rev. Lett.
95:178104-1– 4.                                                     4
Titus Beu, University ”Babeş-Bolyai”, Faculty of Physics

Molecular Dynamics Simulation of biological ion channels

   Ion channels – proteins that control the passage of ions (Na+, K+ etc) across
cell membranes

   Molecular dynamics – solving Newton’s law for all particles

   The electrolyte – 1M NaCl solution: 600 H2O molecules, 8 Na+ and 8 Cl-

   Water – rigid molecules:
• Site-site intermolecular potential TIP4P
• Rigid-body dynamics – rotation about CM – quaternions

   Periodic boundary conditions

   Coulomb interactions – Ewald sum technique with lattice-based charge
distribution and Fast Fourier Transform – increases speed substantially         5
Titus Beu, University ”Babeş-Bolyai”, Faculty of Physics

The model membrane channel
   similar to nicotine acetycloline receptor
   388 interaction sites: charges (-0.5e, -0.35e, +0.35e, +0.5e, neutral)
+ Lennard-Jones interactions

11 20-atom rings
relative rotation 9°

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SNAPSHOT

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Center for Fundamental and Advanced Technical Research

Lattice Boltzmann method

Boltzmann equation:



  vr  F v  f (r, v,t)  f (r, v,t)


   t         m                       t        collisions
Phase space discretized Boltzmann equations with BGK approximation

1                      1
 f (x,t)  e f (x,t)      F [e  u (x,t)] f  [ f (x,t)  f eq (x,t)]
t i         i i          k T      i            i  i           i
B
         relaxation time
F         the force term

Equilibrium distribution functions
                                     
eq  w n 1 ei u  (ei u)  u u
            2                        
                                     
f        i                                            
i            c2 2 2c4 2c2






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Center for Fundamental and Advanced Technical Research

Objective: investigation of two - dimensional, non - isothermal fluid flow
phenomena in micro – electro – mechanical systems (MEMS)

Approach:       development of appropiate numerical schemes; implementation of diffuse
reflection boundary conditions; parallel computing

thermal transpiration

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Center for Fundamental and Advanced Technical Research

Rarefaction effects in micro-channels

Velocity slip and temperature jump in Couette flow

pressure-driven
Flow

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Faculty of Physics, West University of Timisoara

goal: understanding of relation between crystal properties and
the conditions (parameters) of the crystal growth process
Process             Growth           Formation of            Crystal
parameters           conditions       crystal defects         properties

b

T(x,y,t,t)    svm

e.g. geometry,   e.g. temperature T     desired (doping),      defined by
heating power     and stress svm        undesired (e.g.    application, e.g.
distribution          dislocation)     LED, Laser diode

forward

inverse
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Faculty of Physics, West University of Timisoara

Development of Simulation Programs for Crystal Growth
Reduction of the complexity
Global 3D-modeling is
very expensive.               • by using symmetry effects (e.g. axi-symmetric)
• simplification of geometry (partial model)

2D axi-symmetric                  partial 3D
global 3D            problem: 3D-phenomena     STHAMAS3D – developed in
collaboration with Fraunhofer
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Institute, Erlangen, Germany
Challenges in Computational Power
1 PFlop/s
1000000
ASCI
100000
Performance [GFlop/s]

Earth Simulator
10000    Sum

1000                      1 TFlop/s
N=1
100
N=10
10

1
N=500
0.1
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No 6

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0
n-

n-

n-

n-

n-

n-
v-

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v-

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NANOSIM – cluster at West University
No

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No
Ju

Ju

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Ju

of Timisoara, Faculty of Physics

•Computing speeds advances (uni- and multi-processor systems), Grid Computing
• Systems Software
•Applications Advances (parallel & grid computing)
•Algorithms advances (parallel &grid computing, numeric and non-numeric
techniques: dynamic meshing, data assimilation)
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Conclusions

•Challenge is to integrate what is happening on the atomic level with the
mesoscopic and macroscopic classical level. Collaboration between
scientists ‘working at every level’ is strongly necessary

•Theoretical and computational skills can be learned by training,
meaningful applications is achieved only with experience. User friendly
software should be developed.

•Grids and Service Oriented Architectures are necessary (worldwide
networks of interconnected computers that behave as a single entity) to
increase computational power

•Local hardware infrastructure development necessary

•While computational experiment is much less expensive than real
experiment it is necessary to develop an application oriented
computational culture and community
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Acknowledgements

The authors would like to acknowledge the Romanian
Ministry of Education and Research for the financial
assistance under CEEX 11/2005

15

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