Incorporating hydrodynamics into monte carlo simulations
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Incorporating Hydrodynamics into Monte Carlo Simulations. R C Ball, Physics Theory Group and Centre for Complexity Science University of Warwick assoc. member Centre for Scientific Computing. Outline. Monte Carlo simulation and Diffusion

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Incorporating hydrodynamics into monte carlo simulations
Incorporating Hydrodynamics into Monte Carlo Simulations

R C Ball,

Physics Theory Group and

Centre for Complexity Science

University of Warwick

assoc. member

Centre for Scientific Computing


Outline
Outline

  • Monte Carlo simulation and Diffusion

  • Challenge of long range hydrodynamic coupling – important in many soft matter systems.

  • Fourier method: order N^2 per unit time

    • application to polymer dynamics

  • Wavelet adaptation approaching order N




Particles in a fluid
Particles in a fluid

a

p

q

  • Micro Hydrodynamics

  • Macromolecules

  • Bacteria

  • Colloids

  • Some studies just use Cholesky …

  • Banchio & Brady: long range part slow to change – update less often (JCP 2003)

  • Present approach: (i) Fourier (ii) Wavelets




Polymer chain
Polymer chain

N=1000 monomers

Using ‘phantom’ chains so

that eq’m initial configurations available


Polymer diffusion
Polymer diffusion

CoM

Monomers rel to CoM

monomer motion

N=100 monomer chains

Centre of Mass motion


N=400

N=1000


Hydrodynamic scaling
Hydrodynamic scaling

abs

rel CoM

N=1000 monomers

monomers

Centre of Mass




Limitations and prospects
Limitations and Prospects

  • Imposing relative motion and strain: applicable to SOFT matter only.

  • Not capturing close-to-contact “lubrication friction”

  • Potential to beat conventional MC at equilibration

    • hydrodynamics accelerates large scale relaxation

      • E.g. polymer D ~ 1/N → 1/R

    • motion more concerted

  • Opens up hydrodynamic coupling

  • Background flow (e.g. simple shear) can be added

  • Walls easy to add by Fourier, challenging by Wavelets


Acknowledgements
Acknowledgements

  • Line of enquiry prompted by collaboration on translocation with D Panja and G Berkema: hydrodynamics crucial.

  • CSC CoW

  • ITS desktop

  • CSC seminar


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