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
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(No Transcript)
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Outline

• Monte Carlo simulation and Diffusion
• Challenge of long range hydrodynamic coupling
  important in many soft matter systems.
• Fourier method order N2 per unit time
• application to polymer dynamics
• Wavelet adaptation approaching order N

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MC of particle systems
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More practical interpretation
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Particles in a fluid

• Some studies just use Cholesky
• Banchio Brady long range part slow to change
  update less often (JCP 2003)
• Present approach (i) Fourier (ii) Wavelets

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Fourier Approach
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Limitation to timestep
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Polymer chain
N1000 monomers
Using phantom chains so that eqm initial
configurations available
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Polymer diffusion
CoM
Monomers rel to CoM
monomer motion
N100 monomer chains
Centre of Mass motion
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N400
N1000
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Hydrodynamic scaling
abs rel CoM
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Wavelet version (untested)
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Move limits and costs
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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

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Acknowledgements

• Line of enquiry prompted by collaboration on
  translocation with D Panja and G Berkema
  hydrodynamics crucial.
• CSC CoW
• ITS desktop
• CSC seminar