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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. Monte Carlo simulation and Diffusion

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Incorporating Hydrodynamics into Monte Carlo Simulations

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  1. 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

  2. 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

  3. MC of particle systems

  4. More practical interpretation

  5. 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

  6. Fourier Approach

  7. Limitation to timestep

  8. Polymer chain N=1000 monomers Using ‘phantom’ chains so that eq’m initial configurations available

  9. Polymer diffusion CoM Monomers rel to CoM monomer motion N=100 monomer chains Centre of Mass motion

  10. N=400 N=1000

  11. Hydrodynamic scaling abs rel CoM N=1000 monomers monomers Centre of Mass

  12. Wavelet version (untested)

  13. Move limits and costs

  14. 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

  15. 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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