1. Stochastic rotation dynamics
Christopher Pooley
Norio Kikuchi
Jennifer Ryder
Matthew Webster
Julia Yeomans
Rudolf Peierls Centre for Theoretical Physics
University of Oxford

2. The stochastic rotation algorithm
Streaming step
Collision step

3. Deriving the transport coefficients
Write down evolution equations for the conserved quantities
Calculate the fluxes in terms of the moments of the distribution function
Work out steady state values for the moments
Read off the transport coefficients
Add the collisional contribution to the viscosity

4. 1. Evolution equations for the conserved quantities

5. 2. Fluxes in terms of the moments of the distribution functiony x

6. The momentum flux tensor

7. 3. Steady state values for the moments (i) streaming

8. 3. Steady state values for the moments (ii) collisions

13. Average over the number of particles per cell
where

14. 3. Steady state values for the moments
collision
streaming
steady state moment

15. 1.Write down evolution equations for the conserved quantities
2. Calculate the fluxes in terms of the moments of the distribution function
3. Work out steady state values for the moments
4. Read off the transport coefficients

16. 4.The transport coefficients

17. Kinetic viscosity in two dimensions
rotation angle

18. Kinetic viscosity in three dimensions
rotation angle

19. 5.The collisional contribution to the viscosity
position of measurement plane

20. Coupling to polymers

21. Polymer collapse: the role of backflow
radius of
gyration
time

25. A scaling argument
Brownian
Hydrodynamic

26. A scaling argument
Brownian
Hydrodynamic

27. Shear Thinning

36. Tethered Polymers in Flow
100 Beads
Coil Configuration
100 Beads
Trumpet Configuration
100 Beads
Flower Configuration
Across flow Profile
100 Beads
Flower Configuration
Normal to flow profile

37. Distance along flow axis
Radius of polymer plotted against distance along flow axis for different flow velocities
Radial span
Distance along flow axis

38. Stochastic rotation dynamics
Exact expressions can be obtained for the transport coefficients.
Easy to couple to a polymer evolving through molecular dynamics.
Can turn off the hydrodynamics.
Mapping onto real systems?

40. Length of polymer as a function of peak flow velocity

41. Change in peak flow velocity when polymer is present plotted against forcing pressure

42. Thermal conductivity 3d

43. Collisional viscosity 3d