Stochastic rotation dynamics

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Presentation transcript:

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

The stochastic rotation algorithm Streaming step Collision step

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

1. Evolution equations for the conserved quantities

2. Fluxes in terms of the moments of the distribution function y x

The momentum flux tensor

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

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

Average over the number of particles per cell where

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

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

4.The transport coefficients

Kinetic viscosity in two dimensions rotation angle

Kinetic viscosity in three dimensions rotation angle

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

Coupling to polymers

Polymer collapse: the role of backflow radius of gyration time

A scaling argument Brownian Hydrodynamic

A scaling argument Brownian Hydrodynamic

Shear Thinning

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

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

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?

Length of polymer as a function of peak flow velocity

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

Thermal conductivity 3d

Collisional viscosity 3d