Stochastic rotation dynamics

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Stochastic rotation dynamics
Christopher Pooley Norio Kikuchi Jennifer
Ryder Matthew Webster Julia Yeomans Rudolf
Peierls Centre for Theoretical Physics University
of Oxford
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The stochastic rotation algorithm
Streaming step
Collision step
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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

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1. Evolution equations for the conserved
quantities
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2. Fluxes in terms of the moments of the
distribution function
y
x
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The momentum flux tensor
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3. Steady state values for the moments (i)
streaming
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3. Steady state values for the moments (ii)
collisions
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Average over the number of particles per cell
where
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3. Steady state values for the moments
collision
streaming
steady state moment
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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
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4.The transport coefficients
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Kinetic viscosity in two dimensions
kinetic viscosity
rotation angle
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Kinetic viscosity in three dimensions
kinetic viscosity
rotation angle
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5.The collisional contribution to the viscosity
collision viscosity
position of measurement plane
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Coupling to polymers
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Polymer collapse the role of backflow
radius of gyration
time
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A scaling argument
Brownian
Hydrodynamic
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A scaling argument
Brownian
Hydrodynamic
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Shear Thinning
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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
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Radius of polymer plotted against distance along
flow axis for different flow velocities
Radial span
Distance along flow axis
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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?
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Length of polymer as a function of peak flow
velocity
length of polymer
peak flow velocity
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Change in peak flow velocity when polymer is
present plotted against forcing pressure
change in peak flow velocity
pressure
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Thermal conductivity 3d
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Collisional viscosity 3d