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We describe a lattice Boltzmann algorithm to simulate liquid crystal
hydrodynamics. The equations of motion are written in terms of a tensor
order parameter. This allows both the isotropic and the nematic phases
to be considered. Backflow effects and the hydrodynamics of topological
defects are naturally included in the simulations, as are non-Newtonian
flow properties such as shear thinning and shear banding
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