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Starting from a minimal physical model of self-propelled hard rods on a substrate in two dimensions, we derive a modified Smoluchowski equation for the system. Self-propulsion enhances longitudinal diffusion and modifies the mean-field excluded volume interaction. From the Smoluchowski equation we obtain hydrodynamic equations for rod concentration, polarization and nematic order parameter. New results at large scales are a lowering of the density of the isotropic-nematic transition and a strong enhancement of boundary effects in confined self-propelled systems.
Baskaran et al. (Mon,) studied this question.
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