Abstract
The statistical mechanics of the ordering of self-driven
apolar particles has been shown EPL 62 (2003) 196; PRL 96 (2006)
180602; PRL 97 (2006) 090602 to display striking nonequilibrium
features, as a result of the interplay of orientation and particle
density . We study these nonequilibrium phenomena in detail through
particle-based models and stochastic partial differential equations
(PDEs). We derive the PDEs by coarse-graining and show that the
crucial particle-currents induced by director curvature in the PDEs
are an inevitable consequence of the elementary nonequilibrium moves
in the particle model. As a result of these currents, the growth of
nematic order from an initially isotropic, homogeneous state is shown
to be accompanied by a remarkable clumping of the number density
around topological defects. The consequent coarsening of both density
and nematic order are characterised by cusps in the short-distance
behaviour of the correlation functions, a breakdown of Porod's Law. We
identify the origins of this breakdown; in particular, the nature of
the noise terms in the equations of motion is shown to play a key
role.
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