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One of the central questions in biology concerns the formation of
complex highly organized microscopic structures from initially disordered
states. Complex ordered structures are established and maintained through
a dynamic interplay between self-assembly and regulatory processes.
Here we introduce a model for spatio-temporal self-organization of
an ensemble of microtubules interacting via molecular motors. Starting
from a generic stochastic model of inelastic polar rods with an anisotropic
interaction kernel we derive a set of equations for the local rods
concentration and orientation. At large enough mean density of rods and
concentration of motors, the model describes orientational instability.
We demonstrate that the orientational instability leads to the formation
of vortices and (for large density and/or kernel anisotropy) asters seen
in recent experiments. The corresponding phase diagram of vortex-asters
transitions is in qualitative agreement with experiment.
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