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We derive a model describing spatio-temporal organization of an array of microtubules interacting via molecular motors. Starting from a stochastic model of inelastic polar rods with a generic anisotropic interaction kernel we obtain 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.
We derive a model describing spatio-temporal organization of an array of microtubules interacting via molecular motors. Starting from a stochastic model of inelastic polar rods with a generic anisotropic interaction kernel we obtain a set of equation
Neicu and Kudrolli observed experimentally spontaneous formation of the long-range orientational order and large-scale vortices in a system of vibrated macroscopic rods. We propose a phenomenological theory of this phenomenon, based on a coupled syst
Partial differential equations (PDE) have been widely used to reproduce patterns in nature and to give insight into the mechanism underlying pattern formation. Although many PDE models have been proposed, they rely on the pre-request knowledge of phy
We study pattern formation of skin cancers by means of numerical simulation of a binary system consisting of cancer and healthy cells. We extend the conventional Model H for macrophase separations by considering a logistic growth of cancer cells and
We show that an enslaved phase-separation front moving with diffusive speeds U = C T^(-1/2) can leave alternating domains of increasing size in their wake. We find the size and spacing of these domains is identical to Liesegang patterns. For equal co