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arXiv · 1505.05027

Continuum model for linked fibers with alignment interactions

Pierre Degond·Fanny Delebecque·Diane Peurichard
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Abstract

We introduce an individual-based model for fiber elements having the ability to cross-link or unlink each other and to align with each other at the cross links. We first formally derive a kinetic model for the fiber and cross-links distribution functions. We then consider the fast linking/unlinking regime in which the model can be reduced to the fiber distribution function only and investigate its diffusion limit. The resulting macroscopic model consists of a system of nonlinear diffusion equations for the fiber density and mean orientation. In the case of a homogeneous fiber density, we show that the model is elliptic.

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Pierre Degond, Fanny Delebecque, Diane Peurichard. 2015-05-19. Continuum model for linked fibers with alignment interactions. https://arxiv.org/abs/1505.05027

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