Continuum model for linked fibers with alignment interactions

2015/05/19 by Pierre Degond, Degond, Pierre, Fanny Delebecque +3 · 1 citation
Engineering · Mathematics · Physics and Astronomy · #Advanced Materials and Mechanics #Micro and Nano Robotics #Theoretical and Computational Physics #math-ph #math.MP

paper · pdf · doi:10.48550/arxiv.1505.05027

arxiv created 2015/05/19 · arxiv updated 2015/05/20

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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