Continuum model for linked fibers with alignment interactions

• Main Authors: Degond, Pierre, Delebecque, Fanny, Peurichard, Diane
• Format: Journal Article
• Language: English
• Published: 19-05-2015
• Subjects: Mathematics - Mathematical Physics; Physics - Mathematical Physics
• DOI: 10.48550/arxiv.1505.05027

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.