Continuum model for linked fibers with alignment interactions

Authored by Pierre Degond, Fanny Delebecque, Diane Peurichard

Date Published: 2016

DOI: 10.1142/s0218202516400030

Sponsors: French National Center for Scientific Research (CNRS) Royal Society United States National Science Foundation (NSF) Research Councils UK (RCUK) Wolfson foundation

Platforms: No platforms listed

Model Documentation: Other Narrative Mathematical description

Model Code URLs: Model code not found

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.

Tags

Dynamics networks collective motion Self-driven particles