Continuum model for linked fibers with alignment interactions

Pierre Degond (1) , Fanny Delebecque (2) , Diane Peurichard (2)

1 Department of Mathematics [Imperial College London]
2 IMT - Institut de Mathématiques de Toulouse UMR5219

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.

Mots clés: fibers; cross-links; alignment; kinetic equation; diffusion approximation; von Mises Fisher distribution; generalized collision invariant; ellipticity ccode:AMS Subject Classification: 82C31; 82C40; 82C70; 92C10; 92C17

Domaines: Physique mathématique [math-ph]

Pierre Degond, Fanny Delebecque, Diane Peurichard. Continuum model for linked fibers with alignment interactions. Mathematical Models and Methods in Applied Sciences, 2016, vol. 26 (2), pp.269-318. ⟨10.1142/S0218202516400030⟩. ⟨hal-01152347⟩