Continuum model for linked fibers with alignment interactions
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Accepted version
Published version
Author(s)
Degond, P
Delebecque, F
Peurichard, D
Type
Journal Article
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.
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.
Date Issued
2015-11-03
Date Acceptance
2015-07-15
Citation
Mathematical Models and Methods in Applied Sciences, 2015, 26
ISSN
0218-2025
Publisher
World Scientific Publishing
Journal / Book Title
Mathematical Models and Methods in Applied Sciences
Volume
26
Copyright Statement
© The Author(s). This is an open access article published by World Scientific Publishing and distributed under the terms of the Creative Commons Attribution (CC BY) 4.0 License, which permits use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
License URL
Sponsor
The Royal Society
Engineering & Physical Science Research Council (EPSRC)
Grant Number
WM130048
EP/M006883/1
Subjects
fibers
cross-links
alignment
kinetic equation
diffusion approximation
von Mises Fisher distribution
generalized collision invariant
ellipticity
Publication Status
Published
Article Number
269