期刊
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES
卷 26, 期 2, 页码 269-318出版社
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0218202516400030
关键词
Fibers; cross-links; alignment; kinetic equation; diffusion approximation; von Mises Fisher distribution; generalized collision invariant; ellipticity
资金
- Region Midi Pyrenees, under Grant APRTCN
- British Engineering and Physical Research Council [EP/M006883/1]
- Royal Society
- Wolfson Foundation through a Royal Society Wolfson Research Merit Award
- NSF by NSF Grant [RNMS11-07444]
- EPSRC [EP/M006883/1] Funding Source: UKRI
- Engineering and Physical Sciences Research Council [EP/M006883/1] Funding Source: researchfish
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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