MACROSCOPIC MODEL FOR CROSS-LINKED FIBERS WITH ALIGNMENT INTERACTIONS: EXISTENCE THEORY AND NUMERICAL SIMULATIONS

Authored by D Peurichard

Date Published: 2016

DOI: 10.1137/15m1026729

Sponsors: No sponsors listed

Platforms: No platforms listed

Model Documentation: Other Narrative Mathematical description

Model Code URLs: Model code not found

Abstract

In this paper, we study the macroscopic model of {[}P. Degond, F. Delebecque, and D. Peurichard, Math. Models Methods Appl. Sci., 26 (2016), pp. 269-318] for fiber elements having the ability to cross-link, or unlink each other, to align with each other at the cross-links, and subjected to an external potential. We first aim to gain insight into the properties of the solutions of the macroscopic model: we provide an existence result under structural conditions for the external potential and perform numerical simulations. The numerical study of the macroscopic model reveals interesting features such as the emergence of a buckling phenomenon. Physical properties of the macroscopic fiber network are then deduced. We finally propose a numerical comparison between the macroscopic model and the microscopic one, a starting point for the derivation of the macroscopic equations. The numerical simulations reveal a good agreement between both models, providing we adapt the regime of study according to the model parameters.

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Dynamics continuum model vascular networks growth Self-propelled particles Stress Kinetic-model Cytoskeletal networks Cell-movement Tissues