Kinetic theory of particle interactions mediated by dynamical networks

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Title: Kinetic theory of particle interactions mediated by dynamical networks
Authors: Barré, J
Degond, PAA
Zatorska, E
Item Type: Journal Article
Abstract: We provide a detailed multiscale analysis of a system of particles interacting through a dynamical network of links. Starting from a microscopic model, via the mean field limit, we formally derive coupled kinetic equations for the particle and link densities, following the approach of [Degond et al., M3AS, 2016]. Assuming that the process of remodelling the network is very fast, we simplify the description to a macroscopic model taking the form of single aggregation-diffusion equation for the density of particles. We analyze qualitatively this equation, addressing the stability of a homogeneous distribution of particles for a general potential. For the Hookean potential we obtain a precise condition for the phase transition, and, using the central manifold reduction, we characterize the type of bifurcation at the instability onset.
Issue Date: 14-Sep-2017
Date of Acceptance: 18-Apr-2017
ISSN: 1540-3467
Publisher: Society for Industrial and Applied Mathematics
Start Page: 1294
End Page: 1323
Journal / Book Title: Multiscale Modeling & Simulation
Volume: 15
Issue: 3
Copyright Statement: © 2017 SIAM. Published by SIAM under the terms of the Creative Commons 4.0 license
Sponsor/Funder: The Royal Society
Engineering & Physical Science Research Council (EPSRC)
Funder's Grant Number: WM130048
Keywords: math.AP
0102 Applied Mathematics
Applied Mathematics
Publication Status: Published
Appears in Collections:Mathematics
Applied Mathematics and Mathematical Physics
Faculty of Natural Sciences

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