Kinetic theory of particle interactions mediated by dynamical networks
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Published version
Accepted version
Author(s)
Barré, J
Degond, PAA
Zatorska, E
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.
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.
Date Issued
2017-09-14
Date Acceptance
2017-04-18
Citation
Multiscale Modeling & Simulation, 2017, 15 (3), pp.1294-1323
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
License URL
Sponsor
The Royal Society
Engineering & Physical Science Research Council (EPSRC)
Grant Number
WM130048
EP/M006883/1
Subjects
math.AP
0102 Applied Mathematics
Applied Mathematics
Publication Status
Published