Barré, J;
Degond, P;
Zatorska, E;
(2017)
Kinetic theory of particle interactions mediated by dynamical networks.
Multiscale Modeling and Simulation
, 15
(3)
pp. 1294-1323.
10.1137/16M1085310.
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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 [P. Degond, F. Delebecque, and D. Peurichard, Math. Models Methods Appl. Sci., 26 (2016), pp. 269–318]. Assuming that the process of remodeling the network is very fast, we simplify the description to a macroscopic model taking the form of a 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.
| Type: | Article |
|---|---|
| Title: | Kinetic theory of particle interactions mediated by dynamical networks |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1137/16M1085310 |
| Publisher version: | http://dx.doi.org/10.1137/16M1085310 |
| Language: | English |
| Additional information: | © 2017 SIAM. Published by SIAM under the terms of the Creative Commons 4.0 license |
| Keywords: | Individual-based model, meanfield limit, Fokker–Planck, macroscopic limit, aggregation-diffusion, linear stability, phase transition |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10041390 |
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