Kinetic Theory of Particle Interactions Mediated by Dynamical Networks - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal Année : 2017

Kinetic Theory of Particle Interactions Mediated by Dynamical Networks

Résumé

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.

Dates et versions

hal-01819648 , version 1 (20-06-2018)

Identifiants

Citer

Julien Barré, Pierre Degond, Ewelina Zatorska. Kinetic Theory of Particle Interactions Mediated by Dynamical Networks. Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal, 2017, 15 (3), pp.1294 - 1323. ⟨10.1137/16M1085310⟩. ⟨hal-01819648⟩
73 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More