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Kinetic Theory of Particle Interactions Mediated by Dynamical Networks

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.
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https://hal.archives-ouvertes.fr/hal-01819648
Contributor : Julien Barre <>
Submitted on : Wednesday, June 20, 2018 - 5:24:13 PM
Last modification on : Thursday, March 5, 2020 - 5:56:06 PM

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

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