Work

Kinetic theory of particle interactions mediated by dynamical networks

Year: 2016

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.1607.01975

Authors: Barré, Julien, Degond, Pierre, Zatorska, Ewelina

Institutions: Centre National de la Recherche Scientifique, Institut Universitaire de France, Laboratoire Jean-Alexandre Dieudonné, Université Nice Sophia Antipolis, Imperial College London

Language: English

Topic: Stochastic processes and statistical mechanics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Engineering and Physical Sciences Research Council

Award: G8298899259