Barré, J;
Carrillo, JA;
Degond, P;
Peurichard, D;
Zatorska, E;
(2018)
Particle Interactions Mediated by Dynamical Networks: Assessment of Macroscopic Descriptions.
Journal of Nonlinear Science
, 28
(1)
pp. 235-268.
10.1007/s00332-017-9408-z.
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Abstract
We provide a numerical study of the macroscopic model of Barré et al. (Multiscale Model Simul, 2017, to appear) derived from an agent-based model for a system of particles interacting through a dynamical network of links. Assuming that the network remodeling process is very fast, the macroscopic model takes the form of a single aggregation–diffusion equation for the density of particles. The theoretical study of the macroscopic model gives precise criteria for the phase transitions of the steady states, and in the one-dimensional case, we show numerically that the stationary solutions of the microscopic model undergo the same phase transitions and bifurcation types as the macroscopic model. In the two-dimensional case, we show that the numerical simulations of the macroscopic model are in excellent agreement with the predicted theoretical values. This study provides a partial validation of the formal derivation of the macroscopic model from a microscopic formulation and shows that the former is a consistent approximation of an underlying particle dynamics, making it a powerful tool for the modeling of dynamical networks at a large scale.
| Type: | Article |
|---|---|
| Title: | Particle Interactions Mediated by Dynamical Networks: Assessment of Macroscopic Descriptions |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1007/s00332-017-9408-z |
| Publisher version: | http://dx.doi.org/10.1007/s00332-017-9408-z |
| Language: | English |
| Additional information: | Copyright © The Author(s) 2017. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. |
| Keywords: | Dynamical networks, Cross-links, Microscopic model, Kinetic equation, Diffusion approximation, Mean-field limit, Aggregation–diffusion equation, Phase transitions, Fourier analysis, Bifurcations |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices 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/10030644 |
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