Particle interactions mediated by dynamical networks: assessment of macroscopic descriptions

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Title: Particle interactions mediated by dynamical networks: assessment of macroscopic descriptions
Authors: Barré, J
Carrillo de la plata, J
Degond, PAA
Peurichard, D
Zatorska, E
Item Type: Journal Article
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.
Issue Date: 17-Aug-2017
Date of Acceptance: 31-Jul-2017
URI: http://hdl.handle.net/10044/1/50306
DOI: https://dx.doi.org/10.1007/s00332-017-9408-z
ISSN: 0938-8974
Publisher: Springer Verlag
Start Page: 235
End Page: 268
Journal / Book Title: Journal of Nonlinear Science
Volume: 28
Issue: 1
Copyright Statement: © The Author(s) 2017. This article is an open access publication
Sponsor/Funder: The Royal Society
The Royal Society
Engineering & Physical Science Research Council (EPSRC)
Engineering & Physical Science Research Council (EPSRC)
Engineering & Physical Science Research Council (EPSRC)
Engineering & Physical Science Research Council (EPSRC)
Funder's Grant Number: WM120001
WM130048
EP/M006883/1
EP/N014529/1
EP/P013651/1
EP/P031587/1
Keywords: cond-mat.stat-mech
cond-mat.stat-mech
0102 Applied Mathematics
Fluids & Plasmas
Publication Status: Published
Appears in Collections:Mathematics
Applied Mathematics and Mathematical Physics
Faculty of Natural Sciences



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