Particle interactions mediated by dynamical networks: assessment of
macroscopic descriptions
macroscopic descriptions
File(s)
Published version
Author(s)
Barré, J
Carrillo de la plata, J
Degond, PAA
Peurichard, D
Zatorska, E
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.
(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.
Date Issued
2017-08-17
Date Acceptance
2017-07-31
Citation
Journal of Nonlinear Science, 2017, 28 (1), pp.235-268
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
License URL
Sponsor
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)
Grant Number
WM120001
WM130048
EP/M006883/1
EP/N014529/1
EP/P013651/1
EP/P031587/1
Subjects
cond-mat.stat-mech
0102 Applied Mathematics
Fluids & Plasmas
Publication Status
Published