Particle Interactions Mediated by Dynamical Networks: Assessment of Macroscopic Descriptions
Authored by Pierre Degond, Josa A Carrillo, D Peurichard, J Barre, E Zatorska
Date Published: 2018
DOI: 10.1007/s00332-017-9408-z
Sponsors:
Royal Society
United Kingdom Engineering and Physical Sciences Research Council (EPSRC)
United States National Science Foundation (NSF)
Wolfson foundation
Platforms:
No platforms listed
Model Documentation:
Other Narrative
Mathematical description
Model Code URLs:
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Abstract
We provide a numerical study of the macroscopic model of Barr, 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.
Tags
continuum model
phase transitions
Aggregation
Kinetic equation
repulsion
Bifurcations
States
Flow
Equations
Mean-field limit
Dynamical networks
Cross-links
Microscopic model
Diffusion approximation
Aggregation-diffusion
equation
Fourier analysis