Imperial College London

ProfessorPierreDegond

Faculty of Natural SciencesDepartment of Mathematics

Chair in Applied Mathematics
 
 
 
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Contact

 

+44 (0)20 7594 1474p.degond Website CV

 
 
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Location

 

6M38Huxley BuildingSouth Kensington Campus

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Summary

 

Publications

Citation

BibTex format

@article{Barré:2017:10.1007/s00332-017-9408-z,
author = {Barré, J and Carrillo, de la plata J and Degond, PAA and Peurichard, D and Zatorska, E},
doi = {10.1007/s00332-017-9408-z},
journal = {Journal of Nonlinear Science},
pages = {235--268},
title = {Particle interactions mediated by dynamical networks: assessment ofmacroscopic descriptions},
url = {http://dx.doi.org/10.1007/s00332-017-9408-z},
volume = {28},
year = {2017}
}

RIS format (EndNote, RefMan)

TY  - JOUR
AB - 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 asystem of particles interacting through a dynamical network of links. Assuming thatthe network remodeling process is very fast, the macroscopic model takes the formof a single aggregation–diffusion equation for the density of particles. The theoreticalstudy of the macroscopic model gives precise criteria for the phase transitions ofthe steady states, and in the one-dimensional case, we show numerically that thestationary solutions of the microscopic model undergo the same phase transitions andbifurcation types as the macroscopic model. In the two-dimensional case, we show that the numerical simulations of the macroscopic model are in excellent agreement withthe predicted theoretical values. This study provides a partial validation of the formalderivation of the macroscopic model from a microscopic formulation and shows thatthe former is a consistent approximation of an underlying particle dynamics, makingit a powerful tool for the modeling of dynamical networks at a large scale.
AU - Barré,J
AU - Carrillo,de la plata J
AU - Degond,PAA
AU - Peurichard,D
AU - Zatorska,E
DO - 10.1007/s00332-017-9408-z
EP - 268
PY - 2017///
SN - 0938-8974
SP - 235
TI - Particle interactions mediated by dynamical networks: assessment ofmacroscopic descriptions
T2 - Journal of Nonlinear Science
UR - http://dx.doi.org/10.1007/s00332-017-9408-z
UR - http://hdl.handle.net/10044/1/50306
VL - 28
ER -