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:2017:10.1137/16M1085310,
author = {Barré, J and Degond, PAA and Zatorska, E},
doi = {10.1137/16M1085310},
journal = {Multiscale Modeling & Simulation},
pages = {1294--1323},
title = {Kinetic theory of particle interactions mediated by dynamical networks},
url = {http://dx.doi.org/10.1137/16M1085310},
volume = {15},
year = {2017}
}

RIS format (EndNote, RefMan)

TY  - JOUR
AB - We provide a detailed multiscale analysis of a system of particles interacting through a dynamical network of links. Starting from a microscopic model, via the mean field limit, we formally derive coupled kinetic equations for the particle and link densities, following the approach of [Degond et al., M3AS, 2016]. Assuming that the process of remodelling the network is very fast,we simplify the description to a macroscopic model taking the form of single aggregation-diffusion equation for the density of particles. We analyze qualitatively this equation, addressing the stability of a homogeneous distribution of particles for a general potential. For the Hookean potential we obtain a precise condition for the phase transition, and, using the central manifold reduction, we characterize the type of bifurcation at the instability onset.
AU - Barré,J
AU - Degond,PAA
AU - Zatorska,E
DO - 10.1137/16M1085310
EP - 1323
PY - 2017///
SN - 1540-3467
SP - 1294
TI - Kinetic theory of particle interactions mediated by dynamical networks
T2 - Multiscale Modeling & Simulation
UR - http://dx.doi.org/10.1137/16M1085310
UR - http://hdl.handle.net/10044/1/48228
VL - 15
ER -