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@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}
}

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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  -

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