Modelling pattern formation through differential repulsion
File(s)Main_BarreDegondPeurichardZatorska.pdf (8.29 MB)
Accepted version
Author(s)
Barré, Julien
Degond, Pierre
Peurichard, Diane
Zatorska², Ewelina
Type
Journal Article
Abstract
Motivated by experiments on cell segregation, we present a twospecies
model of interacting particles, aiming at a quantitative description of
this phenomenon. Under precise scaling hypothesis, we derive from the microscopic
model a macroscopic one and we analyze it. In particular, we determine
the range of parameters for which segregation is expected. We compare our
analytical results and numerical simulations of the macroscopic model to direct
simulations of the particles, and comment on possible links with experiments.
model of interacting particles, aiming at a quantitative description of
this phenomenon. Under precise scaling hypothesis, we derive from the microscopic
model a macroscopic one and we analyze it. In particular, we determine
the range of parameters for which segregation is expected. We compare our
analytical results and numerical simulations of the macroscopic model to direct
simulations of the particles, and comment on possible links with experiments.
Date Issued
2020-09-01
Date Acceptance
2019-12-11
Citation
Networks and Heterogeneous Media, 2020, 15 (3), pp.307-352
ISSN
1556-1801
Publisher
American Institute of Mathematical Sciences
Start Page
307
End Page
352
Journal / Book Title
Networks and Heterogeneous Media
Volume
15
Issue
3
Copyright Statement
©American Institute of Mathematical Sciences, 2020.
Sponsor
The Royal Society
Engineering & Physical Science Research Council (EPSRC)
Engineering & Physical Science Research Council (EPSRC)
Engineering & Physical Science Research Council (EPSRC)
Grant Number
WM130048
EP/M006883/1
EP/N014529/1
EP/P013651/1
Subjects
Science & Technology
Physical Sciences
Mathematics, Interdisciplinary Applications
Mathematics
Dynamical networks
aggregation-diffusion equations
kinetic equations
modelling for cell segregation
DYNAMICS
SIMULATION
EQUATIONS
ADHESION
SYSTEM
MOTION
math.AP
math.AP
math.NA
Applied Mathematics
0102 Applied Mathematics
0103 Numerical and Computational Mathematics
Publication Status
Published