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SUMMARY:Aggregation-Diffusion Equations for Collective Behaviour in the Sc
iences
DTSTART:20240311T150000Z
DTEND:20240311T160000Z
DTSTAMP:20240418T140800Z
UID:indico-event-11246@indico.math.cnrs.fr
DESCRIPTION:Speakers: JosÃ©-Antonio Carrillo (U. Oxford)\n\nMany phenomena
in the life sciences\, ranging from the microscopic to macroscopic level\
, exhibit surprisingly similar structures. Behaviour at the microscopic le
vel\, including ion channel transport\, chemotaxis\, and angiogenesis\, an
d behaviour at the macroscopic level\, including herding of animal populat
ions\, motion of human crowds\, and bacteria orientation\, are both largel
y driven by long-range attractive forces\, due to electrical\, chemical or
social interactions\, and short-range repulsion\, due to dissipation or f
inite size effects. Various modelling approaches at the agent-based level\
, from cellular automata to Brownian particles\, have been used to describ
e these phenomena. An alternative way to pass from microscopic models to c
ontinuum descriptions requires the analysis of the mean-field limit\, as t
he number of agents becomes large. All these approaches lead to a continuu
m kinematic equation for the evolution of the density of individuals known
as the aggregation-diffusion equation. This equation models the evolution
of the density of individuals of a population\, that move driven by the b
alances of forces: on one hand\, the diffusive term models diffusion of th
e population\, where individuals escape high concentration of individuals\
, and on the other hand\, the aggregation forces due to the drifts modelli
ng attraction/repulsion at a distance. The aggregation-diffusion equation
can also be understood as the steepest-descent curve (gradient flow) of fr
ee energies coming from statistical physics. Significant effort has been d
evoted to the subtle mechanism of balance between aggregation and diffusio
n. In some extreme cases\, the minimisation of the free energy leads to pa
rtial concentration of the mass. Aggregation-diffusion equations are prese
nt in a wealth of applications across science and engineering. Of particul
ar relevance is mathematical biology\, with an emphasis on cell population
models. The aggregation terms\, either in scalar or in system form\, is o
ften used to model the motion of cells as they concentrate or separate fro
m a target or interact through chemical cues. The diffusion effects descri
bed above are consistent with population pressure effects\, whereby groups
of cells naturally spread away from areas of high concentration. This tal
k will give an overview of the state of the art in the understanding of ag
gregation-diffusion equations\, and their applications in mathematical bio
logy.\n\nhttps://indico.math.cnrs.fr/event/11246/
LOCATION:Fokko-du-Cloux (Batiment Braconnier)
URL:https://indico.math.cnrs.fr/event/11246/
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