Clustering of branching Brownian motions in confined geometries.
We study the evolution of a collection of individuals subject to Brownian diffusion, reproduction, and disappearance. In particular, we focus on the case where the individuals are initially prepared at equilibrium within a confined geometry. Such systems are widespread in physics and biology and apply for instance to the study of neutron populations in nuclear reactors and the dynamics of bacterial colonies, only to name a few. The fluctuations affecting the number of individuals in space and time may lead to a strong patchiness, with particles clustered together. We show that the analysis of this peculiar behavior can be rather easily carried out by resorting to a backward formalism based on the Green's function, which allows the key physical observables, namely, the particle concentration and the pair correlation function, to be explicitly derived.
CEA/Saclay, DEN/DANS/DM2S/SERMA/LTSD, 91191 Gif-sur-Yvette, France.
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Zoia
CEA/Saclay, DEN/DANS/DM2S/SERMA/LTSD, 91191 Gif-sur-Yvette, France.
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Dumonteil
CEA/Saclay, DEN/DANS/DM2S/SERMA/LTSD, 91191 Gif-sur-Yvette, France.
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Mazzolo
CEA/Saclay, DEN/DANS/DM2S/SERMA/LTSD, 91191 Gif-sur-Yvette, France and CNRS-Université Paris-Sud, LPTMS, UMR8626, 91405 Orsay Cedex, France.
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de Mulatier
CNRS-Université Paris-Sud, LPTMS, UMR8626, 91405 Orsay Cedex, France.
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Rosso
D003198:Computer Simulation; D004058:Diffusion; D008962:Models, Theoretical; D009010:Monte Carlo Method; D009038:Motion