Clustering of branching Brownian motions in confined geometries

Abstract

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 behaviour 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.

arXiv comment12 pages, 5 figures

References in corpus (13)

• Geometrical structure of Laplacian eigenfunctions
• Fractional Laplacian in Bounded Domains
• Studies of Bacterial Branching Growth using Reaction-Diffusion Models for Colonial Development
• Clustering, advection and patterns in a model of population dynamics with neighborhood-dependent rates
• Statistics at the tip of a branching random walk and the delay of traveling waves
• Spatial extent of an outbreak in animal epidemics
• The survival probability of a branching random walk in presence of an absorbing wall
• Universal Order and Gap Statistics of Critical Branching Brownian Motion
• Collision densities and mean residence times for $d$-dimensional exponential flights
• Properties of branching exponential flights in bounded domains
• Branching exponential flights: travelled lengths and collision statistics
• Neutral Evolution as Diffusion in phenotype space: reproduction with mutation but without selection
• Traveling waves and homogeneous fragmentation

Cited by in corpus (6)

• Spatial Extent of Branching Brownian Motion
• The critical catastrophe revisited
• Neutron fluctuations: the importance of being delayed
• Percolation properties of the neutron population in nuclear reactors
• Clusters in the critical branching Brownian motion
• Space and time correlations for diffusion models with prompt and delayed birth-and-death events