ZB 10 - Soft Condensed Matter (R. Holyst)

Configurational transition in a Fleming-Viot-type model and probabilistic interpretation of Laplacian eigenfunctions

Author(s): Burdzy, K and Holyst, R and Ingerman, D and March, P
Title: Configurational transition in a Fleming-Viot-type model and probabilistic interpretation of Laplacian eigenfunctions
Abstract: We analyse and simulate a two-dimensional Brownian multi-type particle with death and branching (birth) depending on the position of of different types. The system is confined in a box, whose boundaries act as the sink of Brownian The branching rate matches the death rate so that the total of particles is kept constant. In the case of m types of particle a rectangular box of size a x b and elongated shape a much greater b we observe that the stationary distribution of particles to the mth Laplacian eigenfunction. For smaller elongations > b we find a configurational transition to a new limiting The ratio a/b for which the transition occurs is related the value of the mth eigenvalue of the Laplacian with rectangular boundaries.
Pages: 2633-2642
Journal: JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL
Volume: 29
ID: ISI:A1996UP44000004
Year: 1996
DOI: 10.1088/0305-4470/29/11/004