Berlin 2024 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 31: Poster: Statistical Physics

DY 31.20: Poster

Wednesday, March 20, 2024, 15:00–18:00, Poster C

Large-deviation simulation of the Brownian Bee model — •Hartmut Schoon and Alexander K. Hartmann — Institut für Physik, Carl von Ossietzky Universität Oldenburg, 26111 Oldenburg, Germany

The Brownian Bee model is a version of Branching Brownian motion, evolving into a nonequilibrium steady state. The model consists of N particles performing independent Brownian motion. Every particle has the ability to randomly branch and create a new particle at the same position. At those branching events the farthest particle from its origin will be deleted, resulting in a conservation of the particle count. Berestycki et al. [1] showed that at long times the particles form a spherical steady state with radius l₀ which depends on the spatial dimension d. Meerson and Sasorov [2] investigated the probability P(l, N, T) of the maximum distance l of a particle from the origin within a very large time interval 0<t<T. They concluded, that this probability follows a large-deviation form −lnP(l, N, T) ≃ NTR_d(l). Asymptotics for the rate function R_d(l) were provided for l≪ l₀ and l ≫ l₀ and a full analytical solution is given for d=1. We implemented Brownian Bees numerically and computed P(l, N, T) by a large-deviation simulation [3] for various dimensionalities d which allowed us to obtain the distribution down to exponential small probability densities like P ∼ 10⁻¹⁰⁰.

[1] J. Berestycki, et al., Ann. Prob. 50, 2133-2177 (2022)

[2] B. Meerson and P. Sasorov, Phys. Rev. Lett., 103, 032140 (2021)

[3] A.K. Hartmann, Phys. Rev. E , 89, 052103 (2014)

Keywords: Computational Physics; Large Deviations; Branching Brownian motion; Brownian Bees; Nonequilibrium steady states