PMID: 11308828Apr 20, 2001Paper

Branching and annihilating Lévy flights

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
D Vernon, M Howard

Abstract

We consider a system of particles undergoing the branching and annihilating reactions A-->(m+1)A and A+A-->Ø, with m even. The particles move via long-range Lévy flights, where the probability of moving a distance r decays as r(-d-sigma). We analyze this system of branching and annihilating Lévy flights using field theoretic renormalization group techniques close to the upper critical dimension d(c)=sigma with sigma<2. These results are then compared with Monte Carlo simulations in d=1. For sigma close to unity in d=1, the critical point for the transition from an absorbing to an active phase occurs at zero branching. However, for sigma bigger than about 3/2 in d=1, the critical branching rate moves away from zero with increasing sigma, and the transition lies in a different universality class, inaccessible to controlled perturbative expansions. We measure the exponents in both universality classes and examine their behavior as a function of sigma.

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Citations

Dec 20, 2003·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Daniel C Vernon
Aug 16, 2006·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Andrea Jiménez-Dalmaroni
Aug 16, 2013·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Ingo HomrighausenErwin Frey
Jun 25, 2020·Physical Review. E·Su-Chan Park
Sep 26, 2012·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Federico Benitez, Nicolás Wschebor
Jan 22, 2002·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Ligang Chen, Michael W Deem
May 18, 2013·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Carlos E Fiore, Mário J de Oliveira
Jun 19, 2013·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Federico Benitez, Nicolás Wschebor
Aug 7, 2007·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·F C Alcaraz, V Rittenberg

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