Superfast front propagation in reactive systems with non-Gaussian diffusion

¹ Dipartimento di Fisica, Università di Roma “La Sapienza” P.le Aldo Moro 2, I-00185 Roma, Italy
² INFM, Unità di Roma “La Sapienza” - P.le Aldo Moro 2, I-00185 Roma, Italy
³ Istituto per le Applicazioni del Calcolo (IAC)-CNR Viale del Policlinico 137, I-00161, Roma, Italy

Received: 30 May 2002
Accepted: 9 September 2002

Abstract

We study a reactive field transported by a non-Gaussian process instead of a standard diffusion. If the process increments follow a probability distribution with exponential tails, the usual qualitative behaviour of the standard reaction diffusion system, i.e., exponential tails for the reacting field and a constant front speed, are recovered. But, if the process has power law tails and the reaction is pulled, the reacting field shows power law tails and the front speed increases exponentially with time. The comparison with other transport processes which exhibit anomalous diffusion shows that not only the presence of anomalous diffusion, but also its detailed mechanism, is relevant for the front propagation in reactive systems.