Front Dynamics and External Fluctuations

Abstract

The problem of front propagation and velocity selection in pattern-forming systems has been receiving a great deal of attention in recent years, owing mainly to its relevance to a large variety of situations in nonlinear physics, chemistry, and biology [CH93]. The subject has been extensively studied in the recent literature [DL83, BBD–85, Saa87, Saa89, PNJ91, PCGO94, PO94, SHH95], particularly concerning the problem of velocity selection in deterministic systems, for which powerful analytical techniques have been developed. This chapter analyzes the influence of external fluctuations in front propagation. In particular, Section 6.1 deals with the effects of noise on the well-known deterministic scenario. The well-established abovementioned framework, along with the achievements accomplished so far in relation to it, will be used as a starting point in this study. Section 6.2, on the other hand, analyzes the propagation of fronts purely induced by noise. Finally, Section 6.3 studies the influence of the noise spectrum on front propagation dynamics in turbulent media.