Physics – Condensed Matter – Soft Condensed Matter
Scientific paper
2003-08-26
Phys. Rep. 386, 29 (2003)
Physics
Condensed Matter
Soft Condensed Matter
final version with some added references; a single pdf file of the published version is available at http://www.lorentz.leiden
Scientific paper
This paper is an introductory review of the problem of front propagation into unstable states. Our presentation is centered around the concept of the asymptotic linear spreading velocity v*, the asymptotic rate with which initially localized perturbations spread into an unstable state according to the linear dynamical equations obtained by linearizing the fully nonlinear equations about the unstable state. This allows us to give a precise definition of pulled fronts, nonlinear fronts whose asymptotic propagation speed equals v*, and pushed fronts, nonlinear fronts whose asymptotic speed v^dagger is larger than v*. In addition, this approach allows us to clarify many aspects of the front selection problem, the question whether for a given dynamical equation the front is pulled or pushed. It also is the basis for the universal expressions for the power law rate of approach of the transient velocity v(t) of a pulled front as it converges toward its asymptotic value v*. Almost half of the paper is devoted to reviewing many experimental and theoretical examples of front propagation into unstable states from this unified perspective. The paper also includes short sections on the derivation of the universal power law relaxation behavior of v(t), on the absence of a moving boundary approximation for pulled fronts, on the relation between so-called global modes and front propagation, and on stochastic fronts.
No associations
LandOfFree
Front propagation into unstable states does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Front propagation into unstable states, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Front propagation into unstable states will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-58024