Universal Algebraic Relaxation of Fronts Propagating into an Unstable State and Implications for Moving Boundary Approximations
نویسندگان
چکیده
We analyze the relaxation of fronts propagating into unstable states. While “pushed” fronts relax exponentially like fronts propagating into a metastable state, “pulled” or “linear marginal stability” fronts relax algebraically. As a result, for thin fronts of this type, the standard moving boundary approximation fails. The leading relaxation terms for velocity and shape are of order 1yt and 1yt3y2. These universal terms are calculated exactly with a new systematic analysis that unifies various heuristic approaches to front propagation. [S0031-9007(98)05413-1]
منابع مشابه
Universal algebraic relaxation of velocity and phase in pulled fronts generating periodic or chaotic states
We investigate the asymptotic relaxation of so-called pulled fronts propagating into an unstable state, and generalize the universal algebraic velocity relaxation of uniformly translating fronts to fronts that generate periodic or even chaotic states. A surprising feature is that such fronts also exhibit a universal algebraic phase relaxation. For fronts that generate a periodic state, like tho...
متن کاملBreakdown of the standard perturbation theory and moving boundary approximation for pulled’’ fronts
The derivation of a Moving Boundary Approximation or of the response of a coherent structure like a front, vortex or pulse to external forces and noise, is generally valid under two conditions: the existence of a separation of time scales of the dynamics on the inner and outer scale and the existence and convergence of solvability type integrals. We point out that these conditions are not satis...
متن کاملFront propagation into unstable states
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 uns...
متن کاملFront propagation into unstable states: universal algebraic convergence towards uniformly translating pulled fronts
Fronts that start from a local perturbation and propagate into a linearly unstable state come in two classes: pulled fronts and pushed fronts. The term “pulled front” expresses that these fronts are “pulled along” by the spreading of linear perturbations about the unstable state. Accordingly, their asymptotic speed v∗ equals the spreading speed of perturbations whose dynamics is governed by the...
متن کاملRegularization of moving boundaries in a laplacian field by a mixed Dirichlet-Neumann boundary condition: exact results.
The dynamics of ionization fronts that generate a conducting body are in the simplest approximation equivalent to viscous fingering without regularization. Going beyond this approximation, we suggest that ionization fronts can be modeled by a mixed Dirichlet-Neumann boundary condition. We derive exact uniformly propagating solutions of this problem in 2D and construct a single partial different...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1998