Related papers: Additive Noise Induces Front Propagation
Recently it has been shown that when an equation that allows so-called pulled fronts in the mean-field limit is modelled with a stochastic model with a finite number $N$ of particles per correlation volume, the convergence to the speed…
Fronts that start from a local perturbation and propagate into a linearly unstable state come in two classes: pulled and pushed. ``Pulled'' fronts are ``pulled along'' by the spreading of linear perturbations about the unstable state, so…
Several acoustic experiments show a surprising degree of stability in wave fronts propagating over multi-megameter ranges through the ocean's sound channel despite the presence of random-like, sound speed fluctuations. Previous works have…
We study the dynamics of generic reaction-diffusion fronts, including pulses and chemical waves, in the presence of multiplicative noise. We discuss the connection between the reaction-diffusion Langevin-like field equations and the…
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…
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…
Spatially extended systems can support local transient excitations in which just a part of the system is excited. The mechanisms reported so far are local excitability and excitation of a localized structure. Here we introduce an…
We consider planar traveling fronts between stable steady states in two-component singularly perturbed reaction-diffusion-advection equations, where a small quantity $\delta^2$ represents the ratio of diffusion coefficients. The fronts…
We describe the resulting spatiotemporal dynamics when a homogeneous equilibrium loses stability in a spatially extended system. More precisely, we consider reaction-diffusion systems, assuming only that the reaction kinetics undergo a…
The dynamics of a thin Huygens front propagating through turbulent medium is considered. A rigorous asymptotic expression for the effective velocity $v_{F}$ proportional to the front area is derived. The small-scale fluctuations of the…
It has been reported that traveling waves propagate periodically and stably in sub-excitable systems driven by noise [Phys. Rev. Lett. \textbf{88}, 138301 (2002)]. As a further investigation, here we observe different types of traveling…
We analyze ``pulled'' or ``linearly marginally stable'' fronts propagating into unstable states. While ``pushed'' fronts into meta- and unstable states relax exponentially, pulled fronts relax algebraically, and simultaneously the standard…
We analyze experimentally chemical waves propagation in the disordered flow field of a porous medium. The reaction fronts travel at a constant velocity which drastically depends on the mean flow direction and rate. The fronts may propagate…
We study the dynamics of the front separating a spatio-temporally chaotic region from a stable steady region using a simple model applicable to periodically forced systems. In particular, we investigate both the coarsening of the front…
The problem of flame propagation is studied as an example of unstable fronts that wrinkle on many scales. The analytic tool of pole expansion in the complex plane is employed to address the interaction of the unstable growth process with…
The mobility of an overdamped particle, in a periodic potential tilted by a constant external field and moving in a medium with periodic friction coefficient is examined. When the potential and the friction coefficient have the same…
In this paper, we prove some qualitative properties of pushed fronts for the periodic reaction-diffusion-equation with general monostable nonlinearities. Especially, we prove the exponential behavior of pushed fronts when they are…
The influence of the L{\'e}vy noise's properties on wavefront propagation is analyzed on examples of ensembles of locally coupled bistable oscillators and a single bistable delayed-feedback oscillator considered as a spatially-extended…
The current paper is a corrected version of our previous paper arXiv:adap-org/9608001. Similarly to previous version we investigate the problem of flame propagation. This problem is studied as an example of unstable fronts that wrinkle on…
We identify a new mechanism for propagation into unstable states in spatially extended systems, that is based on resonant interaction in the leading edge of invasion fronts. Such resonant invasion speeds can be determined solely based on…