相关论文: Front propagation into unstable states

We study the front propagation in Reaction-Diffusion systems whose reaction dynamics exhibits an unstable fixed point and chaotic or noisy behaviour. We have examined the influence of chaos and noise on the front propagation speed and on…

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…

We study the propagation of a ``pulled'' front with multiplicative noise that is created by a local perturbation of an unstable state. Unlike a front propagating into a metastable state, where a separation of time scales for sufficiently…

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…

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…

We determine the asymptotic spreading speed of the solutions of a Fisher-KPP reaction-diffusion equation, starting from compactly supported initial data, when the diffusion coefficient is a fixed bounded monotone profile that is shifted at…

We study the asymptotic behaviour of solutions to the delayed monostable equation $(*)$: $u_{t}(t,x) = u_{xx}(t,x) - u(t,x) + g(u(t-h,x)),$ $x \in R,\ t >0,$ with monotone reaction term $g: R_+ \to R_+$. Our basic assumption is that this…

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…

We study nonlinear stability of pulled fronts in scalar parabolic equations on the real line of arbitrary order, under conceptual assumptions on existence and spectral stability of fronts. In this general setting, we establish sharp…

We study evolution of pulses propagating through focusing nonlinear media. Small disturbance on the smooth initial non-uniform background leads to formation of the region of strong nonlinear oscillations. We develop here an asymptotic…

A classification of dynamical systems in terms of their variational properties is reviewed. Within this classification, front propagation is discussed in a non-gradient relaxational potential flow. The model is motivated by transient…

The position of propagating population fronts fluctuates because of the discreteness of the individuals and stochastic character of processes of birth, death and migration. Here we consider a Markov model of a population front propagating…

Long, cylindrical metal nanowires have recently been observed to form and be stable for seconds at a time at room temperature. Their stability and structural dynamics is well described by a continuum model, the nanoscale free-electron…

We address the propagation into an unstable state of a localised disturbance in a forward-backward diffusion pseudo-parabolic equation. Three asymptotic regimes are distinguished as t tends to infinity, the first being a regime ahead of the…

Streamer ionization fronts are pulled fronts propagating into a linearly unstable state; the spatial decay of the initial condition of a planar front selects dynamically one specific long time attractor out of a continuous family. A…

We address the problem of a front propagation in chains with a bi-stable nondegenerate on-site potential and a nonlinear gradient coupling. For a generic nonlinear coupling, one encounters a special regime of transitions, characterized by…

The empirical velocity of a reaction-diffusion front, propagating into an unstable state, fluctuates because of the shot noises of the reactions and diffusion. Under certain conditions these fluctuations can be described as a diffusion…

We introduce a novel numerical method for direct simulation of front propagation in the Fisher-KPP equation with a time-dependent parameter on an infinite domain. The method computes a time-dependent boundary condition that accurately…

In this paper we study the invasion fronts of spatially periodic monotone reaction-diffusion systems in a multi-dimensional setting. We study the pulsating traveling waves that connect the trivial equilibrium, for which all components of…