Related papers: Pulled fronts are not (just) pulled
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…
Traveling waves describe diverse natural phenomena from crystal growth in physics to range expansions in biology. Two classes of waves exist with very different properties: pulled and pushed. Pulled waves are driven by high growth rates at…
We consider a propagation of exotermic transition front in a discrete conservative oscillatory chain. Adequate description of such fronts is a key point in prediction of important transient phenomena, including phase transitions and…
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…
The concept of pulled fronts with a cutoff $\epsilon$ has been introduced to model the effects of discrete nature of the constituent particles on the asymptotic front speed in models with continuum variables (Pulled fronts are the fronts…
We investigate the asymptotic relaxation of so-called pulled fronts propagating into an unstable state. The ``leading edge representation'' of the equation of motion reveals the universal nature of their propagation mechanism and allows us…
The problem of flame propagation is studied as an example of unstable fronts that wrinkle on many scales is studied. The analytic tool of pole expansion in the complex plane is emloyed to address the interaction of the unstable growth…
We investigate a specific reaction-diffusion system that admits a monostable pulled front propagating at constant critical speed. When a small parameter changes sign, the stable equilibrium behind the front destabilizes, due to essential…
Front propagation in two dimensional steady and unsteady cellular flows is investigated in the limit of very fast reaction and sharp front, i.e., in the geometrical optics limit. In the steady case, by means of a simplified model, we…
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…
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 establish nonlinear stability of fronts that describe the creation of a periodic pattern through the invasion of an unstable state. Our results concern pushed fronts, that is, fronts whose propagation is driven by a localized mode at the…
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…
We study epidemic arrival times in meta-population disease models through the lens of front propagation into unstable states. We demonstrate that several features of invasion fronts in the PDE context are also relevant to the network case.…
We show that propagation speeds in invasion processes modeled by reaction-diffusion systems are determined by marginal spectral stability conditions, as predicted by the marginal stability conjecture. This conjecture was recently settled in…
We establish sharp nonlinear stability results for fronts that describe the creation of a periodic pattern through the invasion of an unstable state. The fronts we consider are critical, in the sense that they are expected to mediate…
Recent studies have shown that in the presence of noise both fronts propagating into a metastable state and so-called pushed fronts propagating into an unstable state, exhibit diffusive wandering about the average position. In this paper we…
Non-equilibrium dissipative systems usually exhibit multistability, leading to the presence of propagative domain between steady states. We investigate the front propagation into an unstable state in discrete media. Based on a paradigmatic…
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…
We study the biological situation when an invading population propagates and replaces an existing population with different characteristics. For instance, this may occur in the presence of a vertically transmitted infection causing a…