Related papers: Front propagation into unstable and metastable sta…
The dynamics of transient patterns formed by front propagation in extended nonequilibrium systems is considered. Under certain circumstances, the state left behind a front propagating into an unstable homogeneous state can be an unstable…
The dynamics of transient patterns formed by front propagation in extended nonequilibrium systems is considered. Under certain circumstances, the state left behind a front propagating into an unstable homogeneous state can be an unstable…
We discuss the problem of fronts propagating into metastable and unstable states. We examine the time development of the leading edge, discovering a precursor which in the metastable case propagates out ahead of the front at a velocity more…
The interface between an unstable state and a stable state usually develops a single confined front travelling with constant velocity into the unstable state. Recently, the splitting of such an interface into {\em two} fronts propagating…
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…
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…
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…
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…
We investigate the propagation of the slip front in the elastic body on the rigid substrate. We first obtain the slip profile and the slip front velocity of the steady state by employing the local friction law with the quadratic form of the…
Chiral liquid crystals often exhibit periodic modulations in the molecular director; in particular, thin films of the smectic-C* phase show a chiral striped texture. Here, we investigate whether similar chiral modulations can occur in the…
The position of a reaction front, propagating into a metastable state, fluctuates because of the shot noise of reactions and diffusion. A recent theory [B. Meerson, P.V. Sasorov, and Y. Kaplan, Phys. Rev. E 84, 011147 (2011)] gave a closed…
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 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…
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…
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…
A standard drift-diffusion model of space charge wave propagation in semiconductors has been studied numerically and analytically under dc voltage bias. For sufficiently long samples, appropriate contact resistivity and applied voltage -…
A new category of front propagation problems is proposed in which a spreading instability evolves through a singular configuration before saturating. We examine the nature of this front for the viscous Rayleigh instability of a column of…
Under an electric field, chiral smectic liquid crystals transit usually to the unwound SmC* phase where the helical structure is completely unrolled. Sometimes the sample transits initially towards an intermediate polar state before the…
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…
We present an experimental study of the directional-solidification patterns of a nematic - smectic B front. The chosen system is C_4H_9-(C_6H_{10})_2CN (in short, CCH4) in 12 \mu m-thick samples, and in the planar configuration (director…