相关论文: Front propagation in geometric and phase field mod…
The thin interface limit aims at minimizing the effects arising from a numerical interface thickness, inherent in diffuse interface models of solidification and microstructure evolution such as the phase field model. While the original…
We study the existence and stability of propagating fronts in Meinhardt's multivariable reaction-diffusion model of branching in one spatial dimension. We identify a saddle-node-infinite-period (SNIPER) bifurcation of fronts that leads to…
We numerically investigate the geometry and transport properties of infection fronts within the spatial SIR model in two dimensions. The model incorporates short-range correlated quenched random transmission rates. Our findings reveal that…
We consider reaction-diffusion fronts in spatially periodic bistable media with large periods. Whereas the homogenization regime associated with small periods had been well studied for bistable or Fisher-KPP reactions and, in the latter…
In this note we prove that appropriately scaled threshold dynamics-type algorithms corresponding to the fractional Laplacian of order $\alpha \in (0,2)$ converge to moving fronts. When $\alpha \geqq 1$ the resulting interface moves by…
This paper is devoted to the study of travelling fronts of reaction-diffusion equations with periodic advection in the whole plane $\mathbb R^2$. We are interested in curved fronts satisfying some "conical" conditions at infinity. We prove…
Waves in excitable media can be treated by a simple geometric theory. The propagation velocity is assumed known and evolution of wave fronts is determined by elementary physical principles (Fermat's principle, Huygens' principle). Based on…
We consider here a model of accelerating fronts, introduced in [2], consisting of one equation with nonlocal diffusion on a line, coupled via the boundary condition with a reaction-diffusion equation of the Fisher-KPP type in the upper…
In this paper we consider a classical model of gasless combustion in a one dimensional formulation under the assumption of ignition temperature kinetics. We study the propagation of flame fronts in this model when the initial distribution…
We prove that the mean curvature of a smooth surface in $\mathbb{R}^n$, $n\geq 2$, arises as the limit of a sequence of functions that are intrinsically related to the difference between an $n$- and $1$-dimensional fractional Laplacian of a…
We investigate the problem of finding the optimal shape and topology of a system of acoustic lenses in a dissipative medium. The sound propagation is governed by a general semilinear strongly damped wave equation. We introduce a phase-field…
Wave propagation in one-dimensional heterogeneous bistable media is studied using the Schl\"ogl model as a representative example. Starting from the analytically known traveling wave solution for the homogeneous medium, infinitely extended,…
Recent theoretical and experimental advances have shed light on the existence of so-called `perfectly transmitting' wavefronts with transmission coefficients close to 1 in strongly backscattering random media. These perfectly transmitting…
This paper is concerned with some nonlinear propagation phenomena for reaction-advection-diffusion equations with Kolmogrov-Petrovsky-Piskunov (KPP) type nonlinearities in general periodic domains or in infinite cylinders with oscillating…
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 study front propagation when an invading species competes with a resident; we assume nearest-neighbor preemptive competition for resources in an individual-based, two-dimensional lattice model. The asymptotic front velocity exhibits…
We consider the propagation of acoustic time-harmonic waves in a homogeneous media containing periodic lattices of spherical or cylindrical inclusions. It is assumed that the wavelength has the order of the periods of the lattice while the…
Using dynamical density functional theory we calculate the speed of solidification fronts advancing into a quenched two-dimensional model fluid of soft-core particles. We find that solidification fronts can advance via two different…
The problem of front propagation in a stirred medium is addressed in the case of cellular flows in three different regimes: slow reaction, fast reaction and geometrical optics limit. It is well known that a consequence of stirring is the…
The shape of a crack front propagating through a thin sample is studied using a phase field model. The model is shown to have a well defined sharp interface limit. The crack front is found to be an ellipse with large axis the width of the…