Related papers: Front propagation in laminar flows
In this paper we develop and use the two-timing method for a systematic study of a scalar advection caused by a general oscillating velocity field. Mathematically, we study and classify the multiplicity of distinguished limits and…
A fractional diffusion equation with advection term is rigorously derived from a kinetic transport model with a linear turning operator, featuring a fat-tailed equilibrium distribution and a small directional bias due to a given vector…
We consider asymptotic problems concerning the motion of interface separating the regions of large and small values of the solution of a reaction-diffusion equation in the media consisting of domains with different characteristics…
A particle with internal unobserved states diffusing in a force field will generally display effective advection-diffusion. The drift velocity is proportional to the mobility averaged over the internal states, or effective mobility, while…
This paper is concerned with the propagating speeds of transition fronts in $R^N$ for spatially periodic bistable reaction-diffusion equations. The notion of transition fronts generalizes the standard notions of traveling fronts. Under the…
The influence of an underlying carrier flow on the terminal velocity of sedimenting particles is investigated both analytically and numerically. Our theoretical framework works for a general class of (laminar or turbulent) velocity fields…
We are interested in the time asymptotic location of the level sets of solutions to Fisher-KPP reaction-diffusion equations with fractional diffusion in periodic media. We show that the speed of propagation is exponential in time, with a…
We investigate travelling wave solutions in reaction-diffusion models of animal range expansion in the case that population diffusion is density-dependent. We find that the speed of the selected wave depends critically on the strength of…
The system under study is a reaction-diffusion equation in a horizontal strip, coupled to a diffusion equation on its upper boundary via an exchange condition of the Robin type. This class of models was introduced by H. Berestycki, L. Rossi…
We investigate front propagation in a reacting particle system in which particles perform scale-free random walks known as Levy flights. The system is described by a fractional generalization of a reaction-diffusion equation. We focus on…
Spontaneous pattern formation in living systems is driven by reaction-diffusion chemistry and active mechanics. The feedback between chemical and mechanical forces is often essential to robust pattern formation, yet it remains poorly…
We introduce a model of two coupled reaction-diffusion equations to describe the dynamics and propagation of flame fronts in random media. The model incorporates heat diffusion, its dissipation, and its production through coupling to the…
A {\em propagation-dispersion equation} is derived for the first passage distribution function of a particle moving on a substrate with time delays. The equation is obtained as the continuous limit of the {\em first visit equation}, an…
Front propagation in a random environment is studied close to the depinning threshold. At zero temperature we show that the depinning force distribution exhibits a universal behavior. This property is used to estimate the velocity of the…
We consider a passive scalar that is advected by a prescribed mean zero divergence-free velocity field, diffuses, and reacts according to a KPP-type nonlinear reaction. We introduce a quantity, the bulk burning rate, that makes both…
We study the coupling of a Fisher-Kolmogorov-Petrovsky-Piskunov (FKPP) equation to a separate, advection-only transport process. We find that the front dynamics can be described by an FKPP-like equation only at sufficiently fast diffusion…
The problem of two-phase flow in straight capillaries of polygonal cross section displays many of the dynamic characteristics of rapid interfacial motions associated with pore-scale displacements in porous media. Fluid inertia is known to…
We introduce a speed selection mechanism for front propagation in reaction-diffusion systems with multiple fields. This mechanism applies to pulled and pushed fronts alike, and operates by restricting the fields to large "finite" intervals…
We consider an individual-based two-dimensional spatial model with nearest-neighbor preemptive competition to study front propagation between an invader and a resident species. In particular, we investigate the asymptotic front velocity and…
Reaction-advection-diffusion equations, in periodic settings and with general type nonlinearities, admit a threshold known as the minimal speed of propagation. The minimal speed does not have an accessible formula when the nonlinearity is…