Related papers: Proliferating L\'evy Walkers and Front Propagation
We prove maximal speed estimates for nonlinear quantum propagation in the context of the Hartree equation. More precisely, under some regularity and integrability assumptions on the pair (convolution) potential, we construct a set of energy…
L\'evy walk process is one of the most effective models to describe superdiffusion, which underlies some important movement patterns and has been widely observed in the micro and macro dynamics. From the perspective of random walk theory,…
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…
G-equations are level-set type Hamilton-Jacobi partial differential equations modeling propagation of flame front along a flow velocity and a laminar velocity. In consideration of flame stretching, strain rate may be added into the laminar…
A vicious walker system consists of N random walkers on a line with any two walkers annihilating each other upon meeting. We study a system of N vicious accelerating walkers with the velocity undergoing Gaussian fluctuations, as opposed to…
The Levy Walk is the process with continuous sample paths which arises from consecutive linear motions of i.i.d. lengths with i.i.d. directions. Assuming speed 1 and motions in the domain of beta-stable attraction, we prove functional limit…
We consider the spreading dynamics of the Fisher-KPP equation in a shifting environment, by analyzing the limit of the rate function of the solutions. For environments with a weak monotone condition, it was demonstrated in a previous paper…
Random walk is a fundamental concept with applications ranging from quantum physics to econometrics. Remarkably, one specific model of random walks appears to be ubiquitous across many fields as a tool to analyze transport phenomena in…
In the Heliosphere, power-law particle distributions are observed e.g. upstream of interplanetary shocks, which can result from superdiffusive transport. This non-Gaussian transport regime may result from intermittent magnetic field…
A technique of hyperbolic scaling is applied to calculate a reaction front velocity in an irreversible autocatalytic conversion reaction $A+B\,\rightarrow\, 2A$ under subdiffusion. The method, based on the geometric optics approach is a…
We study the asymptotic spreading of Kolmogorov-Petrovsky-Piskunov (KPP) fronts in heterogeneous shifting habitats, with any number of shifting speeds, by further developing the method based on the theory of viscosity solutions of…
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 method of approximate automodel solution for the Green's function of the time-dependent superdiffusive (nonlocal) transport equations (J. Phys. A: Math. Theor. 49 (2016) 255002) is extended to the case of a finite velocity of carriers.…
We study the light-cone and front dynamics of a single particle continuous time extended quantum walk on a one dimensional lattice with finite range hopping. We show that, in general, for an initially localized state, propagating wave…
This article is concerned with pointwise growth and spreading speeds in systems of parabolic partial differential equations. Several criteria exist for quantifying pointwise growth rates. These include the location in the complex plane of…
L\'{e}vy robotic systems combine superdiffusive random movement with emergent collective behaviour from local communication and alignment in order to find rare targets or track objects. In this article we derive macroscopic fractional PDE…
A catalytic branching random walk on a multidimensional lattice, with arbitrary finite number of catalysts, is studied in supercritical regime. The dynamics of spatial spread of the particles population is examined, upon normalization. The…
The movement of organisms and cells can be governed by occasional long distance runs, according to an approximate L\'evy walk. For T cells migrating through chronically-infected brain tissue, runs are further interrupted by long pauses, and…
Front propagation described by Huygens' principle is a fundamental mechanism of spatial spreading of a property or an effect, occurring in optics, acoustics, ecology and combustion. If the local front speed varies randomly due to…
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…