Related papers: Time evolution of the reaction front in a subdiffu…
This paper investigates the dynamics of a reaction-diffusion system with two free boundaries, modeling the invasion of two cooperative species, where the free boundaries represent expanding fronts. We first analyze the long-term behavior of…
The embedded disks surrounding individual Class 0 protostars are structureless. Disks surrounding Class I stars may be continuous or have a ring-gap substructure, whereas all disks around Class II stars have a ring-gap substructure that…
In this work, we investigate an off-lattice version of the diffusion-reaction model, $A + A \leftrightarrow A$. We consider extensive numerical simulation of the radial system obtained from a single seed. Observed fluctuations in such an…
Among the main actors of organism development there are morphogens, which are signaling molecules diffusing in the developing organism and acting on cells to produce local responses. Growth is thus determined by the distribution of such…
The dynamics of fronts, such as chemical reaction fronts, propagating in two-dimensional fluid flows can be remarkably rich and varied. For time-invariant flows, the front dynamics may simplify, settling in to a steady state in which the…
We study slow-subdiffusion in comparison to subdiffusion. Both of the processes are treated as random walks and can be described within continuous time random walk formalism. However, the probability density of the waiting time of a random…
We study the asymptotic speed of traveling fronts of the scalar reaction diffusion for positive reaction terms and with a diffusion coefficient depending nonlinearly on the concentration and on its gradient. We restrict our study to…
Patterns in reaction-diffusion systems often contain two spatial scales; a long scale determined by a typical wavelength or domain size, and a short scale pertaining to front structures separating different domains. Such patterns naturally…
We study flow-induced enhancement of the speed of pulsating traveling fronts for reaction-diffusion equations, and quenching of reaction by fluid flows. We prove, for periodic flows in two dimensions and any combustion-type reaction, that…
We consider the subdiffusion-reaction process with reactions of a type A+B\arrow B (in which particles A are assumed to be mobile whereas B - static) in comparison to the subdiffusion-reaction process with A\rightarrow B reactions which was…
Front propagation in time dependent laminar flows is investigated in the limit of very fast reaction and very thin fronts, i.e. the so-called geometrical optics limit. In particular, we consider fronts evolving in time correlated random…
A number of results for reactions involving subdiffusive species all with the same anomalous exponent gamma have recently appeared in the literature and can often be understood in terms of a subordination principle whereby time t in…
One-dimensional reaction-diffusion systems are mapped through a similarity transformation onto integrable (and a priori non-stochastic) quantum chains. Time-dependent properties of these chemical models can then be found exactly. The…
We propose a method to extract from experimental data the subdiffusion parameter $\alpha$ and subdiffusion coefficient $D_\alpha$ which are defined by means of the relation $<x^2> =2D_\alpha/\Gamma(1+\alpha) t^\alpha$ where $<x^2>$ denotes…
Background: At energies near the Coulomb barrier, capture reactions in heavy-ion collisions result either in fusion or in quasifission. The former produces a compound nucleus in statistical equilibrium, while the second leads to a…
We investigate a reaction-diffusion-advection equation of the form $u_t-u_{xx}+\beta u_x=f(u)$ $(t>0,\,0<x<h(t))$ with mixed boundary condition at $x=0$ and a free boundary condition at $x=h(t)$. Such a model may be applied to describe the…
In this paper we present a mathematical model for the electrochemical deposition aimed at the production of inverse opals. The real system consists of an arrangement of sub micrometer spheres, through which the species in an electrolytic…
It is a well known fact that subdiffusion equations in terms of fractional derivatives can be obtained from Continuous Time Random Walk (CTRW) models with long-tailed waiting time distributions. Over the last years various authors have…
The large-time asymptotics of weak solutions to Maxwell--Stefan diffusion systems for chemically reacting fluids with different molar masses and reversible reactions are investigated. The diffusion matrix of the system is generally neither…
We consider an irreversible autocatalytic conversion reaction A+B -> 2A under subdiffusion described by continuous time random walks. The reactants' transformations take place independently on their motion and are described by constant…