Related papers: Reaction-diffusion fronts under stochastic advecti…
The problem of spontaneous acceleration of premixed flames propagating in open horizontal tubes with smooth walls is revisited. It is proved that in long tubes, this process can be considered quasi-steady, and an equation for the flame…
The dynamic initiation of sliding at planar interfaces between deformable and rigid solids is studied with particular focus on the speed of the slip front. Recent experimental results showed a close relation between this speed and the local…
In this paper, we study stochastic homogenization of a coupled diffusion-reaction system. The diffusion-reaction system is coupled to stochastic differential equations, which govern the changes in the media properties. Though homogenization…
A coupled system of nonlinear mixed-type equations modeling early stages of angiogenesis is analyzed in a bounded domain. The system consists of stochastic differential equations describing the movement of the positions of the tip and stalk…
The dynamics of fronts, or kinks, in dispersive media with gain and losses is considered. It is shown that the front parameters, such as the velocity and width, depend on initial conditions. This result is not typical for dissipative…
A new upscaling procedure that provides 1D representations of 2D mixing-limited reactive transport systems is developed and applied. A key complication with upscaled models in this setting is that the procedure must differentiate between…
We study the persistence and propagation (or blocking) phenomena for a species in periodically hostile environments. The problem is described by a reaction-diffusion equation with zero Dirichlet boundary condition. We first derive the…
Extensive simulations are performed of the diffusion-limited reaction A$+$B$\to 0$ in one dimension, with initially separated reagents. The reaction rate profile, and the probability distributions of the separation and midpoint of the…
Diffusion in an evolving environment is studied by continuos-time Monte Carlo simulations. Diffusion is modelled by continuos-time random walkers on a lattice, in a dynamic environment provided by bubbles between two one-dimensional…
This paper is devoted to reaction-diffusion equations with bistable nonlinearities depending periodically on time. These equations admit two linearly stable states. However, the reaction terms may not be bistable at every time. These may…
Autocatalytic reaction fronts between two reacting species in the absence of fluid flow, propagate as solitary waves. The coupling between autocatalytic reaction front and forced hydrodynamic flow may lead to stationary front whose velocity…
Shock wave formation and propagation in two-dimensional granular materials under vertical vibration are studied by digital high speed photography. The steepen density and temperature wave fronts form near the plate as granular layer…
Motivated by the phenomenon of transport barriers in fusion plasma devices, we write a mathematical model of heat dispersion in a turbulent fluid with a transport barrier, properly idealized; in a scaling limit of the turbulence model with…
Problems of interface growth have received much attention recently Such are, for example, the duffusion limited aggregation (DLA), random sequential adsorption (RSA), Laplacian growth or flame front propagation. We will mainly pay attention…
In this paper, we extend and complement previous works about propagation in kinetic reaction-transport equations. The model we study describes particles moving according to a velocity-jump process, and proliferating according to a reaction…
We study the reaction front for the process A+B -> C in which the reagents move subdiffusively. Our theoretical description is based on a fractional reaction-subdiffusion equation in which both the motion and the reaction terms are affected…
We present a model for the thermally activated propagation of cracks in elastic matrices. The propagation is considered as a subcritical phenomenon, the kinetics of which being described by an Arrhenius law. In this law, we take the thermal…
A reaction-diffusion model which is called the field-road model was introduced by Berestycki, Roquejoffre and Rossi [9] to describe biological invasion with fast diffusion on a line. In this paper, we investigate this model in a…
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…
We study a reaction-diffusion process that involves two species of atoms, immobile and diffusing. We assume that initially only immobile atoms, uniformly distributed throughout the entire space, are present. Diffusing atoms are injected at…