Related papers: On the reaction-diffusion replicator systems: Spat…

I present here some results on the statistical behaviour of large random matrices in an ensemble where the probability distribution is not a function of the eigenvalues only. The perturbative expansion can be cast in a closed form and the…

This article investigates the non-stationary reaction-diffusion-advection equation, emphasizing solutions with internal layers and the associated inverse problems. We examine a nonlinear singularly perturbed partial differential equation…

Many biological and physical systems exhibit behaviour at multiple spatial, temporal or population scales. Multiscale processes provide challenges when they are to be simulated using numerical techniques. While coarser methods such as…

The effect of diffusion rates on the basic reproduction number of a general compartmental reaction-diffusion epidemic model in a heterogeneous environment is considered. It is shown when the diffusion rates tend to zero, the limit of the…

In this note, we present a condition which guarantees spatial uniformity for the asymptotic behavior of the solutions of a reaction-diffusion PDE with Neumann boundary conditions in one dimension, using the Jacobian matrix of the reaction…

Simulation of stochastic spatially-extended systems is a challenging problem. The fundamental quantities in these models are individual entities such as molecules, cells, or animals, which move and react in a random manner. In big systems,…

Self- and cross-diffusion are important nonlinear spatial derivative terms that are included into biological models of predator-prey interactions. Self-diffusion models overcrowding effects, while cross-diffusion incorporates the response…

This paper addresses the question of how population diffusion affects the formation of the spatial patterns in the spatial epidemic model by Turing mechanisms. In particular, we present theoretical analysis to results of the numerical…

Weakly nonlinear amplitude equations are derived for the onset of spatially extended patterns on a general class of n-component bulk-surface reaction-diffusion systems in a ball, under the assumption of linear kinetics in the bulk and…

A multi-phase-field model for the description of the discontinuous precipitation reaction is formulated which takes into account surface diffusion along grain boundaries and interfaces as well as volume diffusion. Simulations reveal that…

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…

Although consensus seems to exist about the validity of equations accounting for radiation reaction in curved space-time, their previous derivations were criticized recently as not fully satisfactory: some ambiguities were noticed in the…

By considering the master equation of the partially asymmetric diffusion process on a one-dimensional lattice, the most general boundary condition (i.e. interactions) for the multi-species reaction-diffusion processes is considered.…

A spatio-temporal evolution of chemicals appearing in a reversible enzyme reaction and modelled by a four component reaction-diffusion system with the reaction terms obtained by the law of mass action is considered. The large time behaviour…

The interactions between diffusing molecules and membrane-bound receptors drive numerous cellular processes. In this work, we develop a spatial model of molecular interactions with membrane receptors by homogenizing the cell membrane and…

The question addressed here is the long time evolution of the solutions to a class of one-dimensional reaction-diffusion equations, in which the diffusion is given by an integral operator. The underlying motivation, discussed in the first…

Reaction-diffusion equations with a nonlinear source have been widely used to model various systems, with particular application to biology. Here, we provide a solution technique for these types of equations in $N$-dimensions. The…

In this paper, we study the relativistic Boltzmann equation in the spatially flat Robertson-Walker spacetime. For a certain class of scattering kernels, global existence of classical solutions is proved. We use the standard method of Illner…

Systems of interacting random replicators are studied using generating functional techniques. While replica analyses of such models are limited to systems with symmetric couplings, dynamical approaches as presented here allow specifically…

The paper discusses the use of amplitude equations to describe the spatio-temporal dynamics of a chemical reaction-diffusion system based on an Oregonator model of the Belousov-Zhabotinsky reaction. Sufficiently close to a supercritical…