Related papers: Reaction-diffusion kinetics in growing domains
The problem of velocity selection of reaction-diffusion fronts has been widely investigated. While the mean field limit results are well known theoretically, there is a lack of analytic progress in those cases in which fluctuations are to…
Among living organisms, there are species that change their patterns on their body surface during their growth process and those that maintain their patterns. Theoretically, it has been shown that large-scale species do not form distinct…
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…
Reaction diffusion systems are often used to study pattern formation in biological systems. However, most methods for understanding their behavior are challenging and can rarely be applied to complex systems common in biological…
Many physical phenomena occur on domains that grow in time. When the timescales of the phenomena and domain growth are comparable, models must include the dynamics of the domain. A widespread intrinsically slow transport process is…
We discuss a reaction-diffusion model in one dimension subjected to an external driving force. Each lattice site may be occupied by at most one particle. The particles hop with asymmetric rates (the sum of which is one) to the right or left…
Chemical reactions involving diffusion of reactants and subsequent chemical fixation steps are generally termed "diffusion-influenced" (DI). Virtually all biochemical processes in living media can be counted among them, together with those…
Models of diffusive processes that occur on evolving domains are frequently employed to describe biological and physical phenomena, such as diffusion within expanding tissues or substrates. Previous investigations into these models either…
We investigate a fast-reaction--diffusion system modelling the effect of autotoxicity on plant-growth dynamics, in which the fast-reaction terms are based on the dichotomy between healthy and exposed roots depending on the toxicity. The…
Many biological activities are induced by cellular chemical reactions of diffusing reactants. The dynamics of such systems can be captured by stochastic reaction networks. A recent numerical study has shown that diffusion can significantly…
Evolution of a system of diffusing and proliferating mortal reactants is analyzed in the presence of randomly moving catalysts. While the continuum description of the problem predicts reactant extinction as the average growth rate becomes…
This paper is devoted to the study of systems of reaction-cross diffusion equations arising in population dynamics. New results of existence of weak solutions are presented, allowing to treat systems of two equations in which one of the…
We investigate non-equilibrium critical phenomena using a nonperturbative renormalization group method. Reaction-diffusion processes are described by a scale dependent effective action which evolution is governed by very generic flow…
Compartmentalization of biochemical processes underlies all biological systems, from the organelle to the tissue scale. Theoretical models to study the interplay between noisy reaction dynamics and compartmentalization are sparse, and…
The reaction of volatile matter plays an important role in the process of bringing matter from the surface of the planet to the atmosphere. Therefore, by simulating the mixing and chemical reaction process of volatile matter in the…
A one-dimensional reaction-diffusion model consisting of two species of particles and vacancies on a ring is introduced. The number of particles in one species is conserved while in the other species it can fluctuate because of creation and…
A parameter estimation problem for a class of semilinear stochastic evolution equations is considered. Conditions for consistency and asymptotic normality are given in terms of growth and continuity properties of the nonlinear part.…
We consider systems of reaction-diffusion equations coupled in zero order terms, with general homogeneous boundary conditions in domains with a particular geometry (annular type domains). We establish Lipschitz stability estimates in L^2…
In this paper we perform a formal asymptotic analysis on a kinetic model for reactive mixtures in order to derive a reaction-diffusion system of Maxwell-Stefan type. More specifically, we start from the kinetic model of simple reacting…
This paper proposes a novel reaction-diffusion system approximation tailored for singular diffusion problems, typified by the fast diffusion equation. While such approximation methods have been successfully applied to degenerate parabolic…