Related papers: Reaction Front in an A+B -> C Reaction-Subdiffusio…
This paper is concerned with a diffusion-controlled moving-boundary problem in drug dissolution, in which the moving front passes from one medium to another for which the diffusion coefficient is many orders of magnitude smaller. It has…
Chemical reactions inside cells are generally considered to happen within fixed-size compartments. Needless to say, cells and their compartments are highly dynamic. Thus, such stringent assumptions may not reflect biochemical reality, and…
Retrosynthesis prediction focuses on identifying reactants capable of synthesizing a target product. Typically, the retrosynthesis prediction involves two phases: Reaction Center Identification and Reactant Generation. However, we argue…
We look for similarity transformations which yield mappings between different one-dimensional reaction-diffusion processes. In this way results obtained for special systems can be generalized to equivalent reaction-diffusion models. The…
Reaction-diffusion models have been used over decades to study biological systems. In this context, evolution equations for probability distribution functions and the associated stochastic differential equations have nowadays become…
The paper deals with reaction-diffusion equations involving a hysteretic discontinuity in the source term, which is defined at each spatial point. In particular, such problems describe chemical reactions and biological processes in which…
We consider the diffusion-controlled annihilation dynamics $A+B\to 0$ with equal species diffusivities in the system where an island of particles $A$ is surrounded by the uniform sea of particles $B$. We show that once the initial number of…
In a recent paper Goriely considers the one--dimensional scalar reaction--diffusion equation $u_t = u_{xx} + f(u)$ with a polynomial reaction term $f(u)$ and conjectures the existence of a relation between a global resonance of the…
A mixing time density of $A + B \to 0$ on a finite one dimensional domain is defined for general initial and boundary conditions in which $A$ and $B$ diffuse at the same rate. The density is a measure of the number of $A$ and $B$ particles…
We consider in this paper a diffusion-convection reaction equation in one space dimension. The main assumptions are about the reaction term, which is monostable, and the diffusivity, which changes sign once or twice; then, we deal with a…
Reaction fronts evolving in a porous medium exhibit a rich dynamical behaviour. In presence of an adverse flow, experiments show that the front slows down and eventually gets pinned, displaying a particular sawtooth shape. Extensive…
Resonantly-forced oscillatory reaction-diffusion systems can exhibit fronts with complicated interfacial structure separating phase-locked homogeneous states. For values of the forcing amplitude below a critical value the front "explodes"…
A $g$--subdiffusion equation with fractional Caputo time derivative with respect to another function $g$ is used to describe a process of a continuous transition from subdiffusion with parameters $\alpha$ and $D_\alpha$ to subdiffusion with…
We study invasion fronts and spreading speeds in two component reaction-diffusion systems. Using a variation of Lin's method, we construct traveling front solutions and show the existence of a bifurcation to locked fronts where both…
Diffusion-mediated surface phenomena are crucial for human life and industry, with examples ranging from oxygen capture by lung alveolar surface to heterogeneous catalysis, gene regulation, membrane permeation and filtration processes.…
Reaction-diffusion processes can be adopted to model a large number of dynamics on complex networks, such as transport processes or epidemic outbreaks. In most cases, however, they have been studied from a fermionic perspective, in which…
We investigate the influence of fluid flows on the propagation of chemical fronts arising in FKPP type models. We develop an asymptotic theory for the front speed in a cellular flow in the limit of small molecular diffusivity and fast…
The empirical speed of travelling reaction-diffusion fronts fluctuates due to the intrinsic shot noise of the reactions and diffusion. Here we study the long-time front speed fluctuations of a stochastic Huxley-Zel'dovich front. It involves…
Phase transitions of reaction-diffusion systems with site occupation restriction and with particle creation that requires n>1 parents and where explicit diffusion of single particles (A) exists are reviewed. Arguments based on mean-field…
In many biological situations, a species arriving from a remote source diffuses in a domain confined between two parallel surfaces until it finds a binding partner. Since such a geometric shape falls in between two- and three-dimensional…