Related papers: Subdiffusion-limited reactions
We consider the coagulation dynamics A+A -> A and the annihilation dynamics A+A -> 0 for particles moving subdiffusively in one dimension, both on a lattice and in a continuum. The analysis combines the "anomalous kinetics" and "anomalous…
We present a theory for the coagulation reaction A+A -> A for particles moving subdiffusively in one dimension. Our theory is tested against numerical simulations of the concentration of $A$ particles as a function of time (``anomalous…
One-dimensional reaction-diffusion models A+A -> 0, A+A -> A, and $A+B -> 0, where in the latter case like particles coagulate on encounters and move as clusters, are solved exactly with anisotropic hopping rates and assuming synchronous…
We study the kinetics of diffusion-limited coalescence, A+A->A, and annihilation, A+A->0, in random media consisting of disconnected domains of reaction. Examples include excitons fusion and annihilation in porous matrices and along polymer…
Reaction dynamics involving subdiffusive species is an interesting topic with only few known results, especially when the motion of different species is characterized by different anomalous diffusion exponents. Here we study the reaction…
Subdiffusion with reaction $A+B\rightarrow B$ is considered in a system which consists of two homogeneous media joined together; the $A$ particles are mobile whereas $B$ are static. Subdiffusion and reaction parameters, which are assumed to…
Deriving evolution equations accounting for both anomalous diffusion and reactions is notoriously difficult, even in the simplest cases. In contrast to normal diffusion, reaction kinetics cannot be incorporated into evolution equations…
The dynamics of a coupled two-component nonequilibrium system is examined by means of continuum field theory representing the corresponding master equation. Particles of species A may perform hopping processes only when particles of…
Recent investigations call attention to the dynamics of anomalous diffusion and its connection with basic principles of statistical mechanics. We present here a short review of those ideas and their implications.
In this article we review the problem of reaction annihilation $A+A \rightarrow \emptyset$ on a real lattice in one dimension, where $A$ particles move ballistically in one direction with a discrete set of possible velocities. We first…
A new method is introduced allowing to solve exactly the reactions A+A->inert and A+A->A on the 1D lattice with synchronous diffusional dynamics (simultaneous hopping of all particles). Exact connections are found relating densities and…
In this article we review classical and recent results in anomalous diffusion and provide mechanisms useful for the study of the fundamentals of certain processes, mainly in condensed matter physics, chemistry and biology. Emphasis will be…
We show analytically that there is anomalous diffusion when the diffusion constant depends on the concentration as a power law with a positive exponent or a negative exponent with absolute value less than one and the initial condition is a…
To capture the dynamic behaviors of reaction-subdiffusion in flow fields, in the present paper we analyze a simple monomolecular conversion A $\rightarrow$ B. We derive the corresponding master equations for the distribution of A and B…
We introduce a method of intervals for the analysis of diffusion-limited annihilation, A+A -> 0, on the line. The method leads to manageable diffusion equations whose interpretation is intuitively clear. As an example, we treat 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…
We study kinetics of diffusion-limited catalytically-activated $A + B \to B$ reactions taking place in three dimensional systems, in which an annihilation of diffusive $A$ particles by diffusive traps $B$ may happen only if the encounter of…
Reaction-diffusion equations are one of the most common mathematical models in the natural sciences and are used to model systems that combine reactions with diffusive motion. However, rather than normal diffusion, anomalous subdiffusion is…
We consider the trapping reaction A + B -> B in space dimension d<=2. By formally eliminating the B particles from the problem we derive an effective dynamics for the A particles from which the survival probability of a given A particle and…
We discuss stationary concentrations of reactants in an A + B -> 0 reaction under subdiffusion and show that they are described by stationary reaction-diffusion equations with a nonlinear diffusion term. We consider stationary profiles of…