Related papers: Annihilation-diffusion processes: an exactly solva…
We consider the totally asymmetric exclusion process in discrete time with generalized updating rules. We introduce a control parameter into the interaction between particles. Two particular values of the parameter correspond to known…
Epidemic spreading often occurs in spatially heterogeneous environments, yet how quenched heterogeneity reshapes its onset and critical dynamics remains poorly understood. The diffusive epidemic process, a minimal reaction-diffusion model…
The problem of eliminating fast-relaxing variables to obtain an effective drift-diffusion process in position is solved in a uniform and straightforward way for models with velocity a function jointly of position and fast variables. A more…
We consider diffusion processes x_{t} on the unit interval. Doob-transformation techniques consist of a selection of x_{t}-paths procedure. The law of the transformed process is the one of a branching diffusion system of particles, each…
An exactly solvable strongly correlated electron model with two independent parameters is constructed in the frame of the quantum inverse scattering method, which can be seen as a generalization of the Bariev model. Through the Bethe ansatz…
We introduce an exactly-solvable family of one-dimensional driven-diffusive systems defined on a discrete lattice. We find the quadratic algebra of this family which has an infinite-dimensional representation. We discuss the phase diagram…
The use of fully or partially absorbing boundary conditions for diffusion-based problems has become paradigmatic in physical chemistry and biochemistry to describe reactions occurring in solutions or in living media. However, as chemical…
This article is concerned with the mathematical analysis of a family of adaptive importance sampling algorithms applied to diffusion processes. These methods, referred to as Adaptive Biasing Potential methods, are designed to efficiently…
Two-particle annihilation reaction, A+A -> inert, for immobile reactants on the Bethe lattice is solved exactly for the initially random distribution. The process reaches an absorbing state in which no nearest-neighbor reactants are left.…
The behavior of the single-species reaction process $A+A\to O$ is examined near an impenetrable boundary, representing the flask containing the reactants. Two types of dynamics are considered for the reactants: diffusive and ballistic…
A model glass with fast and slow processes is studied. The statics is simple and the facilitated slow dynamics is exactly solvable. The main features of a fragile glass take place: Kauzmann transition, Vogel-Fulcher law, Adam-Gibbs relation…
We study three basic diffusion-controlled reaction processes -- annihilation, coalescence, and aggregation. We examine the evolution starting with the most natural inhomogeneous initial configuration where a half-line is uniformly filled by…
We study a reaction-diffusion system on the real line, where the reactions of the species are given by one reversible reaction according to the mass-action law. We describe different positive limits at both sides of infinity and investigate…
The aim of this report is to give an insight into the key features of the phenomenon called Annihilation Catastrophe which may pretend to be one of the most dramatic manifestations of the reaction-diffusion interplay.
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…
The mean-field reaction-diffusion equations of the diffusive pair-annihilation and triplett-annihilation processes are considered. A direct lower bound on the time-dependent mean particle-density is derived. The results are applied to the…
The fast diffusion equation is analyzed on a bounded domain with Dirichlet boundary conditions, for which solutions are known to extinct in finite time. We construct invariant manifolds that provide a finite-dimensional approximation near…
The kinetics of the annihilation process, $A+A\to 0$, with ballistic particle motion is investigated when the distribution of particle velocities is {\it discrete}. This discreteness is the source of many intriguing phenomena. In the mean…
The most general one dimensional reaction-diffusion model with nearest-neighbor interactions, which is exactly-solvable through the empty interval method, has been introduced. Assuming translationally-invariant initial conditions, the…
The exact solution of the asymmetric exclusion problem with particles of first and second class is presented. In this model the particles (size 1) of both classes are attached on lattice points and diffuse with equal asymmetric rates, but…