Related papers: Diffusion limited aggregation as a Markovian proce…
By considering the master equation of asymmetric exclusion process on a one-dimensional lattice, we obtain the most general boundary condition of the multi-species exclusion processes in which the number of particles is constant in time.…
We study diffusion-reaction processes on periodic square planar lattices and simple cubic (sc) lattices. Considered first is a single diffusing reactant undergoing an irreversible reaction upon first encounter with a stationary co-reactant…
A diffusive lattice gas is characterized by the diffusion coefficient depending only on the density. The Green-Kubo formula for diffusivity can be represented as a variational formula, but even when the equilibrium properties of a lattice…
We study the diffusion phenomena on the negatively curved surface made up of congruent heptagons. Unlike the usual two-dimensional plane, this structure makes the boundary increase exponentially with the distance from the center, and hence…
In this paper we present stochastic foundations of fractional dynamics driven by fractional material derivative of distributed order-type. Before stating our main result we present the stochastic scenario which underlies the dynamics given…
The paper presents a generalization of the local limit theorem on the convergence of inhomogeneous Markov chains to the diffusion limit for the case where the corresponding process coefficients satisfy weak regularity conditions and…
Discrete-space kinetic models, i.e., Markov state models, have emerged as powerful tools for reducing the complexity of trajectories generated from molecular dynamics simulations. These models require configuration-space representations…
We introduce a simplified technique for incorporating diffusive phenomena into lattice-gas molecular dynamics models. In this method, spatial interactions take place one dimension at a time, with a separate fractional timestep devoted to…
A finite difference method is constructed to solve singularly perturbed convection-diffusion problems posed on smooth domains. Constraints are imposed on the data so that only regular exponential boundary layers appear in the solution. A…
We study the transport of self-propelled particles in dynamic complex environments. To obtain exact results, we introduce a model of run-and-tumble particles (RTPs) moving in discrete time on a $d$-dimensional cubic lattice in the presence…
A diffusion-limited aggregation process, in which clusters coalesce by means of 3-particle reaction, A+A+A->A, is investigated. In one dimension we give a heuristic argument that predicts logarithmic corrections to the mean-field asymptotic…
A kinetic description of lattice-gas automaton models for reaction-diffusion systems is presented. It provides corrections to the mean-field rate equations in the diffusion-limited regime. When applied to the two-species Maginu model, the…
The Markovian diffusion theory is generalized within the framework of the special theory of relativity using a modification of the mathematical calculus of diffusion on Riemannian manifolds (with definite metric) to describe diffusion on…
Gradient-driven diffusion in crowded, multicomponent mixtures is a topic of high interest because of its role in biological processes such as transport in cell membranes. In partially phase-separated solutions, gradient-driven diffusion…
Discrete diffusion models have emerged as a powerful class of models and a promising route to fast language generation, but practical implementations typically rely on factored reverse transitions ignoring cross-token dependencies and…
A Markov chain model for spatially distributed autocatalytic systems with a quadratic reaction rate is considered. An approximate solution for the local probability distribution is obtained in the form of a perturbation expansion for the…
A standard approach to solving the S$_N$ transport equations is to use source iteration with diffusion synthetic acceleration (DSA). Although this approach is widely used and effective on many problems, there remain some practical issues…
This paper is concerned with the large-time dynamics of bounded solutions of reaction-diffusion equations with bounded or unbounded initial support in R N. We start with a survey of some old and recent results on the spreading speeds of the…
We study the diffusion-reaction-advection model for mobile chemical species together with the dissolution and precipitation of immobile species in a porous medium at the micro-scale. This leads to a system of semilinear parabolic partial…
Established theoretical studies of diffusion in rugged (or rough) potential surfaces have largely focused on quenched energy landscapes. Here we study diffusion on a rugged energy landscape in the presence of dynamic disorder, a situation…