Related papers: Solution of a One-Dimensional Reaction-Diffusion M…
The distribution of exit times is computed for a Brownian particle in spherically symmetric two- dimensional domains (disks, angular sectors, annuli) and in rectangles that contain an exit on their boundary. The governing partial…
We study the one-dimensional diffusion process which takes place between two reflecting boundaries and which is acted upon by a time-dependent and spatially-constant force. The assumed force possesses both the harmonically oscillating and…
This paper treats the solvability of a semilinear reaction-diffusion system, which incorporates transport (diffusion) and reaction effects emerging from two separated spatial scales: $x$ - macro and $y$ - micro. The system's origin connects…
Spatial solitary waves in colloidal suspensions of spherical dielectric nanoparticles are considered. The interaction of the nanoparticles is modelled as a hard-sphere gas, with the Carnahan-Starling formula used for the gas…
The master equation of one-dimensional three-species reaction-diffusion processes is mapped onto an imaginary-time Schr\"odinger equation. In many cases the Hamiltonian obtained is that of an integrable quantum chain. Within this approach…
The relation between relaxation and diffusion is investigated in a Hamiltonian system of globally coupled rotators. Diffusion is anomalous if and only if the system is going towards equilibrium. The anomaly in diffusion is not anomalous…
The theory of spin diffusion is extended to the case of spin lattice relaxation and spin diffusion in an inhomogeneous field in spin systems with non-equidistant energy spectrum. Two coupled equations describing the mutual relaxation and…
We analyze long-time behavior of solutions to a class of problems related to very fast and singular diffusion porous medium equations having nonhomogeneous in space and time source terms with zero mean. In dimensions two and three, we…
Consider a semiclassical Hamiltonian \begin{equation*} H_{V, h} := h^{2} \Delta + V - E \end{equation*} where $h > 0$ is a semiclassical parameter, $\Delta$ is the positive Laplacian on $\mathbb{R}^{d}$, $V$ is a smooth, compactly supported…
We study a non-conserved one-dimensional stochastic process which involves two species of particles $A$ and $B$. The particles diffuse asymmetrically and react in pairs as $A\emptyset\leftrightarrow AA\leftrightarrow BA \leftrightarrow…
One-dimensional non-equilibrium models of particles subjected to a coagulation-diffusion process are important in understanding non-equilibrium dynamics, and fluctuation-dissipation relation. We consider in this paper transport properties…
We analytically investigate a 1d branching-coalescing model with reflecting boundaries in a canonical ensemble where the total number of particles on the chain is conserved. Exact analytical calculations show that the model has two…
We consider the motion of a particle on a surface which is a small perturbation of the standard sphere. One may qualitatively describe the motion by means of a precessing great circle of the sphere. The observation is employed to derive a…
We introduce and study an exactly solvable model of several species of fermions in which particles interact pairwise through a mutual magnetic field; the interaction operates only between particles belonging to different species. After an…
We consider a family of models having an arbitrary positive amount of mass on each site and randomly exchanging an arbitrary amount of mass with nearest neighbor sites. We restrict to the case of diffusive models. We identify a class of…
I consider the coupled one-dimensional diffusion of a cluster of N classical particles with contact repulsion. General expressions are given for the probability distributions, allowing to obtain the transport coefficients. In the limit of…
The classical one-phase Stefan problem describes the temperature distribution in a homogeneous medium undergoing a phase transition, such as ice melting to water. This is accomplished by solving the heat equation on a time-dependent domain…
For hyperbolic first-order systems of linear partial differential equations (master equations), appearing in description of kinetic processes in physics, biology and chemistry we propose a new procedure to obtain their complete closed-form…
Reaction-diffusion equations with a nonlinear source have been widely used to model various systems, with particular application to biology. Here, we provide a solution technique for these types of equations in $N$-dimensions. The…
Stochastic chemical systems with diffusion are modeled with a reaction-diffusion master equation. On a macroscopic level, the governing equation is a reaction-diffusion equation for the averages of the chemical species. On a mesoscopic…