Related papers: Diffusion-Limited Coalescence, A+A<-->A, with a Tr…
Many non-equilibrium systems display dynamic phase transitions from active to absorbing states, where fluctuations cease entirely. Based on a field theory representation of the master equation, the critical behavior can be analyzed by means…
We study theoretically a scheme in which particles from an incident beam are trapped in a potential well when colliding with particles already present in the well. The balance between the arrival of new particles and the evaporation of…
Coupled-channel two-particle systems bound by a harmonic trap are discussed in the present paper. We derive the formula that relates the energy levels of such trapped systems to phase shifts and inelasticity of coupled-channel reactions.…
The stationary phase method is applied to diffusion by a potential barrier for an incoming wave packet with energies greater then the barrier height. It is observed that a direct application leads to paradoxical results. The correct…
In this paper, we study the diffusive limit of the steady state radiative heat transfer system for non-homogeneous Dirichlet boundary conditions in a bounded domain with flat boundaries. A composite approximate solution is constructed using…
This paper develops stability and stabilization results for systems of fully coupled jump diffusions. Such systems frequently arise in numerous applications where each subsystem (component) is operated under the influence of other…
We study the long-time tails of the survival probability $P(t)$ of an $A$ particle diffusing in $d$-dimensional media in the presence of a concentration $\rho$ of traps $B$ that move sub-diffusively, such that the mean square displacement…
We study the dynamics of a system made up of particles of two different species undergoing irreversible quadratic autocatalytic reactions: $A + B \to 2A$. We especially focus on the reaction velocity and on the average time at which the…
The reaction A+B --> B is studied when the reactants diffuse in phase space, i.e. their dynamics is described by the Langevin equation. The steady-state rate constants are calculated for both the target (static A and mobile B's) and…
We analyze the tagged particle diffusion for kinetically constrained models for glassy systems. We present a method, focusing on the Kob-Andersen model as an example, which allows to prove lower and upper bounds for the self diffusion…
In this paper, we present and apply a computer-assisted method to study steady states of a triangular cross-diffusion system. Our approach consist in an a posteriori validation procedure, that is based on using a fxed point argument around…
A generalisation of reaction diffusion systems and their travelling solutions to cases when the productive part of the reaction happens only on a surface in space or on a line on plane but the degradation and the diffusion happen in bulk…
We examine the long-time behaviour of A+B \to 0 reaction-diffusion systems with initially separated species A and B. All of our analysis is carried out for arbitrary (positive) values of the diffusion constant D_A of particles A and initial…
We study the stationary states of an over-damped active Brownian particle (ABP) in a harmonic trap in two dimensions, via mathematical calculations and numerical simulations. In addition to translational diffusion, the ABP self-propels with…
A class of variable coefficient (1+1)-dimensional nonlinear reaction-diffusion equations of the general form $f(x)u_t=(g(x)u^nu_x)_x+h(x)u^m$ is investigated. Different kinds of equivalence groups are constructed including ones with…
We present a simple model for deep bed filtration, where particles suspended in a fluid are trapped while passing through a porous filter. A steady state of the model is reached when filter can not trap additional particles. We find the…
Prolongating our previous paper on the Einstein relation, we study the motion of a particle diffusing in a random reversible environment when subject to a small external forcing. In order to describe the long time behavior of the particle,…
In this paper we present a method to measure transient fluorescent dynamics with single trapped ions in a Paul trap. We use $^{40}$Ca$^+$ ions which exhibit a $\Lambda$-type three-level system and measure the characteristic optical pumping…
We consider three equilibrium concepts proposed in the literature for time-inconsistent stopping problems, including mild equilibria, weak equilibria and strong equilibria. The discount function is assumed to be log sub-additive and the…
We investigate the convergence of spatial discretizations for reaction-diffusion systems with mass-action law satisfying a detailed balance condition. Considering systems on the d-dimensional torus, we construct appropriate space-discrete…