Related papers: Phase coexistence in a weakly stochastic reaction-…
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…
Although the spatially continuous version of the reaction-diffusion equation has been well studied, in some instances a spatially-discretized representation provides a more realistic approximation of biological processes. Indeed,…
A new non-conservative stochastic reaction-diffusion system in which two families of random walks in two adjacent domains interact near the interface is introduced and studied in this paper. Such a system can be used to model the transport…
This paper is concerned with reaction-diffusion systems of two symmetric species in spatial dimension one, having two stable symmetric equilibria connected by a symmetric standing front. The first order variation of the speed of this front…
Time-dependently driven stochastic systems form a vast and manifold class of non-equilibrium systems used to model important applications on small length scales such as bit erasure protocols or microscopic heat engines. One property that…
Collective diffusion coefficient in a two-dimensional lattice gas on a nonhomogeneous substrate is investigated using variational approach. Particles reside at adsorption sites with different well depths potentials and jump randomly between…
Recent experiments by Sato et al. [1] have explored the dynamics of $^4$He superflow through an array of nanopores. These experiments have found that, as the temperature is lowered, phase-slippage in the pores changes its character, from…
We have observed well-defined phase slips between quantized persistent current states around a toroidal atomic (23Na) Bose-Einstein condensate. These phase slips are induced by a weak link (a localized region of reduced superfluid density)…
The global existence of bounded weak solutions to a diffusion system modeling biofilm growth is proven. The equations consist of a reaction-diffusion equation for the substrate concentration and a fourth-order Cahn-Hilliard-type equation…
We study probability distribution of a steady state of a periodically driven system coupled to a thermal bath by using a quantum master equation in the weak coupling limit. It is proved that, even when the external field is strong, the…
Diffraction of elastic waves is considered for a system consisting of two parallel arrays of thin (subwavelength) cylinders that are arranged periodically. The embedding media supports waves with all polarizations, one longitudinal and two…
When particles/molecules diffuse in systems that contain obstacles, the steady-state regime (during which the mean-square displacement scales linearly with time, $\left< r^2 \right> \sim t$) is preceded by a transient regime. It is common…
We develop a theory to calculate the effective phase diffusion coefficient and the mean phase velocity in periodically driven stochastic models with two discrete states. This theory is applied to a dichotomically driven Markovian two state…
Slow-fast dynamics and resonant phenomena can be found in a wide range of physical systems, including problems of celestial mechanics, fluid mechanics, and charged particle dynamics. Important resonant effects that control transport in the…
Chemical and biochemical reactions can exhibit surprisingly different behaviours, ranging from multiple steady-state solutions to oscillatory solutions and chaotic behaviours. These types of systems are often modelled by a system of…
Fluid phase equilibria involving nano-dispersed phases, where at least one of the coexisting phases is confined to a small volume, are investigated by molecular dynamics simulation. Complementing previous studies on nanoscopic droplets,…
We study an interacting box-particle system on a one-dimensional periodic ring involving two species of particles $A$ and $B$. In this model, from a randomly chosen site, a particle of species $A$ can hop to its right neighbor with a rate…
We present a general method for determining the phase diagram of systems of a finite number of one dimensional Hubbard--like systems coupled by single--particle hopping with weak interactions. The technique is illustrated by detailed…
Stochastic dynamical systems arise as models for fluid particle motion in geophysical flows with random velocity fields. Escape probability (from a fluid domain) and mean residence time (in a fluid domain) quantify fluid transport between…
Self-diffusion and radial distribution functions are studied in a strongly confined Lennard-Jones fluid. Surprisingly, in the solid-liquid phase transition region, where the system exhibits dynamic coexistence, the self-diffusion constants…