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Considering the example of interacting Brownian particles we present a linear response derivation of the boundary condition for the corresponding hydrodynamic description (the diffusion equation). This requires us to identify a non-analytic…
An investigation of the effect of surface diffusion in random deposition model is made by analytical methods and reasoning. For any given site, the extent to which a particle can diffuse is decided by the morphology in the immediate…
In this work, we study an inverse problem of recovering a space-time dependent diffusion coefficient in the subdiffusion model from the distributed observation, where the mathematical model involves a Djrbashian-Caputo fractional derivative…
Stochastically gated interfaces play an important role in a variety of cellular diffusion processes. Examples include intracellular transport via stochastically gated ion channels and pores in the plasma membrane of a cell, intercellular…
We consider a system of non-interacting particles on a line with initial positions distributed uniformly with density $\rho$ on the negative half-line. We consider two different models: (i) each particle performs independent Brownian motion…
The study of diffusion with preferential returns to places visited in the past has attracted an increased attention in recent years. In these highly non-Markov processes, a standard diffusive particle intermittently resets at a given rate…
In this paper we consider a class of stochastic reaction-diffusion equations. We provide local well-posedness, regularity, blow-up criteria and positivity of solutions. The key novelties of this work are related to the use transport noise,…
A space discrete approximation to a highly nonlinear reaction-diffusion system endowed with a stochastic dynamical boundary condition is analyzed and the convergence of the discrete scheme to the solution to the corresponding continuum…
Diffusion through semipermeable interfaces has a wide range of applications, ranging from molecular transport through biological membranes to reverse osmosis for water purification using artificial membranes. At the single-particle level,…
We investigate the first passage properties of a Brownian particle diffusing freely inside a $d$-dimensional sphere with absorbing spherical surface subject to stochastic resetting. We derive the mean time to absorption (MTA) as functions…
We investigate the qualitative behaviour of the solutions of a stochastic boundary value problem on the half-line for a nonlinear system of parabolic reaction-diffusion equations, from a numerical point of view. The model describes the…
We consider the classical Shiryaev--Roberts martingale diffusion, $(R_t)_{t\ge0}$, restricted to the interval $[0,A]$, where $A>0$ is a preset absorbing boundary. We take yet another look at the well-known phenomenon of quasi-stationarity…
Large time dynamics of reaction-diffusion systems modeling some irreversible reaction networks are investigated. Depending on initial masses, these networks possibly possess boundary equilibria, where some of the chemical concentrations are…
`Gating' is a widely observed phenomenon in biochemistry that describes the transition between the activated (or open) and deactivated (or closed) states of an ion-channel, which makes transport through that channel highly selective. In…
Reaction-diffusion equations are one of the most common partial differential equations used to model physical phenomenon. They arise as the combination of two physical processes: a driving force $f(u)$ that depends on the state variable $u$…
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…
Cover times quantify the speed of exhaustive search. In this work, we compute exactly the mean cover time associated with a one-dimensional Brownian search under exponentially distributed resetting. We also approximate the moments of cover…
We study analytically the dynamics of an anisotropic particle subjected to different stochastic resetting schemes in two dimensions. The Brownian motion of shape-asymmetric particles in two dimensions results in anisotropic diffusion at…
We investigate the impact of intermittent energy injections on a Brownian particle, modeled as stochastic renewals of its kinetic energy to a fixed value. Between renewals, the particle follows standard underdamped Langevin dynamics. For…
Motivated by applications in economics and finance, in particular to the modeling of limit order books, we study a class of stochastic second-order PDEs with non-linear Stefan-type boundary interaction. To solve the equation we transform…