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Certain biological reactions, such as receptor-ligand binding at cell-cell interfaces and macromolecules binding to biopolymers, require many smaller molecules crowding a reaction site to be cleared. Examples include the T cell interface, a…
Reaction-diffusion equations are studied on bounded, time-periodic domains with zero Dirichlet boundary conditions. The long-time behaviour is shown to depend on the principal periodic eigenvalue of a transformed periodic-parabolic problem.…
We develop a theory of reversible diffusion-controlled reactions with generalized binding/unbinding kinetics. In this framework, a diffusing particle can bind to the reactive substrate after a random number of arrivals onto it, with a given…
We study the one-dimensional motion of a Brownian particle inside a confinement described by two reactive boundaries which can partially reflect or absorb the particle. Understanding the effects of such boundaries is important in physics,…
A new solution to the mono-dimensional diffusion equation for time-variable first kind boundary condition is presented where the time-variable function at the surface is derived proposing a surface saturation model. This solution may be…
Consider a finite system of diffusing particles coupled through a reactive boundary. Each particle is reflected, but may react with the boundary according to a killing mechanism which depends on the current reactivity of the boundary and…
Sticky diffusion processes on bounded domains spend finite time (and finite mean time) on the lower-dimensional space given by the boundary. Once the process hits the boundary, then it starts again after a random amount of time. While on…
We investigate a diffusive motion of a system of interacting Brownian particles in quasi-one-dimensional micropores. In particular, we consider a semi-infinite 1D geometry with a partially absorbing boundary and the hard-core inter-particle…
We investigate the statistics of the first-passage time (FPT) to a fractal self-similar boundary of the Koch snowflake. When the starting position is fixed near the absorbing boundary, the FPT distribution exhibits an apparent power-law…
We study statistical relationships between bubble walls in cosmological first-order phase transitions. We consider the conditional and joint probabilities for different points on the walls to remain uncollided at given times. We use these…
The first passage time for a single diffusing particle has been studied extensively, but the first passage time of a system of many diffusing particles, as is often the case in physical systems, has received little attention until recently.…
We investigate the boundary local time on polygonal boundaries such as finite generations of the Koch snowflake. To reveal the role of angles, we first focus on wedges and obtain the mean boundary local time, its variance, and the…
In this paper, we develop a Monte Carlo based algorithm for estimating the FPT density of a time-homogeneous SDE through a time-dependent frontier. We consider Brownian bridges as well as localized Daniels curve approximations to obtain…
The inverse first-passage time problem determines a boundary such that the first-passage time of a Wiener process to this boundary has a given distribution. An approximation which is based on the starting value of the boundary to a smooth…
Trimolecular reaction models are investigated in the compartment-based (lattice-based) framework for stochastic reaction-diffusion modelling. The formulae for the first collision time and the mean reaction time are derived for the case…
We show a probabilistic functional limit result for one-dimensional diffusion processes that are reflected at an elastic boundary which is a function of the reflection local time. Such processes are constructed as limits of a sequence of…
Recently a general growth curve including the well known growth equations, such as Malthus, logistic, Bertallanfy, Gompertz, has been studied. We now propose two stochastic formulations of this growth equation. They are obtained starting…
We derive a variational expression for the correlation time of physical observables in steady-state diffusive systems. As a consequence of this variational expression, we obtain lower bounds on the correlation time, which provide speed…
We consider a 1-dimensional Brownian motion whose diffusion coefficient varies when it crosses the origin. We study the long time behavior and we establish different regimes, depending on the variations of the diffusion coefficient:…
Advection and dispersion in highly heterogeneous environments involving interfacial discontinuities in the corresponding drift and dispersion rates are described through disparate examples from the physical and biological sciences. A…