Related papers: An encounter-based approach to the escape problem
The escape rate of a Brownian particle over a potential barrier is accurately described by the Kramers theory. A quantitative theory explicitly taking the activity of Brownian particles into account has been lacking due to the inherently…
A transient Poisson-Nernst-Planck system with steric effects is analyzed in a bounded domain with no-flux boundary conditions for the ion concentrations and mixed Dirichlet-Neumann boundary conditions for the electric potential. The steric…
The efficiency of an encounter-controlled two-channel reaction between two independently-mobile reactants on a lattice is characterized by the mean number $\rt$ of steps to reaction. The two reactants are distinguished by their mass with…
We study the diffusive limit approximation for a nonlinear radiative heat transfer system that arises in the modeling of glass cooling, greenhouse effects and in astrophysics. The model is considered with the reflective radiative boundary…
In many biological situations, a species arriving from a remote source diffuses in a domain confined between two parallel surfaces until it finds a binding partner. Since such a geometric shape falls in between two- and three-dimensional…
Motivated by a nonlocal free boundary problem, we study uniform properties of solutions to a singular perturbation problem for a boundary-reaction-diffusion equation, where the reaction term is of combustion type. This boundary problem is…
Continuous-time stochastic processes play an important role in the description of random phenomena, it is therefore of prime interest to study particular variables depending on their paths, like stopping time for example. One approach…
The Poisson-Nernst-Planck (PNP) diffusional model for the immittance or impedance spectroscopy response of an electrolytic cell in a finite-length situation is extended to a general framework. In this new formalism, the bulk behavior of the…
A general and local reactive boundary condition (RBC) for studying first-order equilibrium reactions using the lattice Boltzmann method (LBM) is presented. Its main characteristics are accurate reproduction of wall diffusion, invariance to…
Biochemical reactions can happen on different time scales and also the abundance of species in these reactions can be very different from each other. Classical approaches, such as deterministic or stochastic approach, fail to account for or…
We study a diffusion approximation for a model of stochastic motion of a particle in one spatial dimension. The velocity of the particle is constant but the direction of the motion undergoes random changes with a Poisson clock. Moreover,…
Barrier crossing is a widespread phenomenon across natural and engineering systems. While an abundant cross-disciplinary literature on the topic has emerged over the years, the stochastic underpinnings of the process are yet to be linked…
Transition State Theory overestimates reaction rates in solution because conventional dividing surfaces between reagents and products are crossed many times by the same reactive trajectory. We describe a recipe for constructing a…
We study the escape problem for interacting, self-propelled particles confined to a disc, where particles can exit through one open slot on the circumference. Within a minimal 2D Vicsek model, we numerically study the statistics of escape…
The dynamics of a coupled two-component nonequilibrium system is examined by means of continuum field theory representing the corresponding master equation. Particles of species A may perform hopping processes only when particles of…
Fluids confined to quasi-one-dimensional channels exhibit a dynamic crossover from single file diffusion to normal diffusion as the channel becomes wide enough for particles to hop past each other. In the crossover regime, where hopping…
We investigate reversible diffusion-influenced reactions of an isolated pair in two dimensions. To this end, we employ convolution relations that permit deriving the survival probability of the reversible reaction directly in terms of the…
A number of results for reactions involving subdiffusive species all with the same anomalous exponent gamma have recently appeared in the literature and can often be understood in terms of a subordination principle whereby time t in…
The classical theory of chemical reactions can be understood in terms of diffusive barrier crossing, where the rate of a reaction is determined by the inverse of the mean first passage time (FPT) to cross a free energy barrier. Whenever a…
This paper aims at obtaining, by means of integral transforms, analytical approximations in short times of solutions to boundary value problems for the one-dimensional reaction-diffusion equation with constant coefficients. The general form…