Related papers: Diffusion-controlled reactions with non-Markovian …
We investigate a class of diffusion-controlled reactions that are initiated at the time instance when a prescribed number $K$ among $N$ particles independently diffusing in a solvent are simultaneously bound to a target region. In the…
The reversible A <-> B reaction-diffusion process, when species A and B are initially mixed and diffuse with different diffusion coefficients, is investigated using the boundary layer function method. It is assumed that the ratio of the…
We investigate the reversible diffusion-influenced reaction of an isolated pair in the presence of a non-Markovian generalization of the backreaction boundary condition in two space dimensions. Following earlier work by Agmon and Weiss, we…
We study diffusion of particles on the surface of a sphere toward a partially reactive circular target with partly reversible binding kinetics. We solve the coupled diffusion-reaction equations and obtain the exact expressions for the…
We propose a general theoretical description of chemical reactions occurring on a catalytic surface with heterogeneous reactivity. The propagator of a diffusion-reaction process with eventual absorption on the heterogeneous partially…
In particle-based stochastic reaction-diffusion models, reaction rate and placement kernels are used to decide the probability per time a reaction can occur between reactant particles, and to decide where product particles should be placed.…
In this paper, we investigate the effects of stochastic resetting on diffusion in $\R^d\backslash \calU$, where $\calU$ is a bounded obstacle with a partially absorbing surface $\partial \calU$. We begin by considering a Robin boundary…
Diffusion-mediated surface phenomena are crucial for human life and industry, with examples ranging from oxygen capture by lung alveolar surface to heterogeneous catalysis, gene regulation, membrane permeation and filtration processes.…
We develop an encounter-based approach for describing restricted diffusion with a gradient drift towards a partially reactive boundary. For this purpose, we introduce an extension of the Dirichlet-to-Neumann operator and use its eigenbasis…
An encounter-based approach consists in using the boundary local time as a proxy for the number of encounters between a diffusing particle and a target to implement various surface reaction mechanisms on that target. In this paper, we…
Certain biochemical reactions can only be triggered after binding of a sufficient number of particles to a specific target region such as an enzyme or a protein sensor. We investigate the distribution of the reaction time, i.e., the first…
The classical models for irreversible diffusion-influenced reactions can be derived by introducing absorbing boundary conditions to over-damped continuous Brownian motion (BM) theory. As there is a clear corresponding stochastic process,…
Reaction-diffusion equations deliver a versatile tool for the description of reactions in inhomogeneous systems under the assumption that the characteristic reaction scales and the scales of the inhomogeneities in the reactant…
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…
In this paper we consider a multiparticle version of a recent probabilistic framework for studying diffusion-mediated surface reactions. The basic idea of the probabilistic approach is to consider the joint probability density or…
We revise the encounter-based approach to imperfect diffusion-controlled reactions, which employs the statistics of encounters between a diffusing particle and the reactive region to implement surface reactions. We extend this approach to…
The radiation (reaction, Robin) boundary condition for the continuum diffusion equation is widely used in chemical and biological applications to express reactive boundaries. The underlying trajectories of the diffusing particles are…
In this article we formulate new models for coupled systems of bulk-surface reaction-diffusion equations on stationary volumes. The bulk reaction-diffusion equations are coupled to the surface reaction-diffusion equations through linear…
Many cellular and subcellular biological processes can be described in terms of diffusing and chemically reacting species (e.g. enzymes). Such reaction-diffusion processes can be mathematically modelled using either deterministic…
This chapter aims at emphasizing the crucial role of partial reactivity of a catalytic surface or a target molecule in diffusion-controlled reactions. We discuss various microscopic mechanisms that lead to imperfect reactions, the Robin…