Related papers: An encounter-based approach to the escape problem
A new asymptotic method is presented for the analysis of the traveling waves in the one-dimensional reaction-diffusion system with the diffusion with a finite velocity and Kolmogorov-Petrovskii-Piskunov kinetics. The analysis makes use of…
Reaction-Diffusion systems arise in diverse areas of science and engineering. Due to the peculiar characteristics of such equations, analytic solutions are usually not available and numerical methods are the main tools for approximating the…
We study a large class of 1D reaction diffusion models with quenched disorder using a real space renormalization group method (RSRG) which yields exact results at large time. Particles (e.g. of several species) undergo diffusion with random…
The paper deals with reaction-diffusion equations involving a hysteretic discontinuity in the source term, which is defined at each spatial point. In particular, such problems describe chemical reactions and biological processes in which…
Reaction-diffusion systems offer a powerful framework for understanding self-organized patterns in biological systems, yet controlling these patterns remains a significant challenge. As a consequence, we present a rigorous framework of…
We study a driven many particle system comprising of two identical lanes of finite lengths. On one lane, particles hop diffusively with a bias in a specific direction. On the other lane, particles hop in a specific direction obeying mutual…
Chemical reactions generically require that particles come into contact. In practice, reaction is often imperfect and can necessitate multiple random encounters between reactants. In confined geometries, despite notable recent advances,…
One-dimensional non-equilibrium models of particles subjected to a coagulation-diffusion process are important in understanding non-equilibrium dynamics, and fluctuation-dissipation relation. We consider in this paper transport properties…
Diffusion through semipermeable structures arises in a wide range of processes in the physical and life sciences. Examples at the microscopic level range from artificial membranes for reverse osmosis to lipid bilayers regulating molecular…
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…
We study the blow up solutions of a semilinear reaction diffusion system coupled in both equations and boundary conditions. The main purpose is to understand how the reaction terms and the absorption terms affect the blow-up properties. We…
Several problems, issued from physics, biology or the medical science, lead to parabolic equations set in two sub-domains separated by a membrane with selective permeability to specific molecules. The corresponding boundary conditions,…
We consider one-dimensional diffusions, with polynomial drift and diffusion coefficients, so that in particular the motion can be space-inhomogeneous, interacting via one-sided reflections. The prototypical example is the well-known model…
We derive, through subordination techniques, a generalized Feynman-Kac equation in the form of a time fractional Schrodinger equation. We relate such equation to a functional which we name the subordinated local time. We demonstrate through…
The interaction of a Zeldovich reaction-diffusion front with a localized defect is studied numerically and analytically. For the analysis, we start from conservation laws and develop simple collective variable ordinary differential…
We study a reaction-diffusion process that involves two species of atoms, immobile and diffusing. We assume that initially only immobile atoms, uniformly distributed throughout the entire space, are present. Diffusing atoms are injected at…
The effects of Poissonian resetting at a constant rate $r$ on the reaction time between a Brownian particle and a stochastically gated target are studied. The target switches between a reactive state and a non-reactive one. We calculate the…
A fractional reaction-diffusion equation is derived from a continuous time random walk model when the transport is dispersive. The exit from the encounter distance, which is described by the algebraic waiting time distribution of jump…
We investigate the emergent interactions between two active Brownian particles coupled by an attractive harmonic potential and in contact with a thermal reservoir. By analyzing the stationary distribution of their separation, we demonstrate…
Motivated by a heat radiative transport equation, we consider a particle undergoing collisions in a space-time domain and propose a method to sample its escape time, space and direction from the domain. The first step of the procedure is an…