Related papers: Exact results on diffusion in a piecewise linear p…

We give a very simple method for finding the exact analytical solution for the problem of a particle undergoing diffusive motion on a flat potential in the presence of a gaussian sink function. The diffusion process is modelled by using one…

We give a method for finding the exact analytical solution for the problem of a particle undergoing diffusive motion in a flat potential in the presence of a new localized sink. The Diffusive motion is described using the Smoluchowski…

The Smoluchowski equation with a time dependent sink term is solved exactly. In this method by knowing the probability distribution at the origin P(0,s), one may derive the probability distribution at all positions i.e., P(x,s). Further the…

In the present report, we have introduced the Fredholm integral method to solve the Smoluchowski equation in the Laplace domain. We get an exact semi-analytical solution for the linear potential energy curve in the dynamic diffusion…

We propose an analytical method for finding the time domain solution for the problem of electronic relaxation of a molecule in solution. The relaxation process is modeled by the decay of a diffusing probability distribution through an…

We propose a very simple one dimensional analytically solvable model for understanding the problem of electronic relaxation of molecules in solution. This problem is modeled by a particle diffusing under the influence of parabolic potential…

We give a general method for finding the exact solution for the problem of electronic relaxation in solution, modeled by a particle undergoing diffusive motion under a potential in the presence of a sink of finite width. The solution…

The Smoluchowski equation with a time dependent delta function sink is solved exactly for many special cases. In all other cases the problem can be reduced to an integral equation. It is shown that by knowing the probability distribution at…

The Smoluchowski equation for a free particle with a time dependent sink is solved exactly for many special cases. In this method by knowing the probability distribution at the origin P(0,t), one may derive the probability distribution at…

In undergraduate classes, the potential flow that goes around a circular cylinder is designed for complemental understanding of mathematical technique to handle the Laplace equation with Neumann boundary conditions and the physical concept…

We provide a new approach to solve one dimension Fokker-Planck equation in the Laplace domain for the case where a particle is evolving in a potential energy curve in the presence of general delocalized sink. We also calculate rate…

In this article, we give a semi-analytic expression for survival probability when particles are diffusing in an active potential well. There is no analytic solution available in the literature, due to the requirement of inverse Laplace…

We propose an analytical method for solving the problem of barrierless reactions in solution, modeled by a particle undergoing diffusive motion under the influence of both reactant and product potentials. The coupling between these two…

For the symmetric case of space-fractional diffusion processes (whose basic analytic theory has been developed in 1952 by Feller via inversion of Riesz potential operators) we present three random walk models discrete in space and time. We…

Diffusion mediated reaction models are particularly ubiquitous in the description of physical, chemical or biological processes. The random walk schema is a useful tool for formulating these models. Recently, evanescent random walk models…

A diffusion theory for intramolecular reactions of polymer chain in dilute solution is formulated. We give a detailed analytical expression for calculation of rate of polymer looping in solution. The physical problem of looping can be…

We propose an analytical method for understanding the problem of long range electron transfer reaction in solution, modeled by a particle undergoing diffusive motion under the influence of many potentials which are involved (donor - bridge…

We investigate a single particle on a 3-dimensional, cubic lattice with a random on-site potential (3D Anderson model). We concretely address the question whether or not the dynamics of the particle is in full accord with the diffusion…

A physical-mathematical approach to anomalous diffusion may be based on generalized diffusion equations (containing derivatives of fractional order in space or/and time) and related random walk models. The fundamental solution (for the…

We propose an analytical method for solving the problem of electronic relaxation in solution in time domain, modelled by a particle undergoing diffusion under the influence of two coupled potentials. The coupling between the two potentials…