Related papers: Analytical solution of diffusion probability for a…
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…
We propose a new method for finding the exact analytical solution in Laplace domain for the problem where the probability density of a random walker in a piece-wise linear potential in presence of a rectangular sink of arbitrary width and…
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…
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…
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…
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 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…
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…
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…
A study of the diffusion of a passive Brownian particle on the surface of a sphere and subject to the effects of an external potential, coupled linearly to the probability density of the particle's position, is presented through a numerical…
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…
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…
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 understanding the problem of multi-channel electron transfer reaction in solution, modeled by a particle undergoing diffusive motion under the influence of one donor and several acceptor potentials. The…
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…
We consider the one-dimensional diffusion of a particle on a semi-infinite line and in a piecewise linear random potential. We first present a new formalism which yields an analytical expression for the Green function of the Fokker-Planck…
We calculate the probability distribution function (PDF) of an overdamped Brownian particle moving in a periodic potential energy landscape $U(x)$. The PDF is found by solving the corresponding Smoluchowski diffusion equation. We derive the…
We present an analytical closed form expression, which gives a good approximate propagator for diffusion on the sphere. Our formula is the spherical counterpart of the Gaussian propagator for diffusion on the plane. While the analytical…
In this article, we consider the solution to elliptic diffusion problems on a class of random domains obtained by log-Gaussian random homothety of the unit disk respectively an annulus. We model the problem under consideration and verify…