Related papers: Exact solution of Smoluchowski's equation for reor…
Exact analytic solution for the probability distribution function of the non-inertial rotational diffusion equation, i.e., of the Smoluchowski one, in a symmetric Maier-Saupe uniaxial potential of mean torque is obtained via the confluent…
The Smoluchowski diffusion equation describes diffusion in the presence of external forces. Studying the mechanical response of soft materials to linear forces, such as shear, results in a boundary value problem involving an…
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 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…
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…
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…
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…
Diffusion behavior of Brownian particles in confined spaces was studied for the displacements notably shorter than the confinement size. The confinements, resembling structure of porous solids, were modeled using a spatially-varying…
The Ornstein-Uhlenbeck process of diffusion in the harmonic potential is re-examined in the context of the first-passage time problem. We investigate this problem to the extent that it has not yet been fully resolved and demonstrate exact…
We present a conditionally integrable potential, belonging to the bi-confluent Heun class, for which the Schr\"odinger equation is solved in terms of the confluent hypergeometric functions. The potential involves an attractive inverse…
We find sets of solutions to the generalized spheroidal wave equation (GSWE) or, equivalently, to the confluent Heun equation. Each set is constituted by three solutions, one given by a series of ascending powers of the independent…
Kramers' rate theory forms a cornerstone for thermally activated barrier crossing. However, its reliance on equilibrium quantities excludes analysis of nonequilibrium dynamics at early times. Most works have thus focused on obtaining rates…
The Debye-Stokes-Einstein (DSE) model of rotational diffusion predicts that the rotational correlation times $\tau_{l}$ vary as $[l(l+1)]^{-1}$, where $l$ is the rank of the orientational correlation function (given in terms of the Legendre…
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…
Characterization of composite materials, whose properties vary in space over microscopic scales, has become a problem of broad interdisciplinary interest. In particular, estimation of the inhomogeneous transport coefficients, e.g. the…
The Stokes-Einstein-Sutherland (SES) equation is at the foundation of statistical physics, relating a particle's diffusion coefficient and size with the fluid viscosity, temperature and the boundary condition for the particle-solvent…
We address the problem of minimizing the expected first-passage time of a Brownian motion with Poissonian resetting, with respect to the resetting rate $r.$ We consider both the one-boundary and the two-boundary cases.We investigate the…
Relaxation properties (specifically time-rates) of the Smoluchowski diffusion process on a line, in a confining potential $ U(x) \sim x^m$, $m=2n \geq 2$, can be spectrally quantified by means of the affiliated Schr\"{o}dinger semigroup…
We consider an ideal gas of active Brownian particles that undergo self-propelled motion and both translational and rotational diffusion under the influence of gravity. We solve analytically the corresponding Smoluchowski equation in two…