Related papers: Exact mean exit time for surface-mediated diffusio…
Diffraction in time of a particle confined in a box which its walls are removed suddenly at $t=0$ is studied. The solution of the time-dependent Schr\"{o}dinger equation is discussed analytically and numerically for various initial…
An increasing number of experimental studies employ single particle tracking to probe the physical environment in complex systems. We here propose and discuss new methods to analyze the time series of the particle traces, in particular, for…
We identify the integrable stopping time $\tau_*$ with minimal $L^1$-distance to the last-passage time $\gamma_z$ to a given level $z>0$, for an arbitrary non-negative time-homogeneous transient diffusion $X$. We demonstrate that $\tau_*$…
Spontaneous persistent motions driven by active processes play a central role to maintain the living cells far from equilibrium. In the majority of the research works, the steady state dynamics of an active system has been described in…
After a brief review of the derivation of the standard phase time formula, based on the use of the stationary phase method, we propose, in the opaque limit, an alternative method to calculate the phase time. The new formula for the phase…
We correct a previously erroneous calculation [Phys. Rev. E 62, 6065 (2000)] of the mean first passage time of a subdiffusive process to reach either end of a finite interval in one dimension. The mean first passage time is in fact…
We study the heat equation in the exterior of the unit ball with a linear dynamical boundary condition. Our main aim is to find upper and lower bounds for the rate of convergence to solutions of the Laplace equation with the same dynamical…
We analyze the mean squared displacement of a Brownian particle in a medium with a spatially varying local diffusivity which is assumed to be periodic. When the system is asymptotically diffusive the mean squared displacement,…
A consolidated mathematical formulation of the spherically symmetric mass-transfer problem is presented, with the quasi-stationary approximating equations derived from a perturbation point of view for the leading-order effect. For the…
We consider a diffusion process on an evolving surface with a piecewise Lipschitz-continuous boundary from an energetic point of view. We employ an energetic variational approach with both surface divergence and transport theorems to derive…
We develop the first exact Bayesian methodology for the problem of inference in discretely observed regime switching diffusions. Switching diffusion models extend ordinary diffusions by allowing for jumps in instantaneous drift and…
We prove a short time existence result for a system consisting of a geometric evolution equation for a hypersurface and a parabolic equation on this evolving hypersurface. More precisely, we discuss a mean curvature flow scaled with a term…
In this work, exact solutions are derived for an integer- and fractional-order time-delayed diffusion equation with arbitrary initial conditions. The solutions are obtained using Fourier transform methods in conjunction with the known…
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 present a master equation approach to the \emph{narrow escape time} (NET) problem, i.e. the time needed for a particle contained in a confining domain with a single narrow opening, to exit the domain for the first time. We introduce a…
We determine the survival probability and first-passage time (FPT) to capture for a harmonically trapped particle, diffusing outside an absorbing spherical boundary by directly solving the differential equation for the survival probability.…
We study the flow $M_t$ of a smooth, strictly convex hypersurface by its mean curvature in $\mathrm{R}^{n+1}$. The surface remains smooth and convex, shrinking monotonically until it disappears at a critical time $T$ and point $x^*$ (which…
Diffusion at solid-liquid interfaces is crucial in many technological and biophysical processes. Although its behavior seems deceivingly simple, recent studies showing passive superdiffusive transport suggest diffusion on surfaces may hide…
This paper discusses finite time extinction for a perturbed fast diffusion equation with dynamic boundary conditions. The fast diffusion equation has the characteristic property of decay, such as the solution decays to zero in a finite…
We develop a fully discrete scheme for time-fractional diffusion equations by using a finite difference method in time and a finite element method in space. The fractional derivatives are used in Caputo sense. Stability and error estimates…