Related papers: Sojourn time in an union of intervals for diffusio…
We construct a new statistical physical model of polymer translocation through a pore in a membrane treated as the diffusion process across a free energy barrier. We determine the translocation time in terms of chain flexibility yielding an…
We study an ensemble of random walkers carrying internal noisy phase oscillators which are synchronized among the walkers by local interactions. Due to individual mobility, the interaction partners of every walker change randomly, hereby…
We study the one-dimensional diffusion process which takes place between two reflecting boundaries and which is acted upon by a time-dependent and spatially-constant force. The assumed force possesses both the harmonically oscillating and…
We study Markov processes conditioned so that their local time must grow slower than a prescribed function. Building upon recent work on Brownian motion with constrained local time in [5] and [33], we study transience and recurrence for a…
In this paper we revisit the existence of traveling waves for delayed reaction diffusion equations by the monotone iteration method. We show that Perron Theorem on existence of bounded solution provides a rigorous and constructive framework…
We model two time and space scales discrete observations by using a unique continuous diffusion process with time dependent coefficient. We define new parameters for the large scale model as functions of the small scale distribution…
Lateral diffusion of molecules on surfaces plays a very important role in various biological processes, including lipid transport across the cell membrane, synaptic transmission and other phenomena such as exo- and endocytosis, signal…
Lagrangian motions of fluid particles in a general velocity field oscillating in time are studied with the use of the two-timing method. Our aims are: (i) to calculate systematically the most general and practically usable asymptotic…
A model for diffusion on a cubic lattice with a random distribution of traps is developed. The traps are redistributed at certain time intervals. Such models are useful for describing systems showing dynamic disorder, such as ion-conducting…
Standard diffusion equation is based on Brownian motion of the dispersing species without considering persistence in the movement of the individuals. This description allows for the instantaneous spreading of the transported species over an…
For an arbitrary L\'evy process $X$ which is not a compound Poisson process, we are interested in its occupation times. We use a quite novel and useful approach to derive formulas for the Laplace transform of the joint distribution of $X$…
Cellular networks are often composed of thin tubules connecting much larger node compartments. These structures serve for active or diffusion transport of proteins. Examples are glial networks in the brain, the endoplasmic reticulum in…
The process of diffusion is the most elementary stochastic transport process. Brownian motion, the representative model of diffusion, played a important role in the advancement of scientific fields such as physics, chemistry, biology and…
Under certain circumstances, the time behavior of a random walk is modulated by logarithmic periodic oscillations. The goal of this paper is to present a simple and pedagogical explanation of the origin of this modulation for diffusion on a…
In this paper we extend the encounter-based model of diffusion-mediated surface absorption to the case of an unbiased run-and-tumble particle (RTP) confined to a finite interval $[0,L]$ and switching between two constant velocity states…
We revisit the problem of diffusion in a driven system consisting of an inertial Brownian particle moving in a symmetric periodic potential and subjected to a symmetric time-periodic force. We reveal parameter domains in which diffusion is…
The one-dimensional overdamped Brownian motion in a symmetric periodic potential modulated by external time-reversible noise is analyzed. The calculation of the effective diffusion coefficient is reduced to the mean first passage time…
We solve a model of sluggish stochastic motion in which a Brownian particle diffuses with a diffusion coefficient that decays algebraically with the distance to the origin, as $|x|^{-\alpha}$. Additionally, the particle resets with a…
We revisit the notions of the quantum-mechanical sojourn time in the context of the quantum clocks to enquire whether the sojourn time be clocked without the clock affecting the dynamics of the wave motion. Upon recognizing that the…
We investigate the distribution of the time spent by a random walker to the right of a boundary moving with constant velocity v. For the continuous-time problem (Brownian motion), we provide a simple alternative proof of Newman's recent…