Related papers: Extreme diffusion with point-sink killing field
In this communication, we show that the residence time of a Brownian particle, defined as the cumulative time spent in a given region of space, can be optimized as a function of the diffusion coefficient. We discuss the relevance of this…
First passage time (FPT) theory is often used to estimate timescales in cellular and molecular biology. While the overwhelming majority of studies have focused on the time it takes a given single Brownian searcher to reach a target,…
Escape of active agents from metastable states is of great interest in statistical and biological physics. In this study, we investigate the escape of a flexible active ring, composed of active Brownian particles, from a flat attractive…
Diffusion of colloidal particles in a complex environment such as polymer networks or biological cells is a topic of high complexity with significant biological and medical relevance. In such situations, the interaction between the…
Brownian yet non-Gaussian processes have recently been observed in numerous biological systems and the corresponding theories have been built based on random diffusivity models. Considering the particularity of random diffusivity, this…
A rapidly increasing number of systems is identified in which the stochastic motion of tracer particles follows the Brownian law $\langle\mathbf{r}^2(t) \rangle\simeq Dt$ yet the distribution of particle displacements is strongly…
The fundamental solutions of diffusion equation for the local-equilibrium and nonlocal models are considered as the limiting cases of the solution of a problem related to consideration of the Brownian particles random walks. The differences…
We introduce and investigate the escape problem for random walkers that may eventually die, decay, bleach, or lose activity during their diffusion towards an escape or reactive region on the boundary of a confining domain. In the case of a…
A self-consistent and universal description of friction and diffusion for Brownian particles (grains) in different systems, as a gas with Boltzmann collisions, dusty plasma with ion absorption by grains, and for active particles (e.g.,…
We present a general framework to study the effect of killing sources on moving particles, trafficking inside biological cells. We are merely concerned with the case of spine-dendrite communication, where the number of calcium ions, modeled…
Many events in biology are triggered when a diffusing searcher finds a target, which is called a first passage time (FPT). The overwhelming majority of FPT studies have analyzed the time it takes a single searcher to find a target. However,…
Fractional Brownian motion is a Gaussian stochastic process with stationary, long-time correlated increments and is frequently used to model anomalous diffusion processes. We study numerically fractional Brownian motion confined to a finite…
We study the time behavior of the Fokker-Planck equation in Zwanzig rule (the backward-Ito rule) based on the Langevin equation of Brownian motion with an anomalous diffusion in a complex medium. The diffusion coefficient is a function in…
Using martingale theory, we compute, in very few lines, exact analytical expressions for various first-exit-time statistics associated with one-dimensional biased diffusion. Examples include the distribution for the first-exit time from an…
Barrier crossing is a widespread phenomenon across natural and engineering systems. While an abundant cross-disciplinary literature on the topic has emerged over the years, the stochastic underpinnings of the process are yet to be linked…
Intracellular transport in living cells is often spatially inhomogeneous with an accelerated effective diffusion close to the cell membrane and a ballistic motion away from the centrosome due to active transport along actin filaments and…
A Brownian particle with diffusion coefficient $D$ is confined to a bounded domain of volume $V$ in $\rR^3$ by a reflecting boundary, except for a small absorbing window. The mean time to absorption diverges as the window shrinks, thus…
Under the effect of strong genetic drift, it is highly probable to observe gene fixation or gene loss in a population, shown by infinite peaks on a coherently constructed potential energy landscape. It is then important to ask what such…
In this work a phenomenological stochastic differential equation is proposed to model the time evolution of the radius of a pre-critical molecular cluster during nucleation (the classical order parameter). Such a stochastic differential…
We numerically investigate the mean exit time of an inertial active Brownian particle from a circular cavity with single or multiple exit windows. Our simulation results witness distinct escape mechanisms depending upon the relative…