Related papers: First Passage Time for Many Particle Diffusion in …
We present analytical results for the biased diffusion of particles moving under a constant force in a randomly layered medium. The influence of this medium on the particle dynamics is modeled by a piecewise constant random force. The…
Recently a general growth curve including the well known growth equations, such as Malthus, logistic, Bertallanfy, Gompertz, has been studied. We now propose two stochastic formulations of this growth equation. They are obtained starting…
We study the dynamics of a tagged particle in an environment of point Brownian particles with hard-core interactions in an infinite one dimensional channel (a single-file model). In particular we examine the influence of initial conditions…
We investigate the problem of effusion of particles initially confined in a finite one-dimensional box of size $L$. We study both passive as well active scenarios, involving non-interacting diffusive particles and run-and-tumble particles,…
In biochemical reaction networks, the first passage time (FPT) of a reaction quantifies the time it takes for the reaction to first occur, from the initial state. While the mean FPT historically served as a summary metric, a far more…
This paper studies large deviations of a ``fully coupled" finite state mean-field interacting particle system in a fast varying environment. The empirical measure of the particles evolves in the slow time scale and the random environment…
We discuss the diffusion phenomenon in the parabolic and hyperbolic regimes. New effects related to the finite velocity of the diffusion process are predicted, that can partially explain the strange behavior associated to adsorption…
We solve the first-passage problem for the Heston random diffusion model. We obtain exact analytical expressions for the survival and hitting probabilities to a given level of return. We study several asymptotic behaviors and obtain…
We develop a diffusion approximation for systems subject to fast random resetting by small amplitudes. Equivalently, this describes systems with frequent but small catastrophes. We demonstrate the validity of the approximation by computing…
The motion of self-propelled particles is modeled as a persistent random walk. An analytical framework is developed that allows the derivation of exact expressions for the time evolution of arbitrary moments of the persistent walk's…
The first passage search of a diffusing target (prey) by multiple searchers (predators) in confinement is an important problem in the stochastic process literature. While the analogous problem in open space has been studied in some details,…
We consider the diffusion of independent particles experiencing random accelerations by a space- and time-dependent force as well as viscous damping. This model can exhibit several asymptotic behaviours, depending upon the limiting cases…
Many problems in physics, biology, and economics depend upon the duration of time required for a diffusing particle to cross a boundary. As such, calculations of the distribution of first passage time, and in particular the mean first…
First-passage processes are pervasive across numerous scientific fields, yet a general framework for understanding their response to external perturbations remains elusive. While the fluctuation-dissipation theorem offers a complete linear…
We study the first passage time (FPT) problem in Levy type of anomalous diffusion. Using the recently formulated fractional Fokker-Planck equation, we obtain an analytic expression for the FPT distribution which, in the large passage time…
The transport of particles in cells is influenced by the properties of intracellular networks they traverse while searching for localized target regions or reaction partners. Moreover, given the rapid turnover in many intracellular…
We investigate the mean first passage time of an active Brownian particle in one dimension using numerical simulations. The activity in one dimension is modeled as a two state model; the particle moves with a constant propulsion strength…
A collection of identical and independent rare event first passage times is considered. The problem of finding the fastest out of $N$ such events to occur is called an extreme first passage time. The rare event times are singular and limit…
We consider a Brownian particle diffusing in a one dimensional interval with absorbing end points. We study the ramifications when such motion is interrupted and restarted from the same initial configuration. We provide a comprehensive…
When does a diffusing particle reach its target for the first time? This first-passage time (FPT) problem is central to the kinetics of molecular reactions in chemistry and molecular biology. Here we explain the behavior of smooth FPT…