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New theorems for the moments of the first passage time of one dimensional nonlinear stochastic processes with an entrance boundary are formulated. This important class of one dimensional stochastic processes results among others from…
Motivated by a range of biological applications related to the transport of molecules in cells, we present a modular framework to treat first-passage problems for diffusion in partitioned spaces. The spatial domains can differ with respect…
The determination of the mean first passage time (MFPT) for a Brownian particle in a bounded 2-D domain containing small absorbing traps is a fundamental problem with biophysical applications. The average MFPT is the expected capture time…
This study investigates the first passage time (FPT) properties of particles with a broad class of positive stochastic diffusion coefficients (DCs), representing diffusion in heterogeneous environments or of particles with conformational…
A certain class of viruses replicates inside a cell if they can enter the nucleus through one of many small target pores, before being permanently trapped or degraded. We adopt for viral motion a switching stochastic process model and we…
A considerable number of systems have recently been reported in which Brownian yet non-Gaussian dynamics was observed. These are processes characterised by a linear growth in time of the mean squared displacement, yet the probability…
Is it possible to recover the position of a source from the steady-state fluxes of Brownian particles to small absorbing windows located on the boundary of a domain? To address this question, we develop a numerical procedure to avoid…
A common scenario in a variety of biological systems is that multiple particles are searching in parallel for an immobile target located in a bounded domain, and the fastest among them that arrives to the target first triggers a given…
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…
Despite having been studied for decades, first passage processes remain an active area of research. In this contribution we examine a particle diffusing in an annulus with an inner absorbing boundary and an outer reflective boundary. We…
The first-passage time (FPT), defined as the time a random walker takes to reach a target point in a confining domain, is a key quantity in the theory of stochastic processes. Its importance comes from its crucial role to quantify the…
We propose a minimal model, based on active Brownian particles, for the dynamics of cells confined in a two-state micropattern, composed of two rectangular boxes connected by a bridge, and investigate the transition statistics. A transition…
Two years ago, Blanco and Fournier (Blanco S. and Fournier R., Europhys. Lett. 2003) calculated the mean first exit time of a domain of a particle undergoing a randomly reoriented ballistic motion which starts from the boundary. They showed…
We derive an approximate but fully explicit formula for the mean first-passage time (MFPT) to a small absorbing target of arbitrary shape in a general elongated domain in the plane. Our approximation combines conformal mapping, boundary…
First passage phenomena arise across physics, biology, and finance when stochastic processes first reach a threshold, triggering downstream events. Examples include the irreversible exit from a domain, a biochemical reaction, a financial…
The statistics of the first-encounter time of diffusing particles changes drastically when they are placed under confinement. In the present work, we make use of Monte Carlo simulations to study the behavior of a two-particle system in two-…
We use a first-passage time approach to study the statistics of the trapping times induced by persistent motion of active particles colliding with flat boundaries. The angular first-passage time distribution and mean first-passage time is…
We study the first passage statistics to adsorbing boundaries of a Brownian motion in bounded two-dimensional domains of different shapes and configurations of the adsorbing and reflecting boundaries. From extensive numerical analysis we…
We investigate the ensemble and time averaged mean squared displacements for particle diffusion in a simple model for disordered media by assuming that the local diffusivity is both fluctuating in time and has a deterministic average growth…
We consider active Brownian particles that intermittently switch between active and inactive states. Such behavior is ubiquitous at all scales, from bacteria to animals and in artificial active systems. We derive exact expressions for key…