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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…
Biomolecular folding, at least in simple systems, can be described as a two state transition in a free energy landscape with two deep wells separated by a high barrier. Transition paths are the short part of the trajectories that cross the…
During a random search, resetting the searcher's position from time to time to the starting point often reduces the mean completion time of the process. Although many different resetting models have been studied over the past ten years,…
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…
Fluids confined to quasi-one-dimensional channels exhibit a dynamic crossover from single file diffusion to normal diffusion as the channel becomes wide enough for particles to hop past each other. In the crossover regime, where hopping…
We consider diffusive motion of a particle performing a random walk with L\'evy distributed jump lengths and subject to resetting mechanism bringing the walker to an initial position at uniformly distributed times. In the limit of infinite…
The properties of the mean first passage time in a system characterized by multiple periodic attractors are studied. Using a transformation from a high dimensional space to 1D, the problem is reduced to a stochastic process along the path…
The distributions of "time of flight" (time spent by a single fluid particle between two crossings of the Poincar\'e section) are investigated for five different 3D stationary chaotic mixers. Above all, we study the large tails of those…
We show that the distribution of times for a diffusing particle to first hit an absorber is \emph{independent} of the direction of an external flow field, when we condition on the event that the particle reaches the target for flow away…
Within a concept of the fractional diffusion equation and subordination, the paper examines the influence of a competition between long waiting times and long jumps on the escape from the potential well. Applying analytical arguments and…
Anomalous (or non-Fickian) diffusion has been widely found in fluid reactive transport and the traditional advection diffusion reaction equation based on Fickian diffusion is proved to be inadequate to predict this anomalous transport of…
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,…
We study an asymmetric simple exclusion process in a strip in the presence of a solid impenetrable barrier. We focus on the effect of the barrier on the residence time of the particles, namely, the typical time needed by the particles to…
We study diffusion on a multilayer network where the contact dynamics between the nodes is governed by a random process and where the waiting time distribution differs for edges from different layers. We study the impact on a random walk of…
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…
We explore first-passage phenomenology for biased active processes with a renewal-type structure, focusing in particular on paradigmatic run-and-tumble models in both discrete and continuous state spaces. In general, we show there is no…
Zolotarev proved a duality result that relates stable densities with different indices. In this paper, we show how Zolotarev duality leads to some interesting results on fractional diffusion. Fractional diffusion equations employ fractional…
We investigate a L\'evy-Walk alternating between velocities $\pm v_0$ with opposite sign. The sojourn time probability distribution at large times is a power law lacking its mean or second moment. The first case corresponds to a ballistic…
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…
Understanding excitation and charge transfer in disordered media is a significant challenge in chemistry, biophysics and material science. We study two experimentally-relevant measures for carriers transfer in finite-size chains, the…