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Brownian motion with stochastic resetting-a process combining standard diffusion with random returns to a fixed position-has emerged as a powerful framework with applications spanning statistical physics, chemical kinetics, biology, and…
We derive the equations that describe adsorption of diffusing particles onto a surface followed by additional surface kinetic steps before being transported across the interface. Multistage surface kinetics occurs during membrane protein…
For a diffusion process $X(t)$ of drift $\mu(x)$ and of diffusion coefficient $D=1/2$, we study the joint distribution of the two local times $A(t)= \int_{0}^{t} d\tau \delta(X(\tau)) $ and $B(t)= \int_{0}^{t} d\tau \delta(X(\tau)-L) $ at…
A simple multiscale approach to the diffusion-driven adsorption from a solution to a solid surface is presented. The model combines two important features of the adsorption process: (i) the kinetics of the chemical reaction between…
First passage in a stochastic process may be influenced by the presence of an external confining potential, as well as "stochastic resetting" in which the process is repeatedly reset back to its initial position. Here we study the interplay…
In the context of unitary evolution of a generic quantum system interrupted at random times with non-unitary evolution due to interactions with either the external environment or a measuring apparatus, we adduce a general theoretical…
Local well-posedness is established for a highly nonlocal nonlinear diffusion-adhesion system for bounded initial values with small support. Macroscopic systems of this kind were previously obtained by the authors through upscaling in [32]…
We evaluate the exact equilibrium distribution of gas molecules adsorbed on an active surface with an infinite number of attachment sites. Our result is a Poisson distribution having mean $X = {\mu P P_s \over P_e}$, with $\mu$ the mean gas…
We analyze the mean time t_{app} that a randomly moving particle spends in a bounded domain (sphere) before it escapes through a small window in the domain's boundary. A particle is assumed to diffuse freely in the bulk until it approaches…
We consider a single Brownian particle in one dimension in a medium at a constant temperature in the underdamped regime. We stochastically reset the position of the Brownian particle to a fixed point in the space with a constant rate $r$…
The local time in an ensemble of particles measures the amount of time the particles spend in the vicinity of a given point in space. Here we study fluctuations of the empirical time average $R= T^{-1}\int_{0}^{T}\rho\left(x=0,t\right)\,dt$…
We study experimentally and theoretically the optimal mean time needed by a free diffusing Brownian particle to reach a target at a distance L from an initial position in the presence of resetting. Both the initial position and the…
We study the first-passage time to the origin of a mortal Brownian particle, with mortality rate $ \mu $, diffusing in one dimension. The particle starts its motion from $ x>0 $ and it is subject to stochastic resetting with constant rate $…
We investigate the statistics of the local time $\mathcal{T} = \int_0^T \delta(x(t)) dt$ that a run and tumble particle (RTP) $x(t)$ in one dimension spends at the origin, with or without an external drift. By relating the local time to the…
The adsorption of CO on the surface of MgO has long been a model problem in surface chemistry. Here, we report periodic Gaussian-based calculations for this problem using second-order perturbation theory (MP2) and coupled-cluster theory…
In this paper we analyze the narrow capture problem for a single Brownian particle diffusing in a three-dimensional (3D) bounded domain containing a set of small, spherical traps. The boundary surface of each trap is taken to be a…
We describe the processes obtained by time reversal of a class of stationary jump-diffusion processes that model the dynamics of genetic variation in populations subject to repeated bottlenecks. Assuming that only one lineage survives each…
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…
In this paper we consider the one-dimensional dynamical evolution of a particle traveling at constant speed and performing, at a given rate, random reversals of the velocity direction. The particle is subject to stochastic resetting,…
In the barrier escape problem, a random searcher starting at the energy minima tries to escape the barrier under the effect of thermal fluctuations. If the random searcher is subject to successive restarts at the bottom of the well, then…