Related papers: The Narrow Escape problem in a flat cylindrical mi…
We derive an approximate formula for the mean first-passage time (MFPT) to a small absorbing target of arbitrary shape inside an elongated domain of a slowly varying axisymmetric profile. For this purpose, the original Poisson equation in…
The narrow escape problem concerns the time needed for a diffusing particle to exit a confining domain through a small hole in the boundary. While this problem is now well-understood, determining the escape time for a particle that must…
Activity significantly enhances the escape rate of a Brownian particle over a potential barrier. Whereas constant activity has been extensively studied in the past, little is known about the effect of time-dependent activity on the escape…
We derive a functional equation for the mean first-passage time (MFPT) of a generic self-similar Markovian continuous process to a target in a one-dimensional domain and obtain its exact solution. We show that the obtained expression of the…
We consider an anisotropic needle-like Brownian particle with nematic symmetry confined in a $2D$ domain. For this system, the coupling of translational and rotational diffusion makes the process ${\bf x} (t)$ of the positions of the…
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…
Active Brownian particles (ABPs) are a model for nonequilibrium systems in which the constituent particles are self-propelled in addition to their Brownian motion. Compared to the well-studied mean first passage time (MFPT) of passive…
It is often desirable to know the controlling mechanism of survival probability of nano - or microscale particles in small cavities such as, e.g., confined submicron particles in fiber beds of high-efficiency filter media or ions/small…
We address the problem of minimizing the expected first-passage time of a Brownian motion with Poissonian resetting, with respect to the resetting rate $r.$ We consider both the one-boundary and the two-boundary cases.We investigate the…
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…
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…
The kinetics of a variety of transport-controlled processes can be reduced to the problem of determining the mean time needed to arrive at a given location for the first time, the so called mean first passage time (MFPT) problem. The…
Throughout physics Brownian dynamics are used to describe the behaviour of molecular systems. When the Brownian particle is confined to a bounded domain, a particularly important question arises around determining how long it takes the…
We demonstrate that the source to target mean first passage time (MFPT) is approximately given by the potential difference of an electrostatic problem which shows that the MFPT scales like the resistance between the target and a distant…
The mean time for a diffusing ligand to activate a target protein located on the surface of a microdomain can regulate cellular signaling. When the ligand switches between various states induced by chemical interactions or conformational…
Thermally activated escape of an over-damped particle from a metastable well under the action of a time-ramped force is studied. We express the mean first passage time (MFPT) as the solution to a partial differential equation, which we…
Cells have evolved efficient strategies to probe their surroundings and navigate through complex environments. From metastatic spread in the body to swimming cells in porous materials, escape through narrow constrictions - a key component…
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…
We study the mean first exit time $T_{\ve}$ of a particle diffusing in a circular or a spherical micro-domain with an impenetrable confining boundary containing a small escape window (EW) of an angular size $\ve$. Focusing on the effects of…
We investigate a moving boundary problem for a Brownian particle on the semi-infinite line in which the boundary moves by a distance proportional to the time between successive collisions of the particle and the boundary. Phenomenologically…