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Related papers: Imperfect Narrow Escape problem

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Intracellular transport in living cells is often spatially inhomogeneous with an accelerated effective diffusion close to the cell membrane and a ballistic motion away from the centrosome due to active transport along actin filaments and…

Statistical Mechanics · Physics 2021-10-22 Matthieu Mangeat , Heiko Rieger

The narrow escape problem deals with the calculation of the mean escape time (MET) of a Brownian particle from a bounded domain through a small hole on the domain's boundary. Here we develop a formalism that allows us to evaluate the…

Statistical Mechanics · Physics 2018-03-28 Tal Agranov , Baruch Meerson

The escape of particles through a narrow absorbing gate in confined domains is a abundant phenomenon in various systems in physics, chemistry and molecular biophysics. We consider the narrow escape problem in a cellular flow when the two…

Statistical Mechanics · Physics 2018-12-04 Hui Wang , Jinqiao Duan , Xianguo Geng , Ying Chao

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…

Statistical Mechanics · Physics 2022-11-23 Paul C Bressloff

The stochastic motion of particles in living cells is often spatially inhomogeneous with a higher effective diffusivity in a region close to the cell boundary due to active transport along actin filaments. As a first step to understand the…

Statistical Mechanics · Physics 2019-09-25 Matthieu Mangeat , Heiko Rieger

A popular approach to modeling bimolecular reactions between diffusing molecules is through the use of reactive boundary conditions. One common model is the Smoluchowski partial absorption condition, which uses a Robin boundary condition in…

Biological Physics · Physics 2015-11-17 S. Jonathan Chapman , Radek Erban , Samuel A. Isaacson

We present an exact calculation of the mean first-passage time to a small target on the surface of a 2D or 3D spherical domain, for a molecule performing surface-mediated diffusion. This minimal model of interfacial reactions, which…

Statistical Mechanics · Physics 2015-05-18 O. Bénichou , D. Grebenkov , P. Levitz , C. Loverdo , R. Voituriez

We consider a model of surface-mediated diffusion with alternating phases of pure bulk and surface diffusion. For this process, we compute the mean exit time from a disk through a hole on the circle. We develop a spectral approach to this…

Mathematical Physics · Physics 2014-04-24 O. Bénichou , D. S. Grebenkov , L. Hillairet , L. Phun , R. Voituriez , M. Zinsmeister

We investigate restricted diffusion in a bounded domain towards a small partially reactive target in three- and higher-dimensional spaces. We propose a simple explicit approximation for the principal eigenvalue of the Laplace operator with…

Statistical Mechanics · Physics 2022-10-10 Adrien Chaigneau , Denis S. Grebenkov

We propose a general theoretical description of chemical reactions occurring on a catalytic surface with heterogeneous reactivity. The propagator of a diffusion-reaction process with eventual absorption on the heterogeneous partially…

Chemical Physics · Physics 2019-11-05 Denis S. Grebenkov

We consider a particle undergoing diffusion with stochastic resetting in a bounded domain $\calU\subset \R^d$ for $d=2,3$. The domain is perforated by a set of partially absorbing targets within which the particle may be absorbed at a rate…

Statistical Mechanics · Physics 2021-10-14 Paul C. Bressloff , Ryan D. Schumm

We present an efficient method to solve the narrow capture and narrow escape problems for the sphere. The narrow capture problem models the equilibrium behavior of a Brownian particle in the exterior of a sphere whose surface is reflective,…

Numerical Analysis · Mathematics 2021-08-03 Jason Kaye , Leslie Greengard

We study the narrow escape problem in the disk, which consists in identifying the first exit time and first exit point distribution of a Brownian particle from the ball in dimension 2, with reflecting boundary conditions except on small…

Analysis of PDEs · Mathematics 2024-04-09 Tony Lelièvre , Mohamad Rachid , Gabriel Stoltz

This paper investigates the heat equation on a bounded domain with a Robin boundary condition, where the reactivity parameter (or killing rate) is modeled as a continuous-time Markov chain. We analyze the system under two stochastic…

Probability · Mathematics 2026-05-01 Fausto Colantoni

We consider steady-state diffusion in a bounded planar domain with multiple small targets on a smooth boundary. Using the method of matched asymptotic expansions, we investigate the competition of these targets for a diffusing particle and…

Analysis of PDEs · Mathematics 2025-11-18 Denis S. Grebenkov , Michael J. Ward

In this paper, we consider the large-time behavior of solutions of a reaction diffusion system arising from a nuclear reactor model with the Robin boundary conditions, which consists of two real-valued unknown functions. In particular, we…

Analysis of PDEs · Mathematics 2018-11-12 Kosuke Kita , Mitsuharu Ôtani

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…

Soft Condensed Matter · Physics 2015-05-18 G. Oshanin , M. Tamm , O. Vasilyev

We consider the mixed Steklov-Neumann spectral problem for the modified Helmholtz equation in a bounded domain when the Steklov condition is imposed on a connected subset of the smooth boundary. In order to deduce the asymptotic behavior in…

Computational Physics · Physics 2025-07-22 Denis S. Grebenkov

We study the metastable behavior of diffusion processes in narrow tube domains, where the metastability is induced by entropic barriers. We identify a sequence of characteristic time scales $\{T_\epsilon^i\}_{1 \leq i \leq \abs{V'}}$ and…

Probability · Mathematics 2025-12-16 Wen-Tai Hsu

We investigate the capacity of a flat partially reactive patch of arbitrary shape to trap independent particles that undergo steady-state diffusion in the three-dimensional space. We focus on the total flux of particles onto the patch that…

Chemical Physics · Physics 2026-02-02 Denis S. Grebenkov , Raphael Maurette