Mean exit time for surface-mediated diffusion: spectral analysis and asymptotic behavior

Bénichou, Olivier; Hillairet, Luc; Phun, L.; Voituriez, Raphaël; Zinsmeister, Michel

doi:10.1007/s13324-015-0098-0

Cited by 9 publications

(8 citation statements)

References 25 publications

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“…It can be treated as a special case of the general process presented in the next section. We treat this special case here first since the presented results confirm previous discoveries which were derived for processes that exhibit intermittent dynamics [36,37]. Furthermore this first problem is actually rather simple and thus a good introduction to our general approach.…”

Section: Hard Resettingsupporting

confidence: 65%

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Diffusion with resetting inside a circle

2018

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We study the Brownian motion of a particle in a bounded circular two-dimensional domain in search for a stationary target on the boundary of the domain. The process switches between two modes: one where it performs a two-dimensional diffusion inside the circle and one where it diffuses along the one-dimensional boundary. During the process, the Brownian particle resets to its initial position with a constant rate r. The Fokker-Planck formalism allows us to calculate the mean time to absorption (MTA) as well as the optimal resetting rate for which the MTA is minimized. From the derived analytical results the parameter regions where resetting reduces the search time can be specified. We also provide a numerical method for the verification of our results.

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Section: Hard Resettingsupporting

confidence: 65%

“…This expression is in perfect agreement with Eq. (2.23) of [37]. By using the series expansion of the cotangent function we rewrite this expression as…”

Section: Hard Resettingmentioning

confidence: 99%

Diffusion with resetting inside a circle

2018

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“…For example, a general exact formula for the mean first passage time from a fixed point inside a planar domain to an escape region on its boundary is attained in [12]; high-order asymptotic formulas for the mean first passage time are derived in [14]; approximations for the average mean first passage time are found in [18]; the upper and lower bounds of the mean first passage time for mortal walkers are derived in [26]. Moreover, a spectral approach to derive an exact formula for the mean exit time of a particle through a hole on the boundary is developed in [27]; partial differential equation and probabilistic methods are applied to solve escape problems in [28]; a generalized Kramers formula for the mean escape time through a narrow window is obtained in [30]; and boundary homogenization is used when the boundary contains non-overlapping identical absorbing arcs in [31].…”

Section: Introductionmentioning

confidence: 99%

Mean escape time for randomly switching narrow gates in a steady flow

Wang

Duan

Geng

et al. 2020

Computers & Mathematics with Applications

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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 gates randomly switch between different states with a switching rate k between the two gates. After briefly deriving the coupled partial differential equations for the escape time through two gates, we compute the mean escape time for particles escaping from the gates with different initial states. By numerical simulation under nonuniform boundary conditions, we quantify how narrow escape time is affected by the switching rate k between the two gates, arc length s between two gates, angular velocity w of the cellular flow and diffusion coefficient D. We reveal that the mean escape time decreases with the switching rate k between the two gates, angular velocity w and diffusion coefficient D for fixed arc length, but takes the minimum when the two gates are evenly separated on the boundary for any given switching rate k between the two gates. In particular, we find that when the arc length size ε for the gates is sufficiently small, the average narrow escape time is approximately independent of the gate arc length size. We further indicate combinations of system parameters (regions located in the parameter space) such that the mean escape time is the longest or shortest. Our findings provide mathematical understanding for phenomena such as how ions select ion channels and how chemicals leak in annulus ring containers, when drift vector fields are present.

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“…The basic idea is to consider one-dimensional diffusions of two independent particles as a surface-mediated diffusion of a single particle inside a square. Although the latter problem has been thoroughly investigated for several geometric configurations, [27][28][29][30][31][32][33] the current setting is different and its solution is not yet available. Inspired by former works, we reduce the coupled partial differential equations (PDEs) for the surface-mediated diffusion to a set of linear equations that can be solved either explicitly (in some cases), or approximately, or numerically.…”

Section: Introductionmentioning

confidence: 99%

First passage times for multiple particles with reversible target-binding kinetics

Grebenkov

2017

The Journal of Chemical Physics

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We investigate the first passage problem for multiple particles that diffuse towards a target, partially adsorb there, and then desorb after a finite exponentially distributed residence time. We search for the first time when m particles undergoing such reversible target-binding kinetics are found simultaneously on the target that may trigger an irreversible chemical reaction or a biophysical event. Even if the particles are independent, the finite residence time on the target yields an intricate temporal coupling between particles. We compute analytically the mean first passage time (MFPT) for two independent particles by mapping the original problem to higher-dimensional surface-mediated diffusion and solving the coupled partial differential equations. The respective effects of the adsorption and desorption rates on the MFPT are revealed and discussed.

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Mean exit time for surface-mediated diffusion: spectral analysis and asymptotic behavior

Cited by 9 publications

References 25 publications

Diffusion with resetting inside a circle

Diffusion with resetting inside a circle

Mean escape time for randomly switching narrow gates in a steady flow

First passage times for multiple particles with reversible target-binding kinetics

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