An encounter-based approach for restricted diffusion with a gradient drift

Grebenkov, Denis S

doi:10.1088/1751-8121/ac411a

Cited by 42 publications

(61 citation statements)

References 155 publications

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“…A numerical validation of this approximation in configurations with multiple targets presents an important perspective. Finally, one can investigate other surface reaction mechanisms (beyond the conventional Robin boundary condition) by using an encounter-based approach [27,88,89,91]. Here, the explicit dependence of the reactivity parameter q may allow to access various properties of diffusion-mediated surface phenomena.…”

Section: Discussionmentioning

confidence: 99%

First-passage times to anisotropic partially reactive targets

Chaigneau,

Grebenkov

2022

Preprint

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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 mixed Robin-Neumann boundary conditions. This approximation involves the harmonic capacity and the surface area of the target, the volume of the confining domain, the diffusion coefficient and the reactivity. The accuracy of the approximation is checked by using a finite-elements method. The proposed approximation determines also the mean first-reaction time, the long-time decay of the survival probability, and the overall reaction rate on that target. We identify the relevant length scale of the target, which determines its trapping capacity, and investigate its relation to the target shape. In particular, we study the effect of target anisotropy on the principal eigenvalue by computing the harmonic capacity of prolate and oblate spheroids in various space dimensions. Some implications of these results in chemical physics and biophysics are briefly discussed.

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Section: Discussionmentioning

confidence: 99%

First-passage times to anisotropic partially reactive targets

Chaigneau,

Grebenkov

2022

Preprint

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“…The effect of diversity of species (e.g., a distribution of their diffusion coefficients) can also be analyzed. Second, dynamics beyond ordinary diffusion can be investigated; for instance, the distribution of the boundary local time was recently obtained for diffusion with a gradient drift [81]. The knowledge on the survival probability of more sophisticated stochastic dynamics, such as diffusing diffusivity or switching diffusion models [82][83][84][85], can potentially be employed in the analysis of the stock depletion problem.…”

Section: Discussionmentioning

confidence: 99%

Depletion of Resources by a Population of Diffusing Species

Grebenkov

2022

Preprint

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Depletion of natural and artificial resources is a fundamental problem and a potential cause of economic crises, ecological catastrophes, and death of living organisms. Understanding the depletion process is crucial for its further control and optimized replenishment of resources. In this paper, we investigate a stock depletion by a population of species that undergo an ordinary diffusion and consume resources upon each encounter with the stock. We derive the exact form of the probability density of the random depletion time, at which the stock is exhausted. The dependence of this distribution on the number of species, the initial amount of resources, and the geometric setting is analyzed. Future perspectives and related open problems are discussed.

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“…The construction of the marginal probability density p(x, t|x 0 ) in the case of a partially absorbing surface proceeds as follows [16,17]. Introducing the double Laplace transform…”

Section: Generalized Propagator Bvp Without Switchingmentioning

confidence: 99%

“…Both cases can be modeled by taking the reactivity to be a function of the boundary local time. Recently, a probabilistic framework for analyzing this more general class of partially absorbing boundary has been developed using a so-called encounter-based approach [16,17]. The underlying idea is that the Robin boundary condition is equivalent to imposing a stopping condition for the local time ℓ t of the particle: T = inf{t > 0 : ℓ t > ℓ}, where ℓ is a stopping local time with an exponential probability distribution.…”

Section: Introductionmentioning

confidence: 99%

Stochastically switching diffusion with partially reactive surfaces

Bressloff

2022

Preprint

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In this paper we develop a hybrid version of the encounter-based approach to diffusion-mediated absorption at a reactive surface, which takes into account stochastic switching of a diffusing particle's conformational state. For simplicity, we consider a two-state model in which the probability of surface absorption depends on the current particle state and the amount of time the particle has spent in a neighborhood of the surface in each state. The latter is determined by a pair of local times ℓn,t, n = 0, 1, which are Brownian functionals that keep track of particlesurface encounters over the time interval [0, t]. We proceed by constructing a differential Chapman-Kolmogorov equation for a pair of generalized propagators Pn(x, ℓ0, ℓ1, t), where Pn is the joint probability density for the set (Xt, ℓ0,t, ℓ1,t) when Nt = n, where Xt denotes the particle position and Nt is the corresponding conformational state. Performing a double Laplace transform with respect to ℓ0, ℓ1 yields an effective system of equations describing diffusion in a bounded domain Ω, in which there is switching between two Robin boundary conditions on ∂Ω. The corresponding constant reactivities are κj = Dzj, j = 0, 1, where zj is the Laplace variable corresponding to ℓj and D is the diffusivity. Given the solution for the propagators in Laplace space, we construct a corresponding probabilistic model for partial absorption, which requires finding the inverse Laplace transform with respect to z0, z1. We illustrate the theory by considering diffusion of a particle on the half-line with the boundary at x = 0 effectively switching between a totally reflecting and a partially absorbing state. We calculate the flux due to absorption and use this to compute the resulting MFPT in the presence of a renewal-based stochastic resetting protocol. The latter resets the position and conformational state of the particle as well as the corresponding local times. Finally, we indicate how to extend the analysis to higher spatial dimensions using the spectral theory of Dirichlet-to-Neumann operators.

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An encounter-based approach for restricted diffusion with a gradient drift

Cited by 42 publications

References 155 publications

First-passage times to anisotropic partially reactive targets

First-passage times to anisotropic partially reactive targets

Depletion of Resources by a Population of Diffusing Species

Stochastically switching diffusion with partially reactive surfaces

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