Diffusion-mediated surface reactions and stochastic resetting

Bressloff, Paul C.

doi:10.48550/arxiv.2202.01119

Cited by 3 publications

(11 citation statements)

References 27 publications

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“…This means that T r (x 0 ) is either a monotonically increasing or a unimodal function of r, depending on the initial position x 0 [32]. These various results also extend to partial absorbing boundaries in the absence of local time resetting [3]. Returning to the current example of threshold surface reactions with local time resetting, it is clear that even when the MFPT is finite in the absence of resetting, it becomes infinite when resetting is included.…”

Section: Threshold Surface Reactions With Position and Local Time Res...mentioning

confidence: 66%

“…In a previous paper we considered diffusion-mediated surface reactions in which only the position of the particle resets [3]. The only modification of the BVP for the propagator occurs in equation (2.18a), which becomes…”

Section: Threshold Surface Reactions With Position Resettingmentioning

confidence: 99%

“…That is, the absorption probability depends on the number of encounters between particle and boundary, which has to be preserved during resetting. This means that the resetting protocol is not given by a renewal process [3]. Nevertheless, we showed that for simple geometric configurations the survival probability with resetting can be expressed in terms of the survival probability without resetting, and can thus be calculated explicitly.…”

Section: Introductionmentioning

confidence: 99%

“…We recently extended the theory of diffusion-mediated surface reactions to include the effects of stochastic resetting, where the position of the particle is reset to its initial location at a constant resetting rate r [3]. Stochastic resetting was originally studied within the context of diffusion in R d and in bounded domains with totally absorbing surfaces [8,9,10].…”

Section: Introductionmentioning

confidence: 99%

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Threshold surface reactions and local time resetting

Bressloff¹

2022

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In this paper we consider a threshold surface absorption mechanism for a particle diffusing in a domain containing a single target U . The target boundary ∂U is taken to be a reactive surface that modifies an internal state of the particle when in contact with the surface, such that absorption occurs as soon as the so-called boundary local time reaches some critical threshold. The boundary local time is a Brownian functional that determines the amount of time that the particle spends in a neighborhood of ∂U . We first consider diffusion without resetting and show how to formulate the threshold surface reaction in terms of the joint probability density or propagator P 0 (x, ℓ, t|x 0 ) for the pair (Xt, ℓt) in the case of a perfectly reflecting surface, where Xt and ℓt denote the particle position and local time at time t, respectively, and x 0 is the initial position. We then introduced a generalized stochastic resetting protocol in which both the position of the particle and its internal state are reset to their initial values at a constant rate r. In order to construct the resulting probability density for particle position, it is necessary to calculate the corresponding propagator Pr(x, ℓ, t|x 0 ) for reflected Brownian motion under the resetting rule Xt → x 0 and ℓt → 0. Since resetting is given by a renewal process, Pr and P 0 are related according to a renewal equation. Laplace transforms can then be used to calculate the associated non-equilibrium stationary state (NESS). We illustrate the theory using the simple examples of diffusion on the half-line and a spherical target in a spherical domain.

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Section: Threshold Surface Reactions With Position and Local Time Res...mentioning

confidence: 66%

Section: Threshold Surface Reactions With Position Resettingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Threshold surface reactions and local time resetting

Bressloff¹

2022

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“…We have previously shown how to modify the resetting rule in the case of a boundary that randomly switches between a totally absorbing state and a totally reflecting state [26], see also [27]. More recently, we have also considered diffusion with resetting in a domain with a partially absorbing boundary and no switching [28]. Based on these studies, suppose that prior to absorption, the following resetting protocol occurs at a Poisson rate r [29]:…”

Section: Survival Probability and First-passage Time (Fpt) Densitymentioning

confidence: 99%

Stochastically switching diffusion with partially reactive surfaces

Bressloff

2022

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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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Diffusion in a partially absorbing medium with position and occupation time resetting

Bressloff

2022

Preprint

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In this paper we consider diffusion in a domain Ω containing a partially absorbing target M with position and occupation time resetting. The occupation time At is a Brownian functional that determines the amount of time that the particle spends in M over the time interval [0, t]. We assume that there exists some internal state Ut of the particle at time t which is modified whenever the particle is diffusing within M. The state Ut is taken to be a monotonically increasing function of At, and absorption occurs as soon as Ut crosses some fixed threshold. We first show how to analyze threshold absorption in terms of the joint probability density or generalized propagator P (x, a, t|x 0 ) for the pair (Xt, At) in the case of a non-absorbing substrate M, where Xt is the particle position at time t and x 0 is the initial position. We then introduce a generalized stochastic resetting protocol in which both the position Xt and the internal state Ut are reset to their initial values, Xt → x 0 and Ut → 0, at a Poisson rate r. The latter is mathematically equivalent to resetting the occupation time, At → 0. Since resetting is governed by a renewal process, the survival probability with resetting can be expressed in terms of the survival probability without resetting, which means that the statistics of absorption can be determined by calculating the double Laplace transform of P (x, a, t|x 0 ) with respect to t and a. In order to develop the basic theory, we focus on one-dimensional (1D) diffusion with M given by a finite or semi-infinite interval, and explore how the MFPT with resetting depends on various model parameters. We also compare the threshold mechanism with the classical case of a constant absorption rate.

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Diffusion-mediated surface reactions and stochastic resetting

Cited by 3 publications

References 27 publications

Threshold surface reactions and local time resetting

Threshold surface reactions and local time resetting

Stochastically switching diffusion with partially reactive surfaces

Diffusion in a partially absorbing medium with position and occupation time resetting

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