Diffusion with optimal resetting

By M. Evans, Satya N. Majumdar. 2011

366 citations recorded by the source corpus.

We consider the mean time to absorption by an absorbing target of a diffusive particle with the addition of a process whereby the particle is reset to its initial position with rate r. We consider several generalizations of the model of Evans and Majumdar (2011 Phys. Rev. Lett. 106 160601): (i) a space-dependent resetting rate r(x); (ii) resetting to a random position z drawn from a resetting distribution ; and (iii) a spatial distribution for the absorbing target PT(x). As an example of (i) we show that the introduction of a non-resetting window around the initial position can reduce the mean time to absorption provided that the initial position is sufficiently far from the target. We address the problem of optimal resetting, that is, minimizing the mean time to absorption for a given target distribution. For an exponentially decaying target distribution centred at the origin we show that a transition in the optimal resetting distribution occurs as the target distribution narrows.

Subfields: Molecular Biology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/33623d0f63c77059c5bc13299811da4467c77540

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Molecular Biology

1. Shamik Gupta
2. A. Jayannavar
3. G. Schehr
4. Satya N. Majumdar
5. M. Evans
6. Arnab K. Pal

In Statistical and Nonlinear Physics

1. Satya N. Majumdar
2. Shamik Gupta
3. A. Jayannavar
4. M. Evans
5. G. Schehr
6. Arnab K. Pal

Citations in the corpus

• Stochastic Resetting: A (Very) Brief Review (2021, background): “Reference [29] addressed resetting of a diffusing particle for a space-dependent resetting rate, and resetting to a random position drawn from a resetting distribution, Ref.”
• Extreme value statistics of correlated random variables: A pedagogical review (2019, background): “Although the mean first passage time is divergent when r = 0 [92], a finite resetting rate renders the mean first passage time finite and thus facilitates a diffusion-mediated-search which is otherwise detrimental [155, 156].”
• Optimal diffusive search: nonequilibrium resetting versus equilibrium dynamics (2012, background): “The initial position x of the searcher can be treated as a variable leading to a backward FokkerPlanck equation for Q(x, x0, t) [13, 14].”
• Diffusion with resetting in arbitrary spatial dimension (2014, background): “Equation (63) may be used to study the optimal choices of resetting distribution to optimize for example the mean time to absorption [13].”