Mean first passage time of active Brownian particle in one dimension

Scacchi, Alberto; Sharma, Abhinav

doi:10.1080/00268976.2017.1401743

Cited by 58 publications

(52 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…The discussion has been extended to two and higher dimensions in [17,18]. While for ordinary Brownian motion the optimal resetting rate depends only on the distance x 0 between the target and the origin, and on the diffusion coefficient D of the particle, in the case of active particles it may depend on finer details of motion not comprised in the effective diffusion coefficient [19]. Another search process is the one in which an individual searcher has a random, finite lifetime, and, when it expires, is replaced by a new one starting at the origin [20].…”

Section: Introductionmentioning

confidence: 99%

Scaled Brownian motion with renewal resetting

2019

View full text Add to dashboard Cite

We investigate an intermittent stochastic process in which the diffusive motion with timedependent diffusion coefficient D(t) ∼ t α−1 with α > 0 (scaled Brownian motion) is stochastically reset to its initial position, and starts anew. In the present work we discuss the situation, in which the memory on the value of the diffusion coefficient at a resetting time is erased, so that the whole process is a fully renewal one. The situation when the resetting of coordinate does not affect the diffusion coefficient's time dependence is considered in the other work of this series. We show that the properties of the probability densities in such processes (erazing or retaining the memory on the diffusion coefficient) are vastly different. In addition we discuss the first passage properties of the scaled Brownian motion with renewal resetting and consider the dependence of the efficiency of search on the parameters of the process.

show abstract

Section: Introductionmentioning

confidence: 99%

Scaled Brownian motion with renewal resetting

2019

View full text Add to dashboard Cite

show abstract

“…Characterisation of such a non-equilibrium stationary sate has recently become a major focus of activity in statistical physics [23][24][25]. The field enjoys a broad range of applications including RNA polymerisation processes [26,27], active matter [28][29][30] and randomised searching problems [31] (see the review [32] and references therein).…”

Section: Introductionmentioning

confidence: 99%

Non-conserving zero-range processes with extensive rates under resetting

Grange

2020

J. Phys. Commun.

View full text Add to dashboard Cite

We consider a non-conserving zero-range process with hopping rate proportional to the number of particles at each site. Particles are added to the system with a site-dependent creation rate, and vanish with a uniform annihilation rate. On a fully-connected lattice with a large number of sites, the meanfield geometry leads to a negative binomial law for the number of particles at each site, with parameters depending on the hopping, creation and annihilation rates. This model can be mapped to population dynamics (if the creation rates are reproductive fitnesses in a haploid population, and the hopping rate is the mutation rate). It can also be mapped to a Bianconi-Barabási model of a growing network with random rewiring of links (if creation rates are the rates of acquisition of links by nodes, and the hopping rate is the rewiring rate). The steady state has recently been worked out and gives rise to occupation numbers that reproduce Kingman's house-of-cards model of selection and mutation. In this paper we solve the master equation using a functional method, which yields integral equations satisfied by the occupation numbers. The occupation numbers are shown to forget initial conditions at an exponential rate that decreases linearly with the fitness level. Moreover, they can be computed exactly in the Laplace domain, which allows to obtain the steady state of the system under resetting. The result modifies the house-of-cards result by simply adding a skewed version of the initial conditions, and by adding the resetting rate to the hopping rate.

show abstract

“…For these two extreme cases, the mean first passage time (MFPT) is well estimated by the theory presented in Ref. [3] and can be obtained analytically using Eq. (7).…”

Section: Model and Theorymentioning

confidence: 83%

“…These parameters are chosen to be the same as in Refs. [2] and [3]. The initial self-propelled speed is set to v 0 = 10, leading to an initial rotational diffusion coefficient D 0 a = 2.5.…”

Section: Model and Theorymentioning

confidence: 99%

Escape rate of transiently active Brownian particle in one dimension

2019

Self Cite

View full text Add to dashboard Cite

Activity significantly enhances the escape rate of a Brownian particle over a potential barrier. Whereas constant activity has been extensively studied in the past, little is known about the effect of time-dependent activity on the escape rate of the particle. In this paper we study the escape problem for a Brownian particle that is transiently active; the activity decreases rapidly during the escape process. Using the effective equilibrium approach we analytically calculate the escape rate, under the assumption that the particle is either completely passive or fully active when crossing the barrier. We perform numerical simulations of the escape process in one dimension and find good agreement with the theoretical predictions.

show abstract

Mean first passage time of active Brownian particle in one dimension

Cited by 58 publications

References 9 publications

Scaled Brownian motion with renewal resetting

Scaled Brownian motion with renewal resetting

Non-conserving zero-range processes with extensive rates under resetting

Escape rate of transiently active Brownian particle in one dimension

Contact Info

Product

Resources

About