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Stochastic resetting and first arrival subjected to Gaussian noise and Poisson white noise
Physical Review E ( IF 2.4 ) Pub Date : 2021-09-09 , DOI: 10.1103/physreve.104.034113
Koushik Goswami 1 , Rajarshi Chakrabarti 1
Affiliation  

We study the dynamics of an overdamped Brownian particle subjected to Poissonian stochastic resetting in a nonthermal bath, characterized by a Poisson white noise and a Gaussian noise. Applying the renewal theory we find an exact analytical expression for the spatial distribution at the steady state. Unlike the single exponential distribution as observed in the case of a purely thermal bath, the distribution is double exponential. Relaxation of the transient spatial distributions to the stationary one, for the limiting cases of Poissonian rate, is investigated carefully. In addition, we study the first-arrival properties of the system in the presence of a delta-function sink with strength κ, where κ=0 and κ= correspond to fully nonreactive and fully reactive sinks, respectively. We explore the effect of two competitive mechanisms: the diffusive spread in the presence of two noises and the increase in probability density around the initial position due to stochastic resetting. We show that there exists an optimal resetting rate, which minimizes the mean first-arrival time (MFAT) to the sink for a given value of the sink strength. We also explore the effect of the strength of the Poissonian noise on MFAT, in addition to sink strength. Our formalism generalizes the diffusion-limited reaction under resetting in a nonequilibrium bath and provides an efficient search strategy for a reactant to find a target site, relevant in a range of biophysical processes.

中文翻译:

受高斯噪声和泊松白噪声影响的随机复位和初到

我们研究了在非热浴中受到泊松随机重置的过阻尼布朗粒子的动力学,其特征是泊松白噪声和高斯噪声。应用更新理论,我们找到了稳态空间分布的精确解析表达式。与在纯热浴中观察到的单指数分布不同,该分布是双指数分布。对于泊松率的极限情况,仔细研究了瞬态空间分布到静止空间分布的松弛。此外,我们研究了系统在存在强度为κ, 在哪里 κ=0κ=分别对应于完全无反应和完全反应的汇。我们探索了两种竞争机制的影响:存在两种噪声时的扩散传播和由于随机重置导致的初始位置周围概率密度的增加。我们表明存在最佳重置率,对于给定的汇强度值,它可以最小化到达汇的平均首次到达时间(MFAT)。除了汇强度之外,我们还探讨了泊松噪声强度对 MFAT 的影响。我们的形式主义概括了非平衡浴中重置下的扩散限制反应,并为反应物提供了一种有效的搜索策略,以找到与一系列生物物理过程相关的目标位点。
更新日期:2021-09-10
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