TY - JOUR

T1 - Péclet number governs transition to acceleratory restart in drift-diffusion

AU - Ray, Somrita

AU - Mondal, Debasish

AU - Reuveni, Shlomi

N1 - Publisher Copyright:
© 2019 IOP Publishing Ltd.

PY - 2019/5/29

Y1 - 2019/5/29

N2 - First-passage processes can be divided in two classes: those that are accelerated by the introduction of restart and those that display an opposite response. In physical systems, a transition between the two classes may occur as governing parameters are varied to cross a universal tipping point. However, a fully tractable model system to teach us how this transition unfolds is still lacking. To bridge this gap, we quantify the effect of stochastic restart on the first-passage time of a drift-diffusion process to an absorbing boundary. There, we find that the transition is governed by the Péclet number (Pe) - the ratio between the rates of advective and diffusive transport. When Pe > 1 the process is drift-controlled and restart can only hinder its completion. In contrast, when the process is diffusion-controlled and restart can speed-up its completion by a factor of ∼1/Pe. Such speedup occurs when the process is restarted at an optimal rate r∗ ≃ r∗ 0 (1-Pe), where stands for the optimal restart rate in the pure-diffusion limit. The transition considered herein stands at the core of restart phenomena and is relevant to a large variety of processes that are driven to completion in the presence of noise. Each of these processes has unique characteristics, but our analysis reveals that the restart transition resembles other phase transitions - some of its central features are completely generic.

AB - First-passage processes can be divided in two classes: those that are accelerated by the introduction of restart and those that display an opposite response. In physical systems, a transition between the two classes may occur as governing parameters are varied to cross a universal tipping point. However, a fully tractable model system to teach us how this transition unfolds is still lacking. To bridge this gap, we quantify the effect of stochastic restart on the first-passage time of a drift-diffusion process to an absorbing boundary. There, we find that the transition is governed by the Péclet number (Pe) - the ratio between the rates of advective and diffusive transport. When Pe > 1 the process is drift-controlled and restart can only hinder its completion. In contrast, when the process is diffusion-controlled and restart can speed-up its completion by a factor of ∼1/Pe. Such speedup occurs when the process is restarted at an optimal rate r∗ ≃ r∗ 0 (1-Pe), where stands for the optimal restart rate in the pure-diffusion limit. The transition considered herein stands at the core of restart phenomena and is relevant to a large variety of processes that are driven to completion in the presence of noise. Each of these processes has unique characteristics, but our analysis reveals that the restart transition resembles other phase transitions - some of its central features are completely generic.

KW - Peclet number

KW - drift-diffusion

KW - first-passage under restart

KW - phase transition

UR - http://www.scopus.com/inward/record.url?scp=85065862564&partnerID=8YFLogxK

U2 - 10.1088/1751-8121/ab1fcc

DO - 10.1088/1751-8121/ab1fcc

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AN - SCOPUS:85065862564

SN - 1751-8113

VL - 52

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

IS - 25

M1 - 255002

ER -