Diffusion with resetting inside a circle

被引：40

作者：

Chatterjee, Abhinava ^{[1
,2
]}

Christou, Christos ^{[1
]}

Schadschneider, Andreas ^{[1
]}

机构：

[1] Univ Cologne, Inst Theoret Phys, Zulpicher Str 77, D-50937 Cologne, Germany

[2] Indian Inst Sci Educ & Res Kolkata, Dept Phys Sci, Mohanpur 741246, India

来源：

PHYSICAL REVIEW E | 2018年 / 97卷 / 06期

关键词：

Numerical methods;

D O I：

10.1103/PhysRevE.97.062106

中图分类号：

O35 [流体力学]; O53 [等离子体物理学];

学科分类号：

070204 ; 080103 ; 080704 ;

摘要：

We study the Brownian motion of a particle in a bounded circular two-dimensional domain in search for a stationary target on the boundary of the domain. The process switches between two modes: one where it performs a two-dimensional diffusion inside the circle and one where it diffuses along the one-dimensional boundary. During the process, the Brownian particle resets to its initial position with a constant rate r. The Fokker-Planck formalism allows us to calculate the mean time to absorption (MTA) as well as the optimal resetting rate for which the MTA is minimized From the derived analytical results the parameter regions where resetting reduces the search time can be specified. We also provide a numerical method for the verification of our results.

引用

页数：10

共 40 条

[1] Optimal search behavior and classic foraging theory [J].

Bartumeus, F. ;

Catalan, J. .

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 2009, 42 (43)

[2] Restart Could Optimize the Probability of Success in a Bernoulli Trial [J].

Belan, Sergey .

PHYSICAL REVIEW LETTERS, 2018, 120 (08)

[3] Intermittent search process and teleportation [J].

Benichou, O. ;

Moreau, M. ;

Suet, P.-H. ;

Voituriez, R. .

JOURNAL OF CHEMICAL PHYSICS, 2007, 126 (23)

[4] Mean exit time for surface-mediated diffusion: spectral analysis and asymptotic behavior [J].

Benichou, O. ;

Grebenkov, D. S. ;

Hillairet, L. ;

Phun, L. ;

Voituriez, R. ;

Zinsmeister, M. .

ANALYSIS AND MATHEMATICAL PHYSICS, 2015, 5 (04) :321-362

[5] Intermittent search strategies [J].

Benichou, O. ;

Loverdo, C. ;

Moreau, M. ;

Voituriez, R. .

REVIEWS OF MODERN PHYSICS, 2011, 83 (01) :81-129

[6] Optimal Reaction Time for Surface-Mediated Diffusion [J].

Benichou, O. ;

Grebenkov, D. ;

Levitz, P. ;

Loverdo, C. ;

Voituriez, R. .

PHYSICAL REVIEW LETTERS, 2010, 105 (15)

[7] Searching Fast for a Target on DNA without Falling to Traps [J].

Benichou, O. ;

Kafri, Y. ;

Sheinman, M. ;

Voituriez, R. .

PHYSICAL REVIEW LETTERS, 2009, 103 (13)

[8] Narrow-escape time problem:: Time needed for a particle to exit a confining domain through a small window [J].

Benichou, O. ;

Voituriez, R. .

PHYSICAL REVIEW LETTERS, 2008, 100 (16)

[9] Long time scaling behaviour for diffusion with resetting and memory [J].

Boyer, Denis ;

Evans, Martin R. ;

Majumdar, Satya N. .

JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT, 2017,

[10] Random Walks with Preferential Relocations to Places Visited in the Past and their Application to Biology [J].

Boyer, Denis ;

Solis-Salas, Citlali .

PHYSICAL REVIEW LETTERS, 2014, 112 (24)

← 1 2 3 4 →