Escape and finite-size scaling in diffusion-controlled annihilation

Ben-Naim, Eli; Krapivsky, Paul L.

doi:10.1088/1751-8113/49/50/504004

Title: Escape and finite-size scaling in diffusion-controlled annihilation

Abstract

In this paper, we study diffusion-controlled single-species annihilation with a finite number of particles. In this reaction-diffusion process, each particle undergoes ordinary diffusion, and when two particles meet, they annihilate. We focus on spatial dimensions d>2 where a finite number of particles typically survive the annihilation process. Using scaling techniques we investigate the average number of surviving particles, M, as a function of the initial number of particles, N. In three dimensions, for instance, we find the scaling law M ~ N^1/3 in the asymptotic regime N»1. We show that two time scales govern the reaction kinetics: the diffusion time scale, T ~ N^2/3, and the escape time scale, τ ~ N^4/3. The vast majority of annihilation events occur on the diffusion time scale, while no annihilation events occur beyond the escape time scale.

Authors:

^[1]; Krapivsky, Paul L. ^[2]

Los Alamos National Lab. (LANL), Los Alamos, NM (United States). Theoretical Division and Center for Nonlinear Studies
Boston Univ., MA (United States). Department of Physics

Publication Date:: 2016-12-16

Research Org.:: Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

Sponsoring Org.:: USDOE Laboratory Directed Research and Development (LDRD) Program

OSTI Identifier:: 1337106

Report Number(s):: LA-UR-16-23613
Journal ID: ISSN 1751-8113

Grant/Contract Number:: AC52-06NA25396

Resource Type:: Accepted Manuscript

Journal Name:: Journal of Physics. A, Mathematical and Theoretical

Additional Journal Information:: Journal Volume: 49; Journal Issue: 50; Journal ID: ISSN 1751-8113

Publisher:: IOP Publishing

Country of Publication:: United States

Language:: English

Subject:: 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Mathematics

Citation Formats


                    Ben-Naim, Eli, and Krapivsky, Paul L. Escape and finite-size scaling in diffusion-controlled annihilation.  United States: N. p., 2016. 
Web.  doi:10.1088/1751-8113/49/50/504004.

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                    Ben-Naim, Eli, & Krapivsky, Paul L. Escape and finite-size scaling in diffusion-controlled annihilation.  United States.  https://doi.org/10.1088/1751-8113/49/50/504004

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                    Ben-Naim, Eli, and Krapivsky, Paul L. Fri .  
"Escape and finite-size scaling in diffusion-controlled annihilation".  United States.  https://doi.org/10.1088/1751-8113/49/50/504004.  https://www.osti.gov/servlets/purl/1337106.

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@article{osti_1337106,

  title        = {Escape and finite-size scaling in diffusion-controlled annihilation},

  author       = {Ben-Naim, Eli and Krapivsky, Paul L.},

  abstractNote = {In this paper, we study diffusion-controlled single-species annihilation with a finite number of particles. In this reaction-diffusion process, each particle undergoes ordinary diffusion, and when two particles meet, they annihilate. We focus on spatial dimensions d>2 where a finite number of particles typically survive the annihilation process. Using scaling techniques we investigate the average number of surviving particles, M, as a function of the initial number of particles, N. In three dimensions, for instance, we find the scaling law M ~ N1/3 in the asymptotic regime N»1. We show that two time scales govern the reaction kinetics: the diffusion time scale, T ~ N2/3, and the escape time scale, τ ~ N4/3. The vast majority of annihilation events occur on the diffusion time scale, while no annihilation events occur beyond the escape time scale.},

  doi          = {10.1088/1751-8113/49/50/504004},

  journal      = {Journal of Physics. A, Mathematical and Theoretical},

  number       = 50,

  volume       = 49,

  place        = {United States},

  year         = {2016},

  month        = {12}

}

Copy to clipboard

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Scientific Reports, Vol. 7, Issue 1
DOI: 10.1038/srep42415

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Title: Escape and finite-size scaling in diffusion-controlled annihilation

Abstract

Citation Formats

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Asymptotics for interacting particle systems onZ d
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Kinetics of diffusion‐controlled processes in dense polymer systems. I. Nonentangled regimes
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Diffusion-limited reactions in one dimension
journal, May 1983

Particle–antiparticle annihilation in diffusive motion
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Exact solutions for a diffusion-reaction process in one dimension
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