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

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:
ORCiD logo [1] ;  [2]
  1. Los Alamos National Lab. (LANL), Los Alamos, NM (United States). Theoretical Division and Center for Nonlinear Studies
  2. Boston Univ., MA (United States). Department of Physics
Publication Date:
Report Number(s):
LA-UR-16-23613
Journal ID: ISSN 1751-8113
Grant/Contract Number:
AC52-06NA25396
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
Research Org:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org:
USDOE Laboratory Directed Research and Development (LDRD) Program
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Mathematics
OSTI Identifier:
1337106

Ben-Naim, Eli, and Krapivsky, Paul L. Escape and finite-size scaling in diffusion-controlled annihilation. United States: N. p., Web. doi:10.1088/1751-8113/49/50/504004.
Ben-Naim, Eli, & Krapivsky, Paul L. Escape and finite-size scaling in diffusion-controlled annihilation. United States. doi:10.1088/1751-8113/49/50/504004.
Ben-Naim, Eli, and Krapivsky, Paul L. 2016. "Escape and finite-size scaling in diffusion-controlled annihilation". United States. doi:10.1088/1751-8113/49/50/504004. https://www.osti.gov/servlets/purl/1337106.
@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}
}