Escape and finitesize scaling in diffusioncontrolled annihilation
In this paper, we study diffusioncontrolled singlespecies annihilation with a finite number of particles. In this reactiondiffusion 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]}
;
^{[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:
 Report Number(s):
 LAUR1623613
Journal ID: ISSN 17518113
 Grant/Contract Number:
 AC5206NA25396
 Type:
 Accepted Manuscript
 Journal Name:
 Journal of Physics. A, Mathematical and Theoretical
 Additional Journal Information:
 Journal Volume: 49; Journal Issue: 50; Journal ID: ISSN 17518113
 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
BenNaim, Eli, and Krapivsky, Paul L. Escape and finitesize scaling in diffusioncontrolled annihilation. United States: N. p.,
Web. doi:10.1088/17518113/49/50/504004.
BenNaim, Eli, & Krapivsky, Paul L. Escape and finitesize scaling in diffusioncontrolled annihilation. United States. doi:10.1088/17518113/49/50/504004.
BenNaim, Eli, and Krapivsky, Paul L. 2016.
"Escape and finitesize scaling in diffusioncontrolled annihilation". United States.
doi:10.1088/17518113/49/50/504004. https://www.osti.gov/servlets/purl/1337106.
@article{osti_1337106,
title = {Escape and finitesize scaling in diffusioncontrolled annihilation},
author = {BenNaim, Eli and Krapivsky, Paul L.},
abstractNote = {In this paper, we study diffusioncontrolled singlespecies annihilation with a finite number of particles. In this reactiondiffusion 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 = {10.1088/17518113/49/50/504004},
journal = {Journal of Physics. A, Mathematical and Theoretical},
number = 50,
volume = 49,
place = {United States},
year = {2016},
month = {12}
}