Escape and finite-size scaling in diffusion-controlled annihilation

Journal Article · Fri Dec 16 00:00:00 EST 2016 · Journal of Physics. A, Mathematical and Theoretical

DOI:https://doi.org/10.1088/1751-8113/49/50/504004· OSTI ID:1337106

Ben-Naim, Eli  ^[1]; Krapivsky, Paul L. ^[2]

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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

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.

• Research Organization: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
• Sponsoring Organization: USDOE Laboratory Directed Research and Development (LDRD) Program
• Grant/Contract Number: AC52-06NA25396
• OSTI ID: 1337106
• Report Number(s): LA-UR-16-23613
• Journal Information: Journal of Physics. A, Mathematical and Theoretical, Vol. 49, Issue 50; ISSN 1751-8113
• Publisher: IOP Publishing
• Country of Publication: United States
• Language: English

Related Subjects

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