Escape and Finite-Size Scaling in Diffusion-Controlled Annihilation
| Autor: | Ben-Naim, E., Krapivsky, P. L. |
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| Rok vydání: | 2016 |
| Předmět: | |
| Zdroj: | J. Phys. A 49, 504004 (2016) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1088/1751-8113/49/50/504004 |
| Popis: | 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 the rate equation approach and 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 $M\sim N^{1/3}$ in the asymptotic regime $N\gg 1$. We show that two time scales govern the reaction kinetics: the diffusion time scale, $T\sim N^{2/3}$, and the escape time scale, $\tau\sim N^{4/3}$. The vast majority of annihilation events occur on the diffusion time scale, while no annihilation events occur beyond the escape time scale. Comment: 5 pages, 4 figures |
| Databáze: | arXiv |
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