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Title: Irreversible reactions and diffusive escape: Stationary properties

We study three basic diffusion-controlled reaction processes—annihilation, coalescence, and aggregation. We examine the evolution starting with the most natural inhomogeneous initial configuration where a half-line is uniformly filled by particles, while the complementary half-line is empty. We show that the total number of particles that infiltrate the initially empty half-line is finite and has a stationary distribution. We determine the evolution of the average density from which we derive the average total number N of particles in the initially empty half-line; e.g. for annihilation $$\langle N\rangle = \frac{3}{16}+\frac{1}{4\π}$$ . For the coalescence process, we devise a procedure that in principle allows one to compute P(N), the probability to find exactly N particles in the initially empty half-line; we complete the calculations in the first non-trivial case (N = 1). As a by-product we derive the distance distribution between the two leading particles.
Authors:
 [1] ;  [2]
  1. Boston Univ., Boston, MA (United States)
  2. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Publication Date:
Report Number(s):
LA-UR-15-21782
Journal ID: ISSN 1742-5468
Grant/Contract Number:
AC52-06NA25396
Type:
Accepted Manuscript
Journal Name:
Journal of Statistical Mechanics
Additional Journal Information:
Journal Volume: 2015; Journal Issue: 5; Journal ID: ISSN 1742-5468
Publisher:
IOP Publishing
Research Org:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org:
USDOE
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; exact results; fluctuations (theory); stochastic particle dynamics (theory); diffusion-limited aggregation (theory)
OSTI Identifier:
1193678

Krapivsky, Paul L., and Ben-Naim, Eli. Irreversible reactions and diffusive escape: Stationary properties. United States: N. p., Web. doi:10.1088/1742-5468/2015/05/P05003.
Krapivsky, Paul L., & Ben-Naim, Eli. Irreversible reactions and diffusive escape: Stationary properties. United States. doi:10.1088/1742-5468/2015/05/P05003.
Krapivsky, Paul L., and Ben-Naim, Eli. 2015. "Irreversible reactions and diffusive escape: Stationary properties". United States. doi:10.1088/1742-5468/2015/05/P05003. https://www.osti.gov/servlets/purl/1193678.
@article{osti_1193678,
title = {Irreversible reactions and diffusive escape: Stationary properties},
author = {Krapivsky, Paul L. and Ben-Naim, Eli},
abstractNote = {We study three basic diffusion-controlled reaction processes—annihilation, coalescence, and aggregation. We examine the evolution starting with the most natural inhomogeneous initial configuration where a half-line is uniformly filled by particles, while the complementary half-line is empty. We show that the total number of particles that infiltrate the initially empty half-line is finite and has a stationary distribution. We determine the evolution of the average density from which we derive the average total number N of particles in the initially empty half-line; e.g. for annihilation $\langle N\rangle = \frac{3}{16}+\frac{1}{4\π}$ . For the coalescence process, we devise a procedure that in principle allows one to compute P(N), the probability to find exactly N particles in the initially empty half-line; we complete the calculations in the first non-trivial case (N = 1). As a by-product we derive the distance distribution between the two leading particles.},
doi = {10.1088/1742-5468/2015/05/P05003},
journal = {Journal of Statistical Mechanics},
number = 5,
volume = 2015,
place = {United States},
year = {2015},
month = {5}
}