Irreversible reactions and diffusive escape: Stationary properties
We study three basic diffusioncontrolled reaction processes—annihilation, coalescence, and aggregation. We examine the evolution starting with the most natural inhomogeneous initial configuration where a halfline is uniformly filled by particles, while the complementary halfline is empty. We show that the total number of particles that infiltrate the initially empty halfline 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 halfline; 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 halfline; we complete the calculations in the first nontrivial case (N = 1). As a byproduct we derive the distance distribution between the two leading particles.
 Authors:

^{[1]};
^{[2]}
 Boston Univ., Boston, MA (United States)
 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Publication Date:
 Report Number(s):
 LAUR1521782
Journal ID: ISSN 17425468
 Grant/Contract Number:
 AC5206NA25396
 Type:
 Accepted Manuscript
 Journal Name:
 Journal of Statistical Mechanics
 Additional Journal Information:
 Journal Volume: 2015; Journal Issue: 5; Journal ID: ISSN 17425468
 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); diffusionlimited aggregation (theory)
 OSTI Identifier:
 1193678
Krapivsky, Paul L., and BenNaim, Eli. Irreversible reactions and diffusive escape: Stationary properties. United States: N. p.,
Web. doi:10.1088/17425468/2015/05/P05003.
Krapivsky, Paul L., & BenNaim, Eli. Irreversible reactions and diffusive escape: Stationary properties. United States. doi:10.1088/17425468/2015/05/P05003.
Krapivsky, Paul L., and BenNaim, Eli. 2015.
"Irreversible reactions and diffusive escape: Stationary properties". United States.
doi:10.1088/17425468/2015/05/P05003. https://www.osti.gov/servlets/purl/1193678.
@article{osti_1193678,
title = {Irreversible reactions and diffusive escape: Stationary properties},
author = {Krapivsky, Paul L. and BenNaim, Eli},
abstractNote = {We study three basic diffusioncontrolled reaction processes—annihilation, coalescence, and aggregation. We examine the evolution starting with the most natural inhomogeneous initial configuration where a halfline is uniformly filled by particles, while the complementary halfline is empty. We show that the total number of particles that infiltrate the initially empty halfline 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 halfline; 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 halfline; we complete the calculations in the first nontrivial case (N = 1). As a byproduct we derive the distance distribution between the two leading particles.},
doi = {10.1088/17425468/2015/05/P05003},
journal = {Journal of Statistical Mechanics},
number = 5,
volume = 2015,
place = {United States},
year = {2015},
month = {5}
}