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:

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 Boston Univ., Boston, MA (United States)
 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Publication Date:
 OSTI Identifier:
 1193678
 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 Laboratory (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)