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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.
 [1] ;  [2]
  1. Boston Univ., Boston, MA (United States)
  2. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Publication Date:
OSTI Identifier:
Report Number(s):
Journal ID: ISSN 1742-5468
Grant/Contract Number:
Accepted Manuscript
Journal Name:
Journal of Statistical Mechanics
Additional Journal Information:
Journal Volume: 2015; Journal Issue: 5; Journal ID: ISSN 1742-5468
IOP Publishing
Research Org:
Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
Sponsoring Org:
Country of Publication:
United States
97 MATHEMATICS AND COMPUTING exact results; fluctuations (theory); stochastic particle dynamics (theory); diffusion-limited aggregation (theory)