Irreversible reactions and diffusive escape: Stationary properties
- Boston Univ., Boston, MA (United States)
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
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.
- Research Organization:
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
- Sponsoring Organization:
- USDOE
- Grant/Contract Number:
- AC52-06NA25396
- OSTI ID:
- 1193678
- Report Number(s):
- LA-UR-15-21782
- Journal Information:
- Journal of Statistical Mechanics, Vol. 2015, Issue 5; ISSN 1742-5468
- Publisher:
- IOP PublishingCopyright Statement
- Country of Publication:
- United States
- Language:
- English
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