H J Hilhorst et al 2004 J. Phys. A: Math. Gen. 37 7063 doi:10.1088/0305-4470/37/28/001
Segregation in diffusion-limited multispecies pair annihilation
H J Hilhorst1, O Deloubrière2, M J Washenberger2 and U C Täuber2
Show affiliationsThe kinetics of the q species pair annihilation reaction (Ai + Aj → ∅ for 1 ≤ i < j ≤ q) in d dimensions is studied by means of analytical considerations and Monte Carlo simulations. In the long-time regime the total particle density decays as ρ(t) ~ t−α. For d = 1 the system segregates into single-species domains, yielding a different value of α for each q; for a simplified version of the model in one dimension we derive α(q) = (q − 1)/(2q). Within mean-field theory, applicable in d ≥ 2, segregation occurs only for q < 1 + (4/d). The only physical realization of this scenario is the two-species process (q = 2) in d = 2 and d = 3, governed by an extra local conservation law. For d ≥ 2 and q ≥ 1 + (4/d) the system remains disordered and its density is shown to decay universally with the mean-field power law (α = 1) that also characterizes the single-species annihilation process A + A → ∅.
- PACS
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02.50.Ng Distribution theory and Monte Carlo studies
05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion
- MSC
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82B30 Statistical thermodynamics (See also 80-XX)
82B80 Numerical methods (Monte Carlo, series resummation, etc.) (See also 65-XX, 81T80)
- Subjects
- Dates
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Issue 28 (16 July 2004)
Received 10 March 2004, in final form 1 June 2004
Published 30 June 2004
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Segregation in diffusion-limited multispecies pair annihilation
H J Hilhorst et al 2004 J. Phys. A: Math. Gen. 37 7063
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