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Fraction of uninfected walkers in the one-dimensional Potts model | | S. J. O’Donoghue
; A. J. Bray
; | | Date: |
9 Nov 2001 | | Journal: | Phys. Rev. E 65, 051114 (2002) | | Subject: | Statistical Mechanics | cond-mat.stat-mech | | Abstract: | The dynamics of the one-dimensional q-state Potts model, in the zero temperature limit, can be formulated through the motion of random walkers which either annihilate (A + A -> 0) or coalesce (A + A -> A) with a q-dependent probability. We consider all of the walkers in this model to be mutually infectious. Whenever two walkers meet, they experience mutual contamination. Walkers which avoid an encounter with another random walker up to time t remain uninfected. The fraction of uninfected walkers is investigated numerically and found to decay algebraically, U(t) sim t^{-phi(q)}, with a nontrivial exponent phi(q). Our study is extended to include the coupled diffusion-limited reaction A+A -> B, B+B -> A in one dimension with equal initial densities of A and B particles. We find that the density of walkers decays in this model as
ho(t) sim t^{-1/2}. The fraction of sites unvisited by either an A or a B particle is found to obey a power law, P(t) sim t^{- heta} with heta simeq 1.33. We discuss these exponents within the context of the q-state Potts model and present numerical evidence that the fraction of walkers which remain uninfected decays as U(t) sim t^{-phi}, where phi simeq 1.13 when infection occurs between like particles only, and phi simeq 1.93 when we also include cross-species contamination. | | Source: | arXiv, cond-mat/0111159 | | Other source: | [GID 827504] pmid12059536 | | Services: | Forum | Review | PDF | Favorites | |
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