Fraction of uninfected walkers in the one-dimensional Potts model

Details Fraction of uninfected walkers in the one-dimensional Potts model Fraction of uninfected walkers in the one-dimensional Potts model

2001-11-09

arxiv.org/abs/cond-mat/0111159v3

Phys. Rev. E 65, 051114 (2002)

Physics

Condensed Matter

Statistical Mechanics

Expanded introduction with more discussion of related work

Scientific paper

10.1103/PhysRevE.65.051114

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 \rho(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^{-\theta} with \theta \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.

Affiliated with

Also associated with

No associations

Rating

Fraction of uninfected walkers in the one-dimensional Potts model does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Fraction of uninfected walkers in the one-dimensional Potts model, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Fraction of uninfected walkers in the one-dimensional Potts model will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-539154