Persistence in the One-Dimensional A+B -> 0 Reaction-Diffusion Model

Details Persistence in the One-Dimensional A+B -> 0 Reaction-Diffusion Model Persistence in the One-Dimensional A+B -> 0 Reaction-Diffusion Model

2001-05-03

arxiv.org/abs/cond-mat/0105074v1

Phys. Rev. E 64, 041105 (2001)

Physics

Condensed Matter

Statistical Mechanics

11 RevTeX pages, 19 EPS figures

Scientific paper

10.1103/PhysRevE.64.041105

The persistence properties of a set of random walkers obeying the A+B -> 0 reaction, with equal initial density of particles and homogeneous initial conditions, is studied using two definitions of persistence. The probability, P(t), that an annihilation process has not occurred at a given site has the asymptotic form $P(t) -> const + t^{-\theta}$, where $\theta$ is the persistence exponent (``type I persistence''). We argue that, for a density of particles $\rho >> 1$, this non-trivial exponent is identical to that governing the persistence properties of the one-dimensional diffusion equation, where $\theta \approx 0.1207$. In the case of an initially low density, $\rho_0 << 1$, we find $\theta \approx 1/4$ asymptotically. The probability that a site remains unvisited by any random walker (``type II persistence'') is also investigated and found to decay with a stretched exponential form, $P(t) \sim \exp(-const \rho_0^{1/2}t^{1/4})$, provided $\rho_0 << 1$. A heuristic argument for this behavior, based on an exactly solvable toy model, is presented.

Affiliated with

Also associated with

No associations

Rating

Persistence in the One-Dimensional A+B -> 0 Reaction-Diffusion 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 Persistence in the One-Dimensional A+B -> 0 Reaction-Diffusion Model, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Persistence in the One-Dimensional A+B -> 0 Reaction-Diffusion Model will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-477711