Diffusive epidemic process: theory and simulation

Details Diffusive epidemic process: theory and simulation Diffusive epidemic process: theory and simulation

2006-08-07

arxiv.org/abs/cond-mat/0608162v1

Physics

Condensed Matter

Statistical Mechanics

19 pages, 5 figures

Scientific paper

10.1088/0953-8984/19/6/065143

We study the continuous absorbing-state phase transition in the one-dimensional diffusive epidemic process via mean-field theory and Monte Carlo simulation. In this model, particles of two species (A and B) hop on a lattice and undergo reactions B -> A and A + B -> 2B; the total particle number is conserved. We formulate the model as a continuous-time Markov process described by a master equation. A phase transition between the (absorbing) B-free state and an active state is observed as the parameters (reaction and diffusion rates, and total particle density) are varied. Mean-field theory reveals a surprising, nonmonotonic dependence of the critical recovery rate on the diffusion rate of B particles. A computational realization of the process that is faithful to the transition rates defining the model is devised, allowing for direct comparison with theory. Using the quasi-stationary simulation method we determine the order parameter and the survival time in systems of up to 4000 sites. Due to strong finite-size effects, the results converge only for large system sizes. We find no evidence for a discontinuous transition. Our results are consistent with the existence of three distinct universality classes, depending on whether A particles diffusive more rapidly, less rapidly, or at the same rate as B particles.

Affiliated with

Also associated with

No associations

Rating

Diffusive epidemic process: theory and simulation 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 Diffusive epidemic process: theory and simulation, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Diffusive epidemic process: theory and simulation will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-600666