Velocity of front propagation in the epidemic model A+B→2A

2006/07/11 by Kumar, Niraj, Tripathy, Goutam
#FOS: Physical sciences #Statistical Mechanics (cond-mat.stat-mech)

paper · doi:10.48550/arxiv.cond-mat/0607268

Abstract

We study front propagation in the irreversible epidemic model A+B→ 2A in one dimension. Here, we allow the particles A and B to diffuse with rates D_A and D_B, which, in general, may be different. We find analytic estimates for the front velocity by writing truncated master equation in a frame moving with the rightmost A particle. The results obtained are in reasonable agreement with the simulation results and are amenable to systematic improvement. We also observe a crossover from the linear dependence of front velocity V on D_A for smaller values of D_A to V∝ √(D_A) for larger D_A, but numerically still significantly different from the mean field value. The deviations reflect the role of internal fluctuations which is neglected in the mean field description.

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