$A+A\to \varnothing$ model with a bias towards nearest neighbor

Abstract

We have studied $A+A\to \varnothing$ reaction-diffusion model on a ring, with a bias $\epsilon$ $(0\le \epsilon \le 0.5)$ of the random walkers $A$ to hop towards their nearest neighbor. Though the bias is local in space and time, we show that it alters the universality class of the problem. The $z$ exponent, which describes the growth of average spacings between the walkers with time, changes from the value 2 at $\epsilon =0$ to the mean-field value of unity for any non-zero $\epsilon$. We study the problem analytically using independent interval approximation and compare the scaling results with that obtained from simulation. The distribution $P(k,t)$ of the spacing $k$ between two walkers (per site) is given by $t^{-2/z}f(k/t^{1/z})$ as expected; however, the scaling function shows different behaviour in the two approaches.

Fig 1 replaced with correct label, typos in published version corrected

References in corpus (2)

• A new model of binary opinion dynamics: coarsening and effect of disorder
• Opinion dynamics model with domain size dependent dynamics: novel features and new universality class

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