偏向最近邻的$A+A \rightarrow \emptyset $模型
$A+A \rightarrow \emptyset $ model with a bias towards nearest neighbor
摘要：
研究了环上的$A+A \rightarrow \emptyset$反应扩散模型，其中随机游动者$A$的$ε$ $(0 \leq ε\leq 0.5)$偏向于跳向最近邻.虽然偏见是当地的空间和时间，我们表明，它改变了普遍性类的问题。描述步行者之间的平均间距随时间增长的$z$指数从$ε=0$的值2变为任何非零$ε$的平均场值1。我们研究的问题分析使用独立的区间近似和比较的缩放结果与模拟得到的。两个步行者之间的间距$k$（每个站点）的分布$P(k,t)$由$t^{-2/z} f(k/t^{1/z})$给出，正如预期的那样;然而，缩放函数在两种方法中显示出不同的行为。
英文摘要：
We have studied $A+A \rightarrow \emptyset$ reaction-diffusion model on a ring, with a bias $ε$ $(0 \leq ε\leq 0.5)$ 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 $ε=0$ to the mean-field value of unity for any non-zero $ε$. 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.
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