A one dimensional $A+A\to 0̸$ system where the direction of motion of the particles is determined by the position of the nearest neighbours is studied. The particles move with a probability $0.5+ϵ$ towards their nearest neighbours with $-0.5\le ϵ\le 0.5$. This implies a stochastic motion towards the nearest neighbour or away from it for positive and negative values of $ϵ$ respectively, with $ϵ=\pm 0.5$ the two deterministic limits. The position of the particles are updated in parallel. The macroscopic as well as tagged particle dynamics are studied which show drastic changes from the diffusive case $ϵ=0$. The decay of particle density shows departure from the usual power law behaviour as found in $ϵ=0$, on both sides of $ϵ=0$. The persistence probability $P\left(t\right)$ is also calculated that shows a power law decay, $P\left(t\right)\propto t^{-\theta }$, for $ϵ=0$, where $\theta \approx 0.75$, twice of what is obtained in asynchronous updating. For $ϵ<0$, $P\left(t\right)$ decays in a stretched exponential manner and switches over to a behaviour compatible with $P\left(t\right)\propto t^{-\theta }lnt$ for $ϵ>0$. The $ϵ=0.5$ point is characterised by the presence of permanent dimers, which are isolated pairs of particles on adjacent sites. Under the parallel dynamics and for attractive interaction these particles may go on swapping their positions for a long time, in particular, for $ϵ=0.5$ these may survive permanently. Interestingly, for a chosen special initial condition that inhibits the formation of dimers, one recovers the asynchronous behaviour, manifesting the role of the dimers in altering the scaling behaviour for $ϵ>0$. For the tagged particle, the probability distribution $\Pi (x,t)$ that the particle has undergone a displacement $x$ at time $t$ shows the existence of a scaling variable $x∕t^{\nu }$ where $\nu =0.55\pm 0.05$ for $ϵ>0$ and varies with $ϵ$ for $ϵ<0$. Finally, a comparative analysis for the behaviour of all the relevant quantities for the system using parallel and asynchronous dynamics (studied recently) shows that there are significant differences for $ϵ>0$ while the results are qualitatively similar for $ϵ<0$.

一维 $\mathrm{一个}+\mathrm{一个}\to 0̸$研究了粒子运动方向由最近邻的位置决定的系统。粒子有可能移动$0。5+ϵ$ 向他们最近的邻居 $-0。5\le ϵ\le 0。5$。这意味着对于的正负值，朝着最近的邻居或远离它的方向随机运动。$ϵ$ 分别与 $ϵ=\pm 0。5$两个确定性限制。粒子的位置将并行更新。研究了宏观的和标记的粒子动力学，这些动力学显示了扩散情况的剧烈变化$ϵ=0$。粒子密度的衰减表明与通常的幂律行为背离。$ϵ=0$，在 $ϵ=0$。持续概率$P（Ť）$ 还可以计算出幂律衰减 $P（Ť）\propto {Ť}^{-\theta }$，对于 $ϵ=0$，在哪里 $\theta \approx 0。75$，是异步更新中获得的两倍。对于$ϵ<0$， $P（Ť）$ 以拉伸的指数方式衰减并转换为与 $P（Ť）\propto {Ť}^{-\theta }lnŤ$ 对于 $ϵ>0$。的$ϵ=0。5$该点的特征在于存在永久性二聚体，其是在相邻位点上的孤立的颗粒对。在平行动力学和有吸引力的相互作用下，这些粒子可能会长时间交换位置，特别是对于$ϵ=0。5$这些可能会永久生存。有趣的是，对于抑制二聚体形成的选定特殊初始条件，人们恢复了异步行为，这表明了二聚体在改变结垢行为方面的作用。$ϵ>0$。对于标记的粒子，概率分布$\Pi （X，Ť）$ 粒子已经发生位移 $X$ 在时间 $Ť$ 显示缩放比例变量的存在 $X∕{Ť}^{\nu }$ 哪里 $\nu =0。55\pm 0。05$ 对于 $ϵ>0$ 并随 $ϵ$ 对于 $ϵ<0$。最后，使用并行和异步动力学对系统中所有相关量的行为进行比较分析（最近研究）表明，对于$ϵ>0$ 而结果在质量上相似 $ϵ<0$。