论文标题
$ a+ a \ to \ emptyset $ system在一个维
$A+ A \to \emptyset$ system in one dimension with particle motion determined by nearest neighbour distances: results for parallel updates
论文作者
论文摘要
一个尺寸$ a+a \ to \ emptySet $系统，其中粒子的运动方向由最近的邻居的位置确定。粒子以$ 0.5 + \ epsi $的概率移动到其最近的邻居，$ -0.5 \ leq \ epsi \ leq 0.5 $。这意味着向最近的邻居或远离它的随机运动，分别为$ \ epsi $的正值和负值，$ \ epsi = \ pm 〜0.5 $这两个确定性限制。颗粒的位置并联更新。研究了宏观和标记的粒子动力学，从扩散情况$ \ epsi = 0 $中显示出巨大的变化。粒子密度的衰减显示出与$ \ epsi = 0 $的常规功率定律行为背道而驰，在$ \ epsi = 0 $的两边，并且以$ \ epsi> 0 $的价格获得了缩放制度。 $ \ epsi = 0.5 $点的特征是二聚体的存在，它们是从未被歼灭的相邻位点中孤立的颗粒对。还计算出持久性的概率，即以$ \ epsi <0 $的伸展指数方式衰减，并以$ \ epsi \ geq 0 $切换到Power Law行为，并带有不同的指数，$ \ epsi = 0 $ = 0 $和$ \ epsi> 0 $。对于标记的粒子，概率分布$π（x，t）$在时间$ t $处的位置$ x $显示出存在缩放变量$ x/t^ν$，其中$ v = 0.55 \ pm 0.05 $ for $ \ epsi> 0 $ 0 $，并且因$ \ epsi $ $ \ epsi $ \ epsi <0 $而异。最后，使用并行和异步动力学（最近研究）对系统所有相关数量的行为进行比较分析表明，$ \ epsi> 0 $的比较差异有显着差异，而结果在$ \ epsi <0 $的定性上相似。
A one dimensional $A+A \to \emptyset$ system where the direction of motion of the particles is determined by the position of the nearest neighours is studied. The particles move with a probability $0.5 + \epsi$ towards their nearest neighbours with $-0.5 \leq \epsi \leq 0.5$. This implies a stochastic motion towards the nearest neighbour or away from it for positive and negative values of $\epsi$ respectively, with $\epsi = \pm ~0.5$ 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 $\epsi=0$. The decay of particle density shows departure from the usual power law behaviour as found in $\epsi =0$, on both sides of $\epsi =0$ and a scaling regime is obtained for $\epsi > 0$. The $\epsi =0.5$ point is characterized by the presence of dimers, which are isolated pairs of particles in adjacent sites that are never annihilated. The persistence probability is also calculated that decays in a stretched exponential manner for $\epsi < 0$ and switches over to power law behaviour for $\epsi \geq 0$, with different exponents for $\epsi =0$ and $\epsi > 0$. For the tagged particle, the probability distribution $Π(x,t)$ that it is at position $x$ at time $t$ shows the existence of a scaling variable $x/t^ν$ where $ν= 0.55 \pm 0.05$ for $\epsi > 0$ and varies with $\epsi$ for $\epsi < 0$. 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 $\epsi > 0$ while the results are qualitatively similar for $\epsi < 0$.
