论文标题
入侵渗透中的动态跨界
Dynamical Crossover in Invasion Percolation
论文作者
论文摘要
研究了在平方晶格上的入侵渗透的动力学特性，重点是在受感染部位不断增长的簇上的几何特性。该集群的外部边界形成了一个关键的循环集合（CLE），其长度$（l）$，半径$（r）$以及粗糙度$（w）$符合有限尺寸的缩放假设。 CLE的动态分形维度定义为$ L $和$ r $之间比例关系的指数，估计为$ d_f = 1.81 \ pm0.02 $。通过研究这些数量的自相关函数，我们重要地表明，在两个时间方案之间存在一个交叉，其中这些函数在小型时期将行为从小型时期变为长时间的指数衰减。在此交叉时间附近，这些函数由对数正态函数估算。我们还表明，所考虑的统计数量的增量与控制观察者的动力学的随机力有关，在交叉发生时经历了反相关/相关转变。
The dynamical properties of the invasion percolation on the square lattice are investigated with emphasis on the geometrical properties on the growing cluster of infected sites. The exterior frontier of this cluster forms a critical loop ensemble (CLE), whose length $(l)$, the radius $(r)$ and also roughness $(w)$ fulfill the finite size scaling hypothesis. The dynamical fractal dimension of the CLE defined as the exponent of the scaling relation between $l$ and $r$ is estimated to be $D_f=1.81\pm0.02$. By studying the autocorrelation functions of these quantities we show importantly that there is a crossover between two time regimes, in which these functions change behavior from power-law at the small times, to exponential decay at long times. In the vicinity of this crossover time, these functions are estimated by log-normal functions. We also show that the increments of the considered statistical quantities, which are related to the random forces governing the dynamics of the observables undergo an anticorrelation/correlation transition at the time that the crossover takes place.
