论文标题
梯度渗透中的岛屿和湖泊大小分布
Island and lake size distributions in Gradient Percolation
论文作者
论文摘要
逐渐渗透的众所周知的问题已重新研究以研究岛屿尺寸的概率分布。据观察，作为普通的渗透，该分布也由幂律腐烂函数描述，但发现相关的临界指数不同。由于职业概率的基本梯度，岛屿尺寸的平均值也具有梯度。已经研究了平均岛屿大小随沿梯度的占领概率的变化以及其缩放分析。此外，我们已经引入并研究了梯度键渗透，并研究了岛屿尺寸分布统计数据，我们获得了非常相似的结果。我们还研究了粒子系统扩散曲线的特征，该晶格最初填充了一半，一半为空。在这里，我们也观察到岛屿尺寸概率分布指数相同的值。最后，已经重复了非线性梯度渗透的同一研究，并且发现岛大小分布指数的值是非线性参数强度的函数。
The well-known problem of gradient percolation has been revisited to study the probability distribution of island sizes. It is observed that as the ordinary percolation, this distribution is also described by a power-law decaying function but the associated critical exponents are found to be different. Because of the underlying gradient for the occupation probability, the average value of the island sizes also has a gradient. The variation of the average island size with the probability of occupation along the gradient has been studied together with its scaling analysis. Further, we have introduced and studied the gradient bond percolation and by studying the island size distribution statistics, we have obtained very similar results. We have also studied the characteristics of the diffusion profile of the particle system on a lattice that is initially half filled and half empty. Here also we observe the same value for the island size probability distribution exponent. Finally, the same study has been repeated for the nonlinear gradient percolation and the value of the island size distribution exponent is found to be a function of the strength of the nonlinear parameter.
