论文标题
随机多孔晶格中的多种型和动态缩放
Multi-multifractality and dynamic scaling in stochastic porous lattice
论文作者
论文摘要
在本文中，我们将随机二元cantor的概念扩展到加权平面随机晶格，该晶格导致随机多孔晶格。该过程始于一个发起者，我们选择为方便起见，它选择为单位区域。然后，我们定义一个将启动器或一个块之一划分的发电机，相对于其区域优先选择，将其水平或垂直分为两个矩形，其中一个以$ q = 1-p $将其删除。我们发现剩余的块及其质量随时间而变化，分别为$ t^{p} $和$ t^{ - q} $。分析解决方案表明，此过程的动力学由无限许多隐藏的保守量来控制，每个量都是多孔结构的多型量度，因为它包含各种不同尺寸的丢失块。分配这些措施的支持是分形的，分形尺寸$ 2P $提供$ 0 <p <1 $。我们发现，如果其余块的特征是其各自的区域，则相应的块尺寸分布函数遵守动态缩放。
In this article, we extend the idea of stochastic dyadic Cantor set to weighted planar stochastic lattice that leads to a stochastic porous lattice. The process starts with an initiator which we choose to be a square of unit area for convenience. We then define a generator that divides the initiator or one of the blocks, picked preferentially with respect to their areas, to divide it either horizontally or vertically into two rectangles of which one of them is removed with probability $q=1-p$. We find that the remaining number of blocks and their mass varies with time as $t^{p}$ and $t^{-q}$ respectively. Analytical solution shows that the dynamics of this process is governed by infinitely many hidden conserved quantities each of which is a multifractal measure with porous structure as it contains missing blocks of various different sizes. The support where these measures are distributed is fractal with fractal dimension $2p$ provided $0<p<1$. We find that if the remaining blocks are characterized by their respective area then the corresponding block size distribution function obeys dynamic scaling.
