Schrenk K J, Posé N, Kranz J J, van Kessenich L V M, Araújo N A M, Herrmann H J
Computational Physics for Engineering Materials, Institute for Building Materials, ETH Zurich, Wolfgang-Pauli-Strasse 27, CH-8093 Zurich, Switzerland.
Computational Physics for Engineering Materials, Institute for Building Materials, ETH Zurich, Wolfgang-Pauli-Strasse 27, CH-8093 Zurich, Switzerland and Departamento de Física, Universidade Federal do Ceará, 60451-970 Fortaleza, Ceará, Brazil.
Phys Rev E Stat Nonlin Soft Matter Phys. 2013 Nov;88(5):052102. doi: 10.1103/PhysRevE.88.052102. Epub 2013 Nov 4.
Long-range power-law correlated percolation is investigated using Monte Carlo simulations. We obtain several static and dynamic critical exponents as functions of the Hurst exponent H, which characterizes the degree of spatial correlation among the occupation of sites. In particular, we study the fractal dimension of the largest cluster and the scaling behavior of the second moment of the cluster size distribution, as well as the complete and accessible perimeters of the largest cluster. Concerning the inner structure and transport properties of the largest cluster, we analyze its shortest path, backbone, red sites, and conductivity. Finally, bridge site growth is also considered. We propose expressions for the functional dependence of the critical exponents on H.
使用蒙特卡罗模拟研究了长程幂律相关渗流。我们获得了几个静态和动态临界指数，它们是赫斯特指数H的函数，赫斯特指数H表征了格点占据之间的空间相关程度。特别地，我们研究了最大簇的分形维数、簇尺寸分布二阶矩的标度行为，以及最大簇的完整和可达周长。关于最大簇的内部结构和输运性质，我们分析了它的最短路径、骨架、红色格点和电导率。最后，还考虑了桥点生长。我们提出了临界指数对H的函数依赖关系的表达式。
