Knackstedt Mark A, Sahimi Muhammad, Sheppard Adrian P
Department of Applied Mathematics, Research School of Physical Sciences and Engineering, Australian National University, Canberra ACT 0200, Australia.
Phys Rev E Stat Nonlin Soft Matter Phys. 2002 Mar;65(3 Pt 2A):035101. doi: 10.1103/PhysRevE.65.035101. Epub 2002 Feb 7.
Employing highly efficient algorithms for simulating invasion percolation (IP) with trapping, we obtain precise estimates for the fractal dimensions of the sample-spanning cluster, the backbone, and the minimal path in a variety of two-dimensional lattices. The results indicate that these quantities are nonuniversal and vary with the coordination number Z of the lattices. In particular, while the fractal dimension D(f) of the sample-spanning cluster in lattices with low Z has the generally accepted value of about 1.82, it crosses over to the value of random percolation, D(f) approximately equal to 1.896, if Z is large enough. Since optimal paths in strongly disordered media and minimum spanning trees on random graphs are related to IP, the implication is that these problems do not also possess universal scaling properties.
通过采用高效算法来模拟具有陷阱的入侵渗流（IP），我们获得了各种二维晶格中样本跨越簇、主干和最小路径的分形维数的精确估计值。结果表明，这些量是非通用的，并且随晶格的配位数Z而变化。特别是，虽然低Z晶格中样本跨越簇的分形维数D(f)通常接受的值约为1.82，但如果Z足够大，它会转变为随机渗流的值，D(f)约等于1.896。由于强无序介质中的最优路径和随机图上的最小生成树与IP相关，这意味着这些问题也不具有通用的标度性质。
