AI 中文总结
研究有向晶格上强连通渗流簇行为，通过多种算法模拟二维正方形晶格等及不同键方向排列，计算临界指数等高精度值，发现其临界行为与传统无向渗流不同，但各键排列属同一普适类。
AI 中文摘要
我们研究具有有向键的晶格上的渗流，重点关注强连通渗流簇的行为，即每个位点都可通过有向路径从其他位点到达的簇。我们考虑二维正方形晶格以及键方向的各种全局各向同性排列。使用一系列算法方法进行模拟，计算每种键排列下键渗流的临界指数、分形维数、穿越概率和渗流阈值的高精度值。我们发现临界行为与传统无向渗流处于明显不同的普适类，但所有键排列似乎都属于同一普适类。
英文摘要
We study percolation on lattices with directed bonds, focusing on the behavior of strongly-connected percolation clusters -- clusters in which every site is reachable from every other along a directed path. We consider the two-dimensional square lattice and various globally isotropic arrangements of the directions of the bonds. Performing simulations using a range of algorithmic approaches, we calculate high-precision values for critical exponents, fractal dimensions, crossing probabilities, and percolation thresholds for bond percolation with each bond arrangement. We find that the critical behavior is in a distinctly different universality class from that of traditional undirected percolation, but that all bond arrangements appear to fall in the same universality class.
Comments16 pages, 14 figures, 3 tables
