论文标题
分形晶格中的刚性渗透
Correlated rigidity percolation in fractal lattices
论文作者
论文摘要
刚性渗透（RP）是网络中机械稳定性的出现。由实验观察到的胶体凝胶和无序纤维网络等材料的分形性，我们在分形网络中研究RP。具体而言，我们计算了SierpińskiGaskets（SG）的位置稀释晶格的关键填料，并具有不同程度的分形迭代。我们的结果表明，尽管这些晶格的RP的相关长度指数和分形维度与常规三角晶格的相同，但由于网络的分形性，临界体积分数大大较低。此外，我们基于单个SG的脆弱性分析为SG晶格开发了一个简化的模型。这种简化的模型为完整分形晶格的临界堆积部分提供了上限，并且该上限严格遵守了分形晶格的RP阈值。我们的结果表征了超低密度分形网络中的刚度。
Rigidity percolation (RP) is the emergence of mechanical stability in networks. Motivated by the experimentally observed fractal nature of materials like colloidal gels and disordered fiber networks, we study RP in a fractal network. Specifically, we calculate the critical packing fractions of site-diluted lattices of Sierpiński gaskets (SG's) with varying degrees of fractal iteration. Our results suggest that although the correlation length exponent and fractal dimension of the RP of these lattices are identical to that of the regular triangular lattice, the critical volume fraction is dramatically lower due to the fractal nature of the network. Furthermore, we develop a simplified model for an SG lattice based on the fragility analysis of a single SG. This simplified model provides an upper bound for the critical packing fractions of the full fractal lattice, and this upper bound is strictly obeyed by the disorder averaged RP threshold of the fractal lattices. Our results characterize rigidity in ultra-low-density fractal networks.
