Auto Daniel M, Moreira André A, Herrmann Hans J, Andrade José S
Departamento de Física, Universidade Federal do Ceará, Campus do Pici, 60451-970 Fortaleza, Ceará, Brazil.
Phys Rev E Stat Nonlin Soft Matter Phys. 2008 Dec;78(6 Pt 2):066112. doi: 10.1103/PhysRevE.78.066112. Epub 2008 Dec 23.
We study the percolation problem on the Apollonian network model. The Apollonian networks display many interesting properties commonly observed in real network systems, such as small-world behavior, scale-free distribution, and a hierarchical structure. By taking advantage of the deterministic hierarchical construction of these networks, we use the real-space renormalization-group technique to write exact iterative equations that relate percolation network properties at different scales. More precisely, our results indicate that the percolation probability and average mass of the percolating cluster approach the thermodynamic limit logarithmically. We suggest that such ultraslow convergence might be a property of hierarchical networks. Since real complex systems are certainly finite and very commonly hierarchical, we believe that taking into account finite-size effects in real-network systems is of fundamental importance.
我们研究阿波罗网络模型上的渗流问题。阿波罗网络展现出许多在真实网络系统中常见的有趣特性，比如小世界行为、无标度分布以及层次结构。通过利用这些网络的确定性层次结构，我们运用实空间重整化群技术来写出精确的迭代方程，这些方程关联了不同尺度下渗流网络的性质。更确切地说，我们的结果表明渗流概率和渗流团簇的平均质量以对数方式趋近于热力学极限。我们认为这种超慢收敛可能是层次网络的一个特性。由于真实的复杂系统肯定是有限的且非常普遍地具有层次结构，我们相信考虑真实网络系统中的有限尺寸效应至关重要。
