Liu Hongxiao, Dolgushev Maxim, Qi Yi, Zhang Zhongzhi
1] School of Computer Science, Fudan University, Shanghai 200433, China [2] Shanghai Key Laboratory of Intelligent Information Processing, Fudan University, Shanghai 200433, China.
Theoretical Polymer Physics, University of Freiburg, Hermann-Herder-Str.3, D-79104 Freiburg, Germany.
Sci Rep. 2015 Mar 12;5:9024. doi: 10.1038/srep09024.
One of the most crucial domains of interdisciplinary research is the relationship between the dynamics and structural characteristics. In this paper, we introduce a family of small-world networks, parameterized through a variable d controlling the scale of graph completeness or of network clustering. We study the Laplacian eigenvalues of these networks, which are determined through analytic recursive equations. This allows us to analyze the spectra in depth and to determine the corresponding spectral dimension. Based on these results, we consider the networks in the framework of generalized Gaussian structures, whose physical behavior is exemplified on the relaxation dynamics and on the fluorescence depolarization under quasiresonant energy transfer. Although the networks have the same number of nodes (beads) and edges (springs) as the dual Sierpinski gaskets, they display rather different dynamic behavior.
跨学科研究中最关键的领域之一是动力学与结构特征之间的关系。在本文中，我们引入了一类小世界网络，通过控制图完备性或网络聚类规模的变量d进行参数化。我们研究这些网络的拉普拉斯特征值，其由解析递归方程确定。这使我们能够深入分析频谱并确定相应的谱维数。基于这些结果，我们在广义高斯结构的框架下考虑这些网络，其物理行为在准共振能量转移下的弛豫动力学和荧光去极化方面得到体现。尽管这些网络与对偶谢尔宾斯基垫片具有相同数量的节点（珠子）和边（弹簧），但它们表现出相当不同的动力学行为。
