Fractal formation mechanism in hierarchically complex systems and fractal design

在这个项目中，我们从理论上研究了复杂系统中出现在几个层次上的分形。本研究包括：(1)阐明结构波动及其起源的普遍性质；(2)了解分形的形成机制；(3)设计理论功能分形结构。特别是分形系统在不同尺度上的统计性质，从宏观的经典系统到纳米尺度的量子系统以及无欧几里得距离的复杂网络，都得到了系统的研究。

In this project, we have studied theoretically the fractality appearing in several hierarchical levels of complex systems. This study involves (1) clarifying universal properties in structural fluctuations and their origins, (2) understanding formation mechanisms of fractals, and (3) designing theoretically functional fractal structures. In particular, statistical properties of fractal systems in different scales, from macroscopic classical systems to nanoscale quantum ones and complex networks with no Euclidean distance, have been systematically studied.