利用多分辨率网络聚类检测眼镜和复杂物理系统中隐藏的空间和时空结构
Detecting hidden spatial and spatio-temporal structures in glasses and complex physical systems by multiresolution network clustering
摘要：
我们阐述了一个一般的方法，我们最近推出的“自然”结构的特征，在复杂的物理系统通过多尺度网络为基础的方法，这种结构的数据挖掘。该方法是基于“社区检测”，其中相互作用的粒子被划分为“一个理想气体“的最佳解耦的粒子组。具体而言，我们构建了一组网络表示（“副本”）的物理系统的基础上原子间的潜力和应用多尺度聚类（“多分辨率社区检测”）分析，使用基于信息的副本之间的相关性。副本可以是（i）相同静态系统的不同表示，或者（ii）通过将副本视为系统的时间分离快照（具有可调时间分离）来体现动态，或者（iii）当不同副本对应于系统在时空中演变时的整个历史的不同表示时，对一般相关性进行编码。我们将我们的方法应用于计算机模拟的二元Kob-Andersen Lennard-Jones系统，三元模型系统，并在ZrPt系统中的原子坐标，通过反向Monte Carlo分析实验确定的结构因子。我们确定的主导结构（不相交或重叠）和一般长度尺度通过分析极值的信息理论措施。我们推测（i）物理过渡或交叉和（ii）通过这种方法发现的结构变化以及与社区检测问题的计算复杂性相关的相变之间可能存在的联系。我们也简要地考虑连续介质的方法，并讨论在弹性介质中的剪切穿透深度，这一长度尺度的增加，系统变得越来越刚性。
英文摘要：
We elaborate on a general method that we recently introduced for characterizing the "natural" structures in complex physical systems via a multiscale network based approach for the data mining of such structures. The approach is based on "community detection" wherein interacting particles are partitioned into "an ideal gas" of optimally decoupled groups of particles. Specifically, we construct a set of network representations ("replicas") of the physical system based on interatomic potentials and apply a multiscale clustering ("multiresolution community detection") analysis using information-based correlations among the replicas. Replicas may be (i) different representations of an identical static system or (ii) embody dynamics by when considering replicas to be time separated snapshots of the system (with a tunable time separation) or (iii) encode general correlations when different replicas correspond to different representations of the entire history of the system as it evolves in space-time. We apply our method to computer simulations of a binary Kob-Andersen Lennard-Jones system, a ternary model system, and to atomic coordinates in a ZrPt system as gleaned by reverse Monte Carlo analysis of experimentally determined structure factors. We identify the dominant structures (disjoint or overlapping) and general length scales by analyzing extrema of the information theory measures. We speculate on possible links between (i) physical transitions or crossovers and (ii) changes in structures found by this method as well as phase transitions associated with the computational complexity of the community detection problem. We briefly also consider continuum approaches and discuss the shear penetration depth in elastic media; this length scale increases as the system becomes increasingly rigid.
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