Aydogan Dogu Baran, Hyttinen Jari
Department of Electronics and Communications Engineering, Tampere University of Technology, , Tampere, Finland.
J R Soc Interface. 2014 Mar 26;11(95):20131042. doi: 10.1098/rsif.2013.1042. Print 2014 Jun 6.
Quantifying the connectivity of material microstructures is important for a wide range of applications from filters to biomaterials. Currently, the most used measure of connectivity is the Euler number, which is a topological invariant. Topology alone, however, is not sufficient for most practical purposes. In this study, we use our recently introduced connectivity measure, called the contour tree connectivity (CTC), to study microstructures for flow analysis. CTC is a new structural connectivity measure that is based on contour trees and algebraic graph theory. To test CTC, we generated a dataset composed of 120 samples and six different types of artificial microstructures. We compared CTC against the Euler parameter (EP), the parameter for connected pairs, the nominal opening dimension (dnom) and the permeabilities estimated using direct pore scale modelling. The results show that dnom is highly correlated with permeability (R2=0.91), but cannot separate the structural differences. The groups are best classified with feature combinations that include CTC. CTC provides new information with a different connectivity interpretation that can be used to analyse and design materials with complex microstructures.
量化材料微观结构的连通性对于从过滤器到生物材料等广泛的应用来说都很重要。目前，最常用的连通性度量是欧拉数，它是一个拓扑不变量。然而，仅靠拓扑结构对于大多数实际应用来说是不够的。在本研究中，我们使用我们最近引入的连通性度量，即轮廓树连通性（CTC），来研究用于流动分析的微观结构。CTC是一种基于轮廓树和代数图论的新的结构连通性度量。为了测试CTC，我们生成了一个由120个样本和六种不同类型的人工微观结构组成的数据集。我们将CTC与欧拉参数（EP）、连通对参数、名义开口尺寸（dnom）以及使用直接孔隙尺度建模估计的渗透率进行了比较。结果表明，dnom与渗透率高度相关（R2 = 0.91），但无法区分结构差异。使用包括CTC的特征组合对这些组进行分类效果最佳。CTC提供了具有不同连通性解释的新信息，可用于分析和设计具有复杂微观结构的材料。
