Random geometric graphs for modelling the pore space of fibre-based materials

Ralf Thiedmann; Ingo Manke; Werner Lehnert; Volker Schmidt

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Random geometric graphs for modelling the pore space of fibre-based materials

机译：用于建模纤维基材料孔隙空间的随机几何图

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A stochastic network model is developed which describes the 3D morphology of the pore space in fibre-based materials. It has the form of a random geometric graph, where the vertex set is modelled by random point processes and the edges are put using tools from graph theory and Markov chain Monte Carlo simulation. The model parameters are fitted to real image data gained by X-ray synchrotron tomography. In particular, they are specified in such a way that the distributions of vertex degrees and edge lengths, respectively, coincide to a large extent for real and simulated data. Furthermore, the network model is used to introduce a morphology-based notion of pores and their sizes. The model is validated by considering physical characteristics which are relevant for transport processes in the pore space, like geometric tortuosity, i.e., the distribution of shortest path lengths through the material relative to its thickness.

机译：建立了一个随机网络模型，该模型描述了纤维基材料中孔隙空间的3D形态。它具有随机几何图的形式，其中顶点集通过随机点过程建模，并且使用图论和马尔可夫链蒙特卡洛模拟工具来放置边缘。模型参数适合通过X射线同步加速器层析成像获得的真实图像数据。特别地，以这样的方式来指定它们，即对于真实和模拟数据，顶点度和边缘长度的分布分别在很大程度上相符。此外，网络模型用于引入基于形态的孔及其大小的概念。通过考虑与孔隙空间中的传输过程相关的物理特征来验证该模型，例如几何曲折，即穿过材料的最短路径长度相对于其厚度的分布。

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《Journal of Materials Science》 |2011年第24期|p.7745-7759|共15页
作者
Ralf Thiedmann; Ingo Manke; Werner Lehnert; Volker Schmidt;
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作者单位

Ulm University, 89069, Ulm, Germany;

Helmholtz-Zentrum Berlin für Energie und Materialien, 14109, Berlin, Germany;

Forschungszentrum Jülich GmbH, 52425, Jülich, Germany;

Ulm University, 89069, Ulm, Germany;

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Random geometric graphs for modelling the pore space of fibre-based materials

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