基于两点关联函数的非均质材料建模：I.基本原则
Modeling Heterogeneous Materials via Two-Point Correlation Functions: I. Basic Principles
摘要：
非均质材料在自然界和人造环境中大量存在。实例包括多孔介质、生物材料和复合材料。这些材料所表现出的多样性和有趣的特性源于其复杂的微观结构，这也使得材料建模变得困难。在这两篇文章的第一部分中，我们收集了标准两点关联函数S ~ 2（r）的已知必要条件，并提出了一个新的猜想。特别地，我们认为，给定一个完整的两点关联函数空间，任何统计上均匀的材料的S2（r）可以表示通过一个映射的功能空间的一组选定的基地。我们提供了可实现的两点关联函数的新的例子，并提出了一组分析基函数。此外，我们设计了一个有效的和各向同性保持的构造算法，即格点算法，以产生材料的实现从他们的两点关联函数的基础上Yeong-Torquato技术。可以对生成的图像进行后续分析以获得所需的宏观性质。这些发展在这里被集成到一个通用的计划，使一个模型和分类的异质材料通过两点关联函数。
英文摘要：
Heterogeneous materials abound in nature and man-made situations. Examples include porous media, biological materials, and composite materials. Diverse and interesting properties exhibited by these materials result from their complex microstructures, which also make it difficult to model the materials. In this first part of a series of two papers, we collect the known necessary conditions on the standard two-point correlation function S2(r) and formulate a new conjecture. In particular, we argue that given a complete two-point correlation function space, S2(r) of any statistically homogeneous material can be expressed through a map on a selected set of bases of the function space. We provide new examples of realizable two-point correlation functions and suggest a set of analytical basis functions. Moreover, we devise an efficient and isotropy- preserving construction algorithm, namely, the Lattice-Point algorithm to generate realizations of materials from their two- point correlation functions based on the Yeong-Torquato technique. Subsequent analysis can be performed on the generated images to obtain desired macroscopic properties. These developments are integrated here into a general scheme that enables one to model and categorize heterogeneous materials via two-point correlation functions.
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