Bücher der Reihe SpringerBriefs in the Mathematics of Materials

This book discusses discrete geometric analysis, especially topological crystallography and discrete surface theory for trivalent discrete surfaces. Topological crystallography, based on graph theory, provides the most symmetric structure among given combinatorial structures by using the variational principle, and it can reproduce crystal structures existing in nature. In this regard, the topological crystallography founded by Kotani and Sunada is explained by using many examples. Carbon structures such as fullerenes are considered as trivalent discrete surfaces from the viewpoint of discrete geometric analysis. Discrete surface theories usually have been considered discretization of smooth surfaces. Here, consideration is given to discrete surfaces modeled by crystal/molecular structures, which are essentially discrete objects.

The introduction and application of topological geometry (soft geometry) to polymer molecules is a crucial requirement to account for the basic geometrical properties of polymer chains uniquely flexible in nature, in contrast to small chemical compounds conceived upon Euclidian geometry (hard geometry) principles.

This book introduces the application of computational homology for structural analysis of metallic glasses. The book begins with a brief basic survey of metallic glasses and computational homology, then goes on to the detailed procedures and interpretation of computational homology analysis for metallic glasses.

This book is the first volume of the SpringerBriefs in the Mathematics of Materials and provides a comprehensive guide to the interaction of mathematics with materials science.