Trivalent discrete surfaces and carbon structures / Hisashi Naito.
Naito, Hisashi, 1961-
2023
QD911
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Title Trivalent discrete surfaces and carbon structures / Hisashi Naito.
Author Naito, Hisashi, 1961-
ISBN 9789819957699 (electronic bk.)
9819957699 (electronic bk.)
9819957680
9789819957682
DOI https://doi.org/10.1007/978-981-99-5769-9
Publication Details Singapore : Springer, 2023.
Language English
Description 1 online resource (113 p.).
Item Number 10.1007/978-981-99-5769-9 doi
Call Number QD911
Dewey Decimal Classification 548.7
Summary 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. .
Access Note Access limited to authorized users.
Series SpringerBriefs in the mathematics of materials ; v. 5.
Available in Other Form Trivalent Discrete Surfaces and Carbon Structures
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Intro
Preface
Contents
1 Overview of This Monograph
2 Graph Theory
2.1 Graph
2.2 Covering Graph
2.3 Graph Laplacian
3 Topological Crystals
3.1 Topological Crystals and Their Standard Realizations
3.2 Construction of Standard Realizations
3.2.1 Explicit Calculations in Cases of Maximal Abelian Coverings
3.2.2 Explicit Calculations for Generic Cases
3.3 Carbon Structures and Standard Realizations
4 Negatively Curved Carbon Structures
4.1 Carbon Structures as Discrete Surfaces
4.2 Constructions of Negatively Curved Carbon Structures ...

5 Trivalent Discrete Surfaces
5.1 Curvatures of Trivalent Discrete Surfaces
5.2 Examples of Trivalent Discrete Surfaces and Their Curvatures
5.3 Construction of Trivalent Minimal Discrete Surfaces
6 Subdivisions of Trivalent Discrete Surfaces
6.1 Goldberg-Coxeter Constructions
6.2 Subdivisions of Trivalent Discrete Surfaces
6.3 Another Method of Subdivision of Trivalent Discrete Surfaces
7 Miscellaneous Topics
7.1 Carbon Nanotubes from Geometric Viewpoints
7.2 Material Properties and Discrete Geometry

7.3 Graph Spectra and Electronic Properties of Carbon Structures
7.3.1 The Hückel Method
7.3.2 Tight-Binding Approximations
7.3.3 The Density Function Theory
7.4 Eigenvalues of Subdivisions of Trivalent Discrete Surfaces
7.5 Graph Algorithms and Miscellaneous Computation Methods
7.5.1 Graph Algorithms
7.5.2 Numerical Methods for Matrices
Appendix References
Index

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