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Structural Analysis of Metallic Glasses with Computational Homology

  • Book
  • © 2016

Overview

Authors:
  1. Akihiko Hirata

    1. Advanced Institute for Materials Re, Tohoku University, Sendai, Japan

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  2. Kaname Matsue

    1. The Institute of Statistical Mathematics, Tachikawa, Tokyo, Japan

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    You can also search for this author in PubMed   Google Scholar

  3. Mingwei Chen

    1. Institute for Material Research, Tohoku University, Sendai, Japan

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  • Describes for the first time the application of computational homology for atomic structures of glasses
  • Introduces a successful example of the collaborative work between materials and mathematical researchers
  • Provides readable and understandable mathematical information for non-specialist readers, especially materials scientists
  • Includes supplementary material: sn.pub/extras

Part of the book series: SpringerBriefs in the Mathematics of Materials (BRIEFSMAMA, volume 2)

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Table of contents (5 chapters)

  1. Front Matter

    Pages i-xiv
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  2. Introduction

    • Akihiko Hirata, Kaname Matsue, Mingwei Chen
    Pages 1-7

  3. Metallic Glasses

    • Akihiko Hirata, Kaname Matsue, Mingwei Chen
    Pages 9-14

  4. Overview of Cubical Homology

    • Akihiko Hirata, Kaname Matsue, Mingwei Chen
    Pages 15-36

  5. Application of Computational Homology to Metallic Glass Structures

    • Akihiko Hirata, Kaname Matsue, Mingwei Chen
    Pages 37-46

  6. Conclusion

    • Akihiko Hirata, Kaname Matsue, Mingwei Chen
    Pages 47-50

  7. Back Matter

    Pages 51-66
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Keywords

About this book

This book introduces the application of computational homology for structural analysis of metallic glasses. Metallic glasses, relatively new materials in the field of metals, are the next-generation structural and functional materials owing to their excellent properties. To understand their properties and to develop novel metallic glass materials, it is necessary to uncover their atomic structures which have no periodicity, unlike crystals. Although many experimental and simulation studies have been performed to reveal the structures, it is extremely difficult to perceive a relationship between structures and properties without an appropriate point of view, or language. The purpose here is to show how a new approach using computational homology gives a useful insight into the interpretation of atomic structures. It is noted that computational homology has rapidly developed and is now widely applied for various data analyses. The book begins with a brief basic survey of metallic glassesand computational homology, then goes on to the detailed procedures and interpretation of computational homology analysis for metallic glasses. Understandable and readable information for both materials scientists and mathematicians is also provided.

Reviews

“This book presents a combination of physical and mathematical chapters aimed to provide an introduction to the methods. … the physical chapters give a clear introduction into the underlying structures and the motivation of the approach, while the mathematical chapters provide a formal description of mathematical methods … . this book not only reviews the obtained results but also shortly formulates open problems and emerging topics in the field of more accurate homological analysis of disordered media.” (Eugene Postnikov, zbMATH 1352.82001, 2017)

Authors and Affiliations

  • Advanced Institute for Materials Re, Tohoku University, Sendai, Japan

    Akihiko Hirata

  • The Institute of Statistical Mathematics, Tachikawa, Tokyo, Japan

    Kaname Matsue

  • Institute for Material Research, Tohoku University, Sendai, Japan

    Mingwei Chen

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