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Ikeda S., Kotani M. A New Direction in Mathematics for Materials Science

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Ikeda S., Kotani M. A New Direction in Mathematics for Materials Science
Springer Tokyo, Heidelberg, New York, Dordrecht, London, 2015, – 93 p. – ISBN-10: 4431558624

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. The anterior part of the book describes a selected history of materials science as well as the interaction between mathematics and materials in history. The emergence of materials science was itself a result of an interdisciplinary movement in the 1950s and 1960s. Materials science was formed by the integration of metallurgy, polymer science, ceramics, solid state physics, and related disciplines. We believe that such historical background helps readers to understand the importance of interdisciplinary interaction such as mathematics–materials science collaboration.
The middle part of the book describes mathematical ideas and methods that can be applied to materials problems and introduces some examples of specific studies—for example, computational homology applied to structural analysis of glassy materials, stochastic models for the formation process of materials, new geometric measures for finite carbon nanotube molecules, mathematical technique predicting a molecular magnet, and network analysis of nanoporous materials. The details of these works will be shown in the subsequent volumes of this SpringerBriefs in the Mathematics of Materials series by the individual authors.
The posterior section of the book presents how breakthroughs based on mathematics–materials science collaborations can emerge. The authors' argument is supported by the experiences at the Advanced Institute for Materials Research (AIMR), where many researchers from various fields gathered and tackled interdisciplinary research.
Topics
Mathematical Applications in the Physical Sciences
Topology
Math. Applications in Chemistry
Contents
A Historical View of Materials Science
Emergence of Materials Science as an Interdisciplinary Field
Classical Fields Within Materials Science
Peculiarity of Materials Science and Partnership with Mathematics
Influence of Mathematics on Materials Science Upto Date
Geometric Structures of Atomic Configurations
Quantum Materials
Pattern Formation
Other Tools
Global Trend to Encourage Mathematics–Materials Science Cooperation
Some Specific Examples of Mathematics–Materials Science Collaboration at AIMR
Elucidation of Metallic Glass Structure by Computational Homology
Application of a Stochastic Model
New Geometric Measures for Finite Carbon Nanotubes
Materials Having Network Structures
Breakthroughs Based on the Mathematics–Materials Science Collaboration
Real Interdisciplinary Integration
Organization Promoting Mathematics–Materials Science Collaboration
Specific Problems and Applications in the Future
Epilogue
Appendix A: Supplements to “Quantum Materials”
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