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Summary:

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.

Table of Contents:

• Preface; Contents; 1 A Historical View of Materials Science; 1.1 Emergence of Materials Science as an Interdisciplinary Field; 1.2 Classical Fields Within Materials Science; 1.3 Peculiarity of Materials Science and Partnership with Mathematics; References; 2 Influence of Mathematics on Materials Science Upto Date; 2.1 Geometric Structures of Atomic Configurations; 2.1.1 Atomism; 2.1.2 The Miracle Year of 1669; The Emergence of Crystallography and Optocrystallography from Mineralogy; 2.1.3 Quasicrystals; 2.1.4 Aperiodic Tiling and Disordered System; 2.1.5 Graph Modeling for Nano-Materials.
• 2.1.6 Crystal Lattices and Their Standard Realizations2.2 Quantum Materials; 2.2.1 Electronic Characteristics of Periodic Materials System: Band Theory; 2.2.2 Spin Current; 2.2.3 Integer Quantum Hall Effect (IQHE); 2.2.4 Hofstadter's Butterfly; 2.2.5 Central Limit Theorem for Magnetic Transition Operators; 2.2.6 Topological Insulator; 2.2.7 Non Commutative Bloch Theory; 2.3 Pattern Formation; 2.3.1 Patterns in Equilibrium: Soap Films, Soap Bubbles; 2.3.2 Fundamentals of Crystal Growth; 2.3.3 Reaction
• Diffusion Equation; 2.3.4 Mean Curvature Flow to Describe Crystal Growth.
• 2.3.5 Level Set Method2.3.6 Phase Field Method; 2.4 Other Tools; 2.4.1 Computed Tomography; 2.4.2 Some Other Computational Tools; 2.5 Global Trend to Encourage Mathematics
• Materials Science Cooperation; References; 3 Some Specific Examples of Mathematics
• Materials Science Collaboration at AIMR; 3.1 Elucidation of Metallic Glass Structure by Computational Homology; 3.2 Application of a Stochastic Model; 3.2.1 Stoichiometry Control Based on a Mathematical Model; 3.2.2 Deformation Analysis of Bulk Metallic Glass Using a Stochastic Model.
• 3.3 New Geometric Measures for Finite Carbon Nanotubes3.4 Materials Having Network Structures; 3.4.1 Mathematical Technique Predicts Molecular Magnet; 3.4.2 Mixing Time of Molecules Inside of Nanoporous Gold; References; 4 Breakthroughs Based on the Mathematics
• Materials Science Collaboration; 4.1 Real Interdisciplinary Integration; 4.2 Organization Promoting Mathematics
• Materials Science Collaboration; 4.3 Specific Problems and Applications in the Future; 5 Epilogue; References; Appendix A Supplements to "Quantum Materials."

Author/Creator:

Ikeda, S. (Susumu) , author

Contributors:

Kotani, Motoko, 1960- , author

Languages:

English

Language Notes:

Item content: English

Main Work:

A new direction in mathematics for materials science [by Ikeda, S.]

Other Related Resources:

Print version: New direction in mathematics for materials science [by Ikeda, S.] (©2015 — ISBN 4431558624; ISBN 9784431558620; OCLC Number 922169107)

Related Series:

SpringerBriefs in the mathematics of materials; v. 1

Subjects:

Materials science — Mathematics

Materials science

General Notes:

Includes bibliographical references.
Description based on: Online resource; title from PDF title page (SpringerLink, viewed December 21, 2015).

Physical Description:

1 online resource : illustrations (some color).

Digital Characteristics:

text file

Call Numbers:

TA403.6 .I343 2015eb

ISBNs:

9784431558644 (electronic bk.)
4431558640 (electronic bk.)
9784431558620 [Invalid]
4431558624 [Invalid]

Other Standard Numbers:

Digital Object Identifier: 10.1007/978-4-431-55864-4

OCLC Numbers:

932016753