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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