06458nam 22007095 450 991030025050332120200705112151.04-431-55864-010.1007/978-4-431-55864-4(CKB)3710000000532751(EBL)4188234(SSID)ssj0001597364(PQKBManifestationID)16297879(PQKBTitleCode)TC0001597364(PQKBWorkID)14886207(PQKB)10654089(DE-He213)978-4-431-55864-4(MiAaPQ)EBC4188234(PPN)190884452(EXLCZ)99371000000053275120151208d2015 u| 0engur|n|---|||||txtccrA New Direction in Mathematics for Materials Science /by Susumu Ikeda, Motoko Kotani1st ed. 2015.Tokyo :Springer Japan :Imprint: Springer,2015.1 online resource (93 p.)SpringerBriefs in the Mathematics of Materials,2365-6336 ;1Description based upon print version of record.4-431-55862-4 Includes bibliographical references at the end of each chapters.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-Materials2.1.6 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 Growth2.3.5 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 Model3.3 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"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.SpringerBriefs in the Mathematics of Materials,2365-6336 ;1Mathematical physicsTopologyChemometricsMathematical Applications in the Physical Scienceshttps://scigraph.springernature.com/ontologies/product-market-codes/M13120Topologyhttps://scigraph.springernature.com/ontologies/product-market-codes/M28000Math. Applications in Chemistryhttps://scigraph.springernature.com/ontologies/product-market-codes/C17004Mathematical physics.Topology.Chemometrics.Mathematical Applications in the Physical Sciences.Topology.Math. Applications in Chemistry.510Ikeda Susumuauthttp://id.loc.gov/vocabulary/relators/aut755715Kotani Motokoauthttp://id.loc.gov/vocabulary/relators/autMiAaPQMiAaPQMiAaPQBOOK9910300250503321A New Direction in Mathematics for Materials Science2536261UNINA