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Mathematical Research in Materials Science

Author: National Research Council

Publisher: National Academies Press

Published: 1993-02-01

Total Pages: 142

ISBN-13: 030904930X

This book describes fruitful past collaborations between the mathematical and materials sciences and indicates future challenges. It seeks both to encourage mathematical sciences research that will complement vital research in materials science and to raise awareness of the value of quantitative methods. The volume encourages both communities to increase cross-disciplinary collaborations, emphasizing that each has much to gain from such an increase, and it presents recommendations for facilitating such work. This book is written for both mathematical and materials science researchers interested in advancing research at this interface; for federal and state agency representatives interested in encouraging such collaborations; and for anyone wanting information on how such cross-disciplinary, collaborative efforts can be accomplished successfully.

A New Direction in Mathematics for Materials Science

Author: Susumu Ikeda

Publisher: Springer

Published: 2015-12-08

Total Pages: 93

ISBN-13: 4431558640

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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.

Mathematical Research in Materials Science

Author: National Research Council (U.S.). Board on Mathematical Sciences

Publisher:

Published: 1993

Total Pages:

ISBN-13:

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Research in Mathematics of Materials Science

Author: Malena I. Español

Publisher: Springer Nature

Published: 2022-09-27

Total Pages: 514

ISBN-13: 3031044967

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This volume highlights contributions of women mathematicians in the study of complex materials and includes both original research papers and reviews. The featured topics and methods draw on the fields of Calculus of Variations, Partial Differential Equations, Functional Analysis, Differential Geometry and Topology, as well as Numerical Analysis and Mathematical Modelling. Areas of applications include foams, fluid-solid interactions, liquid crystals, shape-memory alloys, magnetic suspensions, failure in solids, plasticity, viscoelasticity, homogenization, crystallization, grain growth, and phase-field models.

Mathematical Techniques in Crystallography and Materials Science

Author: Edward Prince

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 236

ISBN-13: 3642187110

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This practical guide and reference serves as a unified source book for students and professionals, and it provides a solid basis for further studies in more specialized literature. Based Prince’s decades of practical experience, it can be recommended as an introduction for beginners in crystallography, as a refresher and handy guide for crystallographers working on specific problems, and as a reference for others seeking a dictionary of basic mathematical and crystallographic terms. The third edition further clarifies key points.

Mathematical Research in Materials Science: Opportunities and Perspectives

Author:

Publisher:

Published: 1993

Total Pages: 141

ISBN-13:

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This National Research Council report from the Board on Mathematical Sciences documents and presents technical details of fruitful collaborations between the mathematical sciences and materials science, and indicates areas of mathematical sciences research holding the most promise for advancing materials science. Written primarily for mathematical and materials science researchers with an interest in advancing research at this interface, as well as for federal and state agency representatives interested in encouraging such collaborations, it focuses on directions for potentially promising collaboration between materials scientists and mathematical scientists, and encourages both communities to increase such collaborations. It emphasizes that both the mathematical sciences and materials science communities have much to gain from an increase in cross-disciplinary collaborations, and presents recommendations for facilitating mathematical sciences research that bears on important issues in materials science, including recommendations on how to attract students and young researchers to this area. It seeks to encourage research directions in the mathematical sciences that complement vital materials science research, and raise awareness of the value of quantitative methods in materials science. It is available through National Academy Press. Mathematical sciences, Materials science, Cross-disciplinary, Research, Biomaterials, Ceramics, Complex fluids, Composites, Fracture, Metals, Polymers, Processing, Synthesis.

Topics in the Mathematical Modelling of Composite Materials

Author: Andrej V. Cherkaev

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 329

ISBN-13: 1461220327

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Andrej V. Cherkaev and Robert V. Kohn In the past twenty years we have witnessed a renaissance of theoretical work on the macroscopic behavior of microscopically heterogeneous mate rials. This activity brings together a number of related themes, including: ( 1) the use of weak convergence as a rigorous yet general language for the discussion of macroscopic behavior; (2) interest in new types of questions, particularly the "G-closure problem," motivated in large part by applications of optimal control theory to structural optimization; (3) the introduction of new methods for bounding effective moduli, including one based on "com pensated compactness"; and (4) the identification of deep links between the analysis of microstructures and the multidimensional calculus of variations. This work has implications for many physical problems involving optimal design, composite materials, and coherent phase transitions. As a result it has received attention and support from numerous scientific communities, including engineering, materials science, and physics as well as mathematics. There is by now an extensive literature in this area. But for various reasons certain fundamental papers were never properly published, circu lating instead as mimeographed notes or preprints. Other work appeared in poorly distributed conference proceedings volumes. Still other work was published in standard books or journals, but written in Russian or French. The net effect is a sort of "gap" in the literature, which has made the subject unnecessarily difficult for newcomers to penetrate.

Numerical Modeling in Materials Science and Engineering

Author: Michel Rappaz

Publisher: Springer Science & Business Media

Published: 2010-03-11

Total Pages: 544

ISBN-13: 3642118216

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Computing application to materials science is one of the fastest-growing research areas. This book introduces the concepts and methodologies related to the modeling of the complex phenomena occurring in materials processing. It is intended for undergraduate and graduate students in materials science and engineering, mechanical engineering and physics, and for engineering professionals or researchers.

Mathematics In Science And Technology: Mathematical Methods, Models And Algorithms In Science And Technology - Proceedings Of The Satellite Conference Of Icm 2010

Author: Abul Hasan Siddiqi

Publisher: World Scientific

Published: 2011-06-30

Total Pages: 558

ISBN-13: 9814462144

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This unique volume presents reviews of research in several important areas of applications of mathematical concepts to science and technology, for example applications of inverse problems and wavelets to real world systems. The book provides a comprehensive overview of current research of several outstanding scholars engaged in diverse fields such as complexity theory, vertex coupling in quantum graphs, mixing of substances by turbulence, network dynamics and architecture, processes with rate — independent hysteresis, numerical analysis of Hamilton Jacobi — Bellman equations, simulations of complex stochastic differential equations, optimal flow control, shape optimal flow control, shape optimization and aircraft designing, mathematics of brain, nanotechnology and DNA structure and mathematical models of environmental problems. The volume also contains contributory talks based on current researches of comparatively young researchers participating in the conference.

A Cross-Disciplinary Report on the Mathematical Sciences Applied to Materials Science

Author:

Publisher:

Published: 1993

Total Pages: 10

ISBN-13:

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This project produced a National Research Council report from the Board on Mathematical Sciences, Mathematical Research in Materials Science. Opportunities and Perspectives, that documents and presents technical details of fruitful collaborations between the mathematical sciences and materials science, and indicates areas of mathematical sciences research holding the most promise for advancing materials science. Written primarily for mathematical and materials science researchers with an interest in advancing research at this interface, as well as for federal and state agency representatives interested in encouraging such collaborations, it focuses on directions for potentially promising collaboration between materials scientists and mathematical scientists, and encourages both communities to increase such collaborations. It emphasizes that both the mathematical sciences and materials science communities have much to pin from an increase in cross-disciplinary collaborations, and presents recommendations for facilitating mathematical sciences research that bears on important issues in materials science, including recommendations on how to attract students and young researchers to this area. It seeks to encourage research directions in the mathematical sciences that complement vital materials science research, and raise awareness of the value of quantitative methods in materials science. The NRC report is available through National Academy Press.