Mathematical Research In Materials Science

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A New Direction In Mathematics For Materials Science

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Author : Susumu Ikeda
language : en
Publisher: Springer
Release Date : 2015-12-18

A New Direction In Mathematics For Materials Science written by Susumu Ikeda and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-12-18 with Mathematics categories.

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

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Author : National Research Council
language : en
Publisher: National Academies Press
Release Date : 1993-02-01

Mathematical Research In Materials Science written by National Research Council and has been published by National Academies Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-02-01 with Technology & Engineering categories.

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.

Mathematical Techniques In Crystallography And Materials Science

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Author : Edward Prince
language : en
Publisher: Springer Science & Business Media
Release Date : 2004-03-23

Mathematical Techniques In Crystallography And Materials Science written by Edward Prince and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-03-23 with Mathematics categories.

""Mathematical techniques in Crystallography and Materials Science" brings together common and less familiar mathematical procedures used in studies of the structures and physical properties of solids. 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.

Mathematical Research In Materials Science

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Author : National Research Council (U.S.). Board on Mathematical Sciences
language : en
Publisher:
Release Date : 1993

Mathematical Research In Materials Science written by National Research Council (U.S.). Board on Mathematical Sciences and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with categories.

Multiscale Modeling And Analysis For Materials Simulation

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Author : Weizhu Bao
language : en
Publisher: World Scientific
Release Date : 2012

Multiscale Modeling And Analysis For Materials Simulation written by Weizhu Bao and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Mathematics categories.

The Institute for Mathematical Sciences at the National University of Singapore hosted a two-month research program on "Mathematical Theory and Numerical Methods for Computational Materials Simulation and Design" from 1 July to 31 August 2009. As an important part of the program, tutorials and special lectures were given by leading experts in the fields for participating graduate students and junior researchers. This invaluable volume collects four expanded lecture notes with self-contained tutorials. They cover a number of aspects on multiscale modeling, analysis and simulations for problems arising from materials science including some critical components in computational prediction of materials properties such as the multiscale properties of complex materials, properties of defects, interfaces and material microstructures under different conditions, critical issues in developing efficient numerical methods and analytic frameworks for complex and multiscale materials models. This volume serves to inspire graduate students and researchers who choose to embark into original research work in these fields.

Mathematics And The Natural Sciences

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Author : Francis Bailly
language : en
Publisher: World Scientific
Release Date : 2011

Mathematics And The Natural Sciences written by Francis Bailly and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Science categories.

The book aims at the identification of the organising concepts of some physical and biological phenomena, by means of an analysis of the foundations of mathematics and of physics. This is done in the perspective of unifying phenomena, of bringing different conceptual universes into dialog. The analysis of the role of “order” and of symmetries in the foundations of mathematics is linked to the main invariants and principles, among which the geodesic principle (a consequence of symmetries), which govern and confer unity to the various physical theories. Moreover, we attempt to understand causal structures, a central element of physical intelligibility, in terms of symmetries and their breakings. The importance of the mathematical tool is also highlighted, enabling us to grasp the differences in the models for physics and biology which are proposed by continuous and discrete mathematics, such as computational simulations. A distinction between principles of (conceptual) construction and principles of proofs, both in physics and in mathematics, guides this part of the work.As for biology, being particularly difficult and not as thoroughly examined at a theoretical level, we propose a “unification by concepts”, an attempt which should always precede mathematisation. This constitutes an outline for unification also basing itself upon the highlighting of conceptual differences, of complex points of passage, of technical irreducibilities of one field to another. Indeed, a monist point of view such as ours should not make us blind: we, the living objects, are surely just big bags of molecules or, at least, this is our main metaphysical assumption. The point though is: which theory can help us to better understand these bags of molecules, as they are, indeed, rather “singular”, from the physical point of view. Technically, this singularity is expressed by the notion of “extended criticality”, a notion that logically extends the pointwise critical transitions in physics.

Research In Mathematics Of Materials Science

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Author : Malena I. Español
language : en
Publisher: Springer Nature
Release Date : 2022-09-27

Research In Mathematics Of Materials Science written by Malena I. Español and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-09-27 with Mathematics categories.

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.

Material Geometry Groupoids In Continuum Mechanics

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Author : Manuel De Leon
language : en
Publisher: World Scientific
Release Date : 2021-04-23

Material Geometry Groupoids In Continuum Mechanics written by Manuel De Leon and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-04-23 with Mathematics categories.

This monograph is the first in which the theory of groupoids and algebroids is applied to the study of the properties of uniformity and homogeneity of continuous media. It is a further step in the application of differential geometry to the mechanics of continua, initiated years ago with the introduction of the theory of G-structures, in which the group G denotes the group of material symmetries, to study smoothly uniform materials.The new approach presented in this book goes much further by being much more general. It is not a generalization per se, but rather a natural way of considering the algebraic-geometric structure induced by the so-called material isomorphisms. This approach has allowed us to encompass non-uniform materials and discover new properties of uniformity and homogeneity that certain material bodies can possess, thus opening a new area in the discipline.

A Mathematical Introduction To Electronic Structure Theory

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Author : Lin Lin
language : en
Publisher: SIAM
Release Date : 2019-06-05

A Mathematical Introduction To Electronic Structure Theory written by Lin Lin and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-06-05 with Mathematics categories.

Based on first principle quantum mechanics, electronic structure theory is widely used in physics, chemistry, materials science, and related fields and has recently received increasing research attention in applied and computational mathematics. This book provides a self-contained, mathematically oriented introduction to the subject and its associated algorithms and analysis. It will help applied mathematics students and researchers with minimal background in physics understand the basics of electronic structure theory and prepare them to conduct research in this area. The book begins with an elementary introduction of quantum mechanics, including the uncertainty principle and the Hartree?Fock theory, which is considered the starting point of modern electronic structure theory. The authors then provide an in-depth discussion of two carefully selected topics that are directly related to several aspects of modern electronic structure calculations: density matrix based algorithms and linear response theory. Chapter 2 introduces the Kohn?Sham density functional theory with a focus on the density matrix based numerical algorithms, and Chapter 3 introduces linear response theory, which provides a unified viewpoint of several important phenomena in physics and numerics. An understanding of these topics will prepare readers for more advanced topics in this field. The book concludes with the random phase approximation to the correlation energy. The book is written for advanced undergraduate and beginning graduate students, specifically those with mathematical backgrounds but without a priori knowledge of quantum mechanics, and can be used for self-study by researchers, instructors, and other scientists. The book can also serve as a starting point to learn about many-body perturbation theory, a topic at the frontier of the study of interacting electrons.

Mathematical Research In Materials Science Opportunities And Perspectives

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Author :
language : en
Publisher:
Release Date : 1993

Mathematical Research In Materials Science Opportunities And Perspectives written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with categories.

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.