Download or read book Mathematical and Computational Aspects of Materials Science written by Maria-Carme T. Calderer and published by . This book was released on 2015 with total page 101 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Introduction to Computational Materials Science written by Richard LeSar and published by Cambridge University Press. This book was released on 2013-03-28 with total page 429 pages. Available in PDF, EPUB and Kindle. Book excerpt: Emphasising essential methods and universal principles, this textbook provides everything students need to understand the basics of simulating materials behaviour. All the key topics are covered from electronic structure methods to microstructural evolution, appendices provide crucial background material, and a wealth of practical resources are available online to complete the teaching package. Modelling is examined at a broad range of scales, from the atomic to the mesoscale, providing students with a solid foundation for future study and research. Detailed, accessible explanations of the fundamental equations underpinning materials modelling are presented, including a full chapter summarising essential mathematical background. Extensive appendices, including essential background on classical and quantum mechanics, electrostatics, statistical thermodynamics and linear elasticity, provide the background necessary to fully engage with the fundamentals of computational modelling. Exercises, worked examples, computer codes and discussions of practical implementations methods are all provided online giving students the hands-on experience they need.

Download or read book Final Technical Report written by and published by . This book was released on 2002 with total page 94 pages. Available in PDF, EPUB and Kindle. Book excerpt: The meeting gathered the interdisciplinary community of scientists working on mathematical and computational aspects of materials science. One goal was to examine recent methodological advances in areas such as analysis of moving interfaces, macroscopic consequences of microstructure, and defects in materials. A second goal was to highlight recent accomplishments in areas such as materials design, synthesis, and processing; simulation of phase transformation dynamics; growth and morphology of thin films; and electromagnetic materials. A third goal was to identify promising directions for new developments of a mathematical or computational nature in areas such as multiscale analysis of materials--from atomic to continuum; nanoscale structures; liquid crystals, glasses, and polymers; and soft materials and bio-materials. There were 270 registered participants. The meeting included both plenary lectures and minisymposia.

Download or read book Computational Materials Engineering written by Koenraad George Frans Janssens and published by Academic Press. This book was released on 2010-07-26 with total page 359 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computational Materials Engineering is an advanced introduction to the computer-aided modeling of essential material properties and behavior, including the physical, thermal and chemical parameters, as well as the mathematical tools used to perform simulations. Its emphasis will be on crystalline materials, which includes all metals. The basis of Computational Materials Engineering allows scientists and engineers to create virtual simulations of material behavior and properties, to better understand how a particular material works and performs and then use that knowledge to design improvements for particular material applications. The text displays knowledge of software designers, materials scientists and engineers, and those involved in materials applications like mechanical engineers, civil engineers, electrical engineers, and chemical engineers. Readers from students to practicing engineers to materials research scientists will find in this book a single source of the major elements that make up contemporary computer modeling of materials characteristics and behavior. The reader will gain an understanding of the underlying statistical and analytical tools that are the basis for modeling complex material interactions, including an understanding of computational thermodynamics and molecular kinetics; as well as various modeling systems. Finally, the book will offer the reader a variety of algorithms to use in solving typical modeling problems so that the theory presented herein can be put to real-world use. Balanced coverage of fundamentals of materials modeling, as well as more advanced aspects of modeling, such as modeling at all scales from the atomic to the molecular to the macro-material Concise, yet rigorous mathematical coverage of such analytical tools as the Potts type Monte Carlo method, cellular automata, phase field, dislocation dynamics and Finite Element Analysis in statistical and analytical modeling

Download or read book Materials Science and Engineering written by S. Samudrala and published by Elsevier Inc. Chapters. This book was released on 2013-07-10 with total page 36 pages. Available in PDF, EPUB and Kindle. Book excerpt: Materials science research has witnessed an increasing use of data-mining techniques in establishing structure–process–property relationships. Significant advances in high-throughput experiments and computational capability have resulted in the generation of huge amounts of data. Various statistical methods are currently employed to reduce the noise, redundancy, and dimensionality of the data to make analysis more tractable. Popular methods for reduction (such as principal component analysis) assume a linear relationship between the input and output variables. Recent developments in nonlinear reduction (neural networks, self-organizing maps), though successful, have computational issues associated with convergence and scalability. This chapter reviews various spectral-based techniques that efficiently unravel linear and nonlinear structures in the data, which can subsequently be used to tractably investigate structure–property–process relationships. We compare and contrast the advantages and disadvantages of these techniques and discuss the mathematical and algorithmic underpinning of these methods. In addition, we describe techniques (based on graph-theoretic analysis) to estimate the optimal dimensionality of the low-dimensional parametric representation. We show how these techniques can be packaged into a modular, computationally scalable software framework with a graphical user interface – Scalable Extensible Toolkit for Dimensionality Reduction (SETDiR). This interface helps to separate out the mathematics and computational aspects from the material science applications, thus significantly enhancing utility to the materials science community. The applicability of the framework in constructing reduced order models of complicated materials data sets is illustrated.

Download or read book Mechanics of Deformable Solids written by Issam Doghri and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 587 pages. Available in PDF, EPUB and Kindle. Book excerpt: Three subjects of major interest in one textbook: linear elasticity, mechanics of structures in linear isotropic elasticity, and nonlinear mechanics including computational algorithms. After the simplest possible, intuitive approach there follows the mathematical formulation and analysis, with computational methods occupying a good portion of the book. There are several worked-out problems in each chapter and additional exercises at the end of the book, plus mathematical expressions are bery often given in more than one notation. The book is intended primarily for students and practising engineers in mechanical and civil engineering, although students and experts from applied mathematics, materials science and other related fields will also find it useful.

Download or read book A New Direction in Mathematics for Materials Science written by Susumu Ikeda and published by Springer. This book was released on 2015-12-08 with total page 93 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Numerical Modeling in Materials Science and Engineering written by Michel Rappaz and published by Springer Science & Business Media. This book was released on 2010-03-11 with total page 544 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Mechanics and Electrodynamics of Magneto and Electro elastic Materials written by Raymond Ogden and published by Springer Science & Business Media. This book was released on 2011-05-25 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents a state-of-the-art overview of the continuum theory of both electro- and magneto-sensitive elastomers and polymers, which includes mathematical and computational aspects of the modelling of these materials from the point of view of material properties and, in particular, the "smart-material" control of their mechanical properties.

Download or read book Multiscale Modeling of Complex Materials written by Tomasz Sadowski and published by Springer. This book was released on 2014-10-14 with total page 285 pages. Available in PDF, EPUB and Kindle. Book excerpt: The papers in this volume deal with materials science, theoretical mechanics and experimental and computational techniques at multiple scales, providing a sound base and a framework for many applications which are hitherto treated in a phenomenological sense. The basic principles are formulated of multiscale modeling strategies towards modern complex multiphase materials subjected to various types of mechanical, thermal loadings and environmental effects. The focus is on problems where mechanics is highly coupled with other concurrent physical phenomena. Attention is also focused on the historical origins of multiscale modeling and foundations of continuum mechanics currently adopted to model non-classical continua with substructure, for which internal length scales play a crucial role.

Download or read book Introduction to Computational Materials Science written by Richard LeSar and published by . This book was released on 2013 with total page 430 pages. Available in PDF, EPUB and Kindle. Book excerpt: Emphasising essential methods and universal principles, this textbook provides everything students need to understand the basics of simulating materials behavior. All the key topics are covered from electronic structure methods to microstructural evolution, appendices provide crucial background material, and a wealth of practical resources are available online to complete the teaching package. Modeling is examined at a broad range of scales, from the atomic to the mesoscale, providing students with a solid foundation for future study and research. Detailed, accessible explanations of the fundamental equations underpinning materials modelling are presented, including a full chapter summarising essential mathematical background. Extensive appendices, including essential background on classical and quantum mechanics, electrostatics, statistical thermodynamics and linear elasticity, provide the background necessary to fully engage with the fundamentals of computational modelling. Exercises, worked examples, computer codes and discussions of practical implementations methods are all provided online giving students the hands-on experience they need.

Download or read book Mathematical and Computational Aspects written by Carlos A. Brebbia and published by Springer Science & Business Media. This book was released on 2013-11-21 with total page 601 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains the edited versions of most of the papers presented at the 9th International Conference on Boundary Elements held at the University of Stuttgart, Germany from August 31st to September 4th, 1987, which was organized in co-operation with the Computational Mechanics Institute and GAMM (Society for Applied Mathematics and Mechanics). This Conference, as the previous ones, aimed to review the latest developments in technique and theory and point out new advanced future trends. The emphasis of the meeting was on the engineering advances versus mathematical formulations, in an effort to consolidate the basis of many new applications. Recently engineers have proposed different techniques to solve non-linear and time dependent problems and many of these formulations needed a better mathematical understanding. Furthermore, new approximate formulations have been proposed for boundary elements which appeared to work in engineering practice, but did not have a proper theoretical background. The Conference also discussed the engineering applications of the method and concentrated on a link between BEM practitioners, industrial users and researchers working on the latest development of the method. The editors would like to express their appreciation and thanks to Ms. Liz Newman and Mr. H. Schmitz for their unstinting work in the preparation of the Conference.

Download or read book Multiscale Paradigms in Integrated Computational Materials Science and Engineering written by Pierre Deymier and published by Springer. This book was released on 2015-11-25 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents cutting-edge concepts, paradigms, and research highlights in the field of computational materials science and engineering, and provides a fresh, up-to-date perspective on solving present and future materials challenges. The chapters are written by not only pioneers in the fields of computational materials chemistry and materials science, but also experts in multi-scale modeling and simulation as applied to materials engineering. Pedagogical introductions to the different topics and continuity between the chapters are provided to ensure the appeal to a broad audience and to address the applicability of integrated computational materials science and engineering for solving real-world problems.

Download or read book Topics in Computational Materials Science written by Ching-yao Fong and published by World Scientific. This book was released on 1998 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes the state-of-the-art research topics in theoretical materials science. It encompasses the computational methods and techniques which can advance more realistic calculations for understanding the physical principles in new growth methods of optoelectronic materials and related surface problems. These principles also govern the photonic, electronic, and structural properties of materials which are essential for device applications. They will also provide the crucial ingredients for the growth of future novel materials.

Download or read book Mathematical Research in Materials Science written by National Research Council and published by National Academies Press. This book was released on 1993-02-01 with total page 142 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Computational Aspects of Modular Forms and Galois Representations written by Bas Edixhoven and published by Princeton University Press. This book was released on 2011-05-31 with total page 438 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modular forms are tremendously important in various areas of mathematics, from number theory and algebraic geometry to combinatorics and lattices. Their Fourier coefficients, with Ramanujan's tau-function as a typical example, have deep arithmetic significance. Prior to this book, the fastest known algorithms for computing these Fourier coefficients took exponential time, except in some special cases. The case of elliptic curves (Schoof's algorithm) was at the birth of elliptic curve cryptography around 1985. This book gives an algorithm for computing coefficients of modular forms of level one in polynomial time. For example, Ramanujan's tau of a prime number p can be computed in time bounded by a fixed power of the logarithm of p. Such fast computation of Fourier coefficients is itself based on the main result of the book: the computation, in polynomial time, of Galois representations over finite fields attached to modular forms by the Langlands program. Because these Galois representations typically have a nonsolvable image, this result is a major step forward from explicit class field theory, and it could be described as the start of the explicit Langlands program. The computation of the Galois representations uses their realization, following Shimura and Deligne, in the torsion subgroup of Jacobian varieties of modular curves. The main challenge is then to perform the necessary computations in time polynomial in the dimension of these highly nonlinear algebraic varieties. Exact computations involving systems of polynomial equations in many variables take exponential time. This is avoided by numerical approximations with a precision that suffices to derive exact results from them. Bounds for the required precision--in other words, bounds for the height of the rational numbers that describe the Galois representation to be computed--are obtained from Arakelov theory. Two types of approximations are treated: one using complex uniformization and another one using geometry over finite fields. The book begins with a concise and concrete introduction that makes its accessible to readers without an extensive background in arithmetic geometry. And the book includes a chapter that describes actual computations.

Download or read book Multiscale Modeling and Analysis for Materials Simulation written by Weizhu Bao and published by World Scientific. This book was released on 2012 with total page 285 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.