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Singularities in Elliptic Boundary Value Problems and Elasticity and Their Connection with Failure Initiation

Singularities in Elliptic Boundary Value Problems and Elasticity and Their Connection with Failure Initiation Author Zohar Yosibash
ISBN-10 9781461415084
Release 2011-12-02
Pages 462
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This introductory and self-contained book gathers as much explicit mathematical results on the linear-elastic and heat-conduction solutions in the neighborhood of singular points in two-dimensional domains, and singular edges and vertices in three-dimensional domains. These are presented in an engineering terminology for practical usage. The author treats the mathematical formulations from an engineering viewpoint and presents high-order finite-element methods for the computation of singular solutions in isotropic and anisotropic materials, and multi-material interfaces. The proper interpretation of the results in engineering practice is advocated, so that the computed data can be correlated to experimental observations. The book is divided into fourteen chapters, each containing several sections. Most of it (the first nine Chapters) addresses two-dimensional domains, where only singular points exist. The solution in a vicinity of these points admits an asymptotic expansion composed of eigenpairs and associated generalized flux/stress intensity factors (GFIFs/GSIFs), which are being computed analytically when possible or by finite element methods otherwise. Singular points associated with weakly coupled thermoelasticity in the vicinity of singularities are also addressed and thermal GSIFs are computed. The computed data is important in engineering practice for predicting failure initiation in brittle material on a daily basis. Several failure laws for two-dimensional domains with V-notches are presented and their validity is examined by comparison to experimental observations. A sufficient simple and reliable condition for predicting failure initiation (crack formation) in micron level electronic devices, involving singular points, is still a topic of active research and interest, and is addressed herein. Explicit singular solutions in the vicinity of vertices and edges in three-dimensional domains are provided in the remaining five chapters. New methods for the computation of generalized edge flux/stress intensity functions along singular edges are presented and demonstrated by several example problems from the field of fracture mechanics; including anisotropic domains and bimaterial interfaces. Circular edges are also presented and the author concludes with some remarks on open questions. This well illustrated book will appeal to both applied mathematicians and engineers working in the field of fracture mechanics and singularities.

A Survey of Computational Physics

A Survey of Computational Physics Author Rubin H. Landau
ISBN-10 9781400841189
Release 2011-10-30
Pages 688
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Computational physics is a rapidly growing subfield of computational science, in large part because computers can solve previously intractable problems or simulate natural processes that do not have analytic solutions. The next step beyond Landau's First Course in Scientific Computing and a follow-up to Landau and Páez's Computational Physics, this text presents a broad survey of key topics in computational physics for advanced undergraduates and beginning graduate students, including new discussions of visualization tools, wavelet analysis, molecular dynamics, and computational fluid dynamics. By treating science, applied mathematics, and computer science together, the book reveals how this knowledge base can be applied to a wider range of real-world problems than computational physics texts normally address. Designed for a one- or two-semester course, A Survey of Computational Physics will also interest anyone who wants a reference on or practical experience in the basics of computational physics. Accessible to advanced undergraduates Real-world problem-solving approach Java codes and applets integrated with text Companion Web site includes videos of lectures

Numerical Solution of Partial Differential Equations Theory Algorithms and Their Applications

Numerical Solution of Partial Differential Equations  Theory  Algorithms  and Their Applications Author Oleg P. Iliev
ISBN-10 9781461471721
Release 2013-06-04
Pages 327
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One of the current main challenges in the area of scientific computing​ is the design and implementation of accurate numerical models for complex physical systems which are described by time dependent coupled systems of nonlinear PDEs. This volume integrates the works of experts in computational mathematics and its applications, with a focus on modern algorithms which are at the heart of accurate modeling: adaptive finite element methods, conservative finite difference methods and finite volume methods, and multilevel solution techniques. Fundamental theoretical results are revisited in survey articles and new techniques in numerical analysis are introduced. Applications showcasing the efficiency, reliability and robustness of the algorithms in porous media, structural mechanics and electromagnetism are presented. Researchers and graduate students in numerical analysis and numerical solutions of PDEs and their scientific computing applications will find this book useful.

Encyclopedia of Thermal Stresses

Encyclopedia of Thermal Stresses Author Richard B. Hetnarski
ISBN-10 9400727380
Release 2013-12-04
Pages 6643
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The Encyclopedia of Thermal Stresses is an important interdisciplinary reference work. In addition to topics on thermal stresses, it contains entries on related topics, such as the theory of elasticity, heat conduction, thermodynamics, appropriate topics on applied mathematics, and topics on numerical methods. The Encyclopedia is aimed at undergraduate and graduate students, researchers and engineers. It brings together well established knowledge and recently received results. All entries were prepared by leading experts from all over the world, and are presented in an easily accessible format. The work is lavishly illustrated, examples and applications are given where appropriate, ideas for further development abound, and the work will challenge many students and researchers to pursue new results of their own. This work can also serve as a one-stop resource for all who need succinct, concise, reliable and up to date information in short encyclopedic entries, while the extensive references will be of interest to those who need further information. For the coming decade, this is likely to remain the most extensive and authoritative work on Thermal Stresses.

Modern Mathematical Methods and High Performance Computing in Science and Technology

Modern Mathematical Methods and High Performance Computing in Science and Technology Author Vinai K. Singh
ISBN-10 9789811014543
Release 2016-08-06
Pages 285
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The book discusses important results in modern mathematical models and high performance computing, such as applied operations research, simulation of operations, statistical modeling and applications, invisibility regions and regular meta-materials, unmanned vehicles, modern radar techniques/SAR imaging, satellite remote sensing, coding, and robotic systems. Furthermore, it is valuable as a reference work and as a basis for further study and research. All contributing authors are respected academicians, scientists and researchers from around the globe. All the papers were presented at the international conference on Modern Mathematical Methods and High Performance Computing in Science & Technology (M3HPCST 2015), held at Raj Kumar Goel Institute of Technology, Ghaziabad, India, from 27–29 December 2015, and peer-reviewed by international experts. The conference provided an exceptional platform for leading researchers, academicians, developers, engineers and technocrats from a broad range of disciplines to meet and discuss state-of-the-art mathematical methods and high performance computing in science & technology solutions. This has brought new prospects for collaboration across disciplines and ideas that facilitate novel breakthroughs.

Applied Mathematics

Applied Mathematics Author Susmita Sarkar
ISBN-10 9788132225478
Release 2015-10-13
Pages 313
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The book is based on research presentations at the international conference, “Emerging Trends in Applied Mathematics: In the Memory of Sir Asutosh Mookerjee, S.N. Bose, M.N. Saha and N.R. Sen”, held at the Department of Applied Mathematics, University of Calcutta, during 12–14 February 2014. It focuses on various emerging and challenging topics in the field of applied mathematics and theoretical physics. The book will be a valuable resource for postgraduate students at higher levels and researchers in applied mathematics and theoretical physics. Researchers presented a wide variety of themes in applied mathematics and theoretical physics—such as emergent periodicity in a field of chaos; Ricci flow equation and Poincare conjecture; Bose–Einstein condensation; geometry of local scale invariance and turbulence; statistical mechanics of human resource allocation: mathematical modelling of job-matching in labour markets; contact problem in elasticity; the Saha equation; computational fluid dynamics with applications in aerospace problems; an introduction to data assimilation, stochastic analysis and bounds on noise for Holling type-II model, graph theoretical invariants of chemical and biological systems; strongly correlated phases and quantum phase transitions of ultra cold bosons; and the mathematical modelling of breast cancer treatment.

Applied and Numerical Partial Differential Equations

Applied and Numerical Partial Differential Equations Author W. Fitzgibbon
ISBN-10 9789048132393
Release 2010-01-08
Pages 248
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Standing at the intersection of mathematics and scientific computing, this collection of state-of-the-art papers in nonlinear PDEs examines their applications to subjects as diverse as dynamical systems, computational mechanics, and the mathematics of finance.

Nonlinear Effects in Fluids and Solids

Nonlinear Effects in Fluids and Solids Author Michael M. Carroll
ISBN-10 9781461303299
Release 2012-12-06
Pages 384
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This volume of scientific papers is dedicated with gratitude and esteem to Ronald Rivlin and is offered as a token of appreciation by former students, col laborators, and friends. Ronald Rivlin's name is synonymous with modem developments in contin uum mechanics. His outstanding pioneering theoretical and experimental re ·search in finite elasticity is a landmark. From his work there has followed a spate of developments in which he played the leading role-the theory of fiber-rein forced materials, the developments of the theory of constitutive equations, the theory of materials with memory, the theory of the fracture of elastomers, the theory of viscoelastic fluids and solids, the development of nonlinear crystal physics, the theory of small deformations superimposed on large, and the effect of large initial strain on wave propagation. It is in Rivlin's work that universal relations were first recognized. Here also are to be found lucid explanations of physical phenomena such as the Poynting effect for elastic rods in torsion. Addi tionally, he and his co-workers predicted the presence of secondary flows for viscoelastic fluids in straight pipes of noncircular cross section under a uniform pressure head. While some others may have displayed a cavalier lack of concern for physical reality and an intoxication with mathematical idiom, Rivlin has al ways been concerned with genuine mathematical and physical content. All of his papers contain interesting and illuminating material-and may be read with profit by anyone interested in continuum mechanics.

Numerical Mathematics and Advanced Applications 2009

Numerical Mathematics and Advanced Applications 2009 Author Gunilla Kreiss
ISBN-10 3642117953
Release 2010-10-19
Pages 939
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Stress Waves in Solids

Stress Waves in Solids Author Herbert Kolsky
ISBN-10 0486495345
Release 2003
Pages 212
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Readable survey of theoretical core of propagation of waves in solids offers a concise account of classical theory, considers its applications to nonelastic solids, and summarizes experimental work. 1963 edition.

Elliptic Operators and Compact Groups

Elliptic Operators and Compact Groups Author M.F. Atiyah
ISBN-10 9783540378112
Release 2006-08-01
Pages 100
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Elliptic Operators and Compact Groups has been writing in one form or another for most of life. You can find so many inspiration from Elliptic Operators and Compact Groups also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Elliptic Operators and Compact Groups book for free.

Algorithms for Approximation

Algorithms for Approximation Author Armin Iske
ISBN-10 9783540465515
Release 2006-12-13
Pages 389
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Approximation methods are vital in many challenging applications of computational science and engineering. This is a collection of papers from world experts in a broad variety of relevant applications, including pattern recognition, machine learning, multiscale modelling of fluid flow, metrology, geometric modelling, tomography, signal and image processing. It documents recent theoretical developments which have lead to new trends in approximation, it gives important computational aspects and multidisciplinary applications, thus making it a perfect fit for graduate students and researchers in science and engineering who wish to understand and develop numerical algorithms for the solution of their specific problems. An important feature of the book is that it brings together modern methods from statistics, mathematical modelling and numerical simulation for the solution of relevant problems, with a wide range of inherent scales. Contributions of industrial mathematicians, including representatives from Microsoft and Schlumberger, foster the transfer of the latest approximation methods to real-world applications.

Mathematical Tools for Physicists

Mathematical Tools for Physicists Author George L. Trigg
ISBN-10 9783527607259
Release 2006-08-21
Pages 686
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Mathematical Tools for Physicists is a unique collection of 18 carefully reviewed articles, each one written by a renowned expert working in the relevant field. The result is beneficial to both advanced students as well as scientists at work; the former will appreciate it as a comprehensive introduction, while the latter will use it as a ready reference. The contributions range from fundamental methods right up to the latest applications, including: - Algebraic/ analytic / geometric methods - Symmetries and conservation laws - Mathematical modeling - Quantum computation The emphasis throughout is ensuring quick access to the information sought, and each article features: - an abstract - a detailed table of contents - continuous cross-referencing - references to the most relevant publications in the field, and - suggestions for further reading, both introductory as well as highly specialized. In addition, a comprehensive index provides easy access to the vast number of key words extending beyond the range of the headlines.

Iris Runge

Iris Runge Author Renate Tobies
ISBN-10 9783034802512
Release 2012-01-05
Pages 442
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This book concerns the origins of mathematical problem solving at the internationally active Osram and Telefunken Corporations during the golden years of broadcasting and electron tube research. The woman scientist Iris Runge, who received an interdisciplinary education at the University of Göttingen, was long employed as the sole mathematical authority at these companies in Berlin. It will be shown how mathematical connections were made between statistics and quality control, and between physical-chemical models and the actual problems of mass production. The organization of industrial laboratories, the relationship between theoretical and experimental work, and the role of mathematicians in these settings will also be explained. By investigating the social, economic, and political conditions that unfolded from the time of the German Empire until the end of the Second World War, the book hopes to build a bridge between specialized fields – mathematics and engineering – and the general culture of a particular era. It hopes, furthermore, to build a bridge between the history of science and industry, on the one hand, and the fields of Gender and Women’s Studies on the other. Finally, by examining the life and work of numerous industrial researchers, insight will be offered into the conditions that enabled a woman to achieve a prominent professional position during a time when women were typically excluded from the scientific workforce.

Mechanics of Poroelastic Media

Mechanics of Poroelastic Media Author A.P.S. Selvadurai
ISBN-10 0792333292
Release 1996-01-31
Pages 398
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Mechanics of Poroelastic Media has been writing in one form or another for most of life. You can find so many inspiration from Mechanics of Poroelastic Media also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Mechanics of Poroelastic Media book for free.


ISBN-10 9781105424045
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Production Factor Mathematics

Production Factor Mathematics Author Martin Grötschel
ISBN-10 364211248X
Release 2010-08-05
Pages 402
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Mathematics as a production factor or driving force for innovation? Those, who want to know and understand why mathematics is deeply involved in the design of products, the layout of production processes and supply chains will find this book an indispensable and rich source. Describing the interplay between mathematical and engineering sciences the book focusses on questions like How can mathematics improve to the improvement of technological processes and products? What is happening already? Where are the deficits? What can we expect for the future? 19 articles written by mixed teams of authors of engineering, industry and mathematics offer a fascinating insight of the interaction between mathematics and engineering.