Application Of Group Theory To Symmetric Structures
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Application Of Group Theory To Symmetric Structures
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Author : Ichiro Ario
language : en
Publisher: CRC Press
Release Date : 2024-04-11
Application Of Group Theory To Symmetric Structures written by Ichiro Ario and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-04-11 with Technology & Engineering categories.
Ario and Zawidzki show readers how to handle symmetric structures in engineering using group-theoretic bifurcation theory as a mathematical tool for the finite element analysis of symmetric structures. They guide the reader from the initial mathematical concepts through to application examples. Readers will gain a solid theoretical grounding in group theory and strong working knowledge of the use of computational frameworks for structural analysis using mathematical representations of symmetry and physical symmetry. First, the authors elaborate an outline of symmetric structures in engineering and then describe the representation of symmetry and group theory. They then discuss block diagonalization theory and finite element analysis models. This provides readers with the base knowledge needed for Chapter 6, which is based on numerical analysis examples of invariant, static FEM model systems and dynamic model systems of the dihedral group. This unique approach is a vital method that will enable readers to reduce the time and computation needed for accurate analysis so that they can better design such structures. The focus on finite element methods and practical examples and case studies throughout provides a strong practical foundation for anyone studying or working in this field. The book is a valuable resource for undergraduate and postgraduate students on various courses such as civil and mechanical engineering, architecture, structural engineering, applied mathematics, and physics. Additionally, it describes vital practical solutions for structural engineers, structural system manufacturers, fabricators of prefabricated elements, and developers of computational mechanics and so on.
Group Theory
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Author : Mildred S. Dresselhaus
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-12-13
Group Theory written by Mildred S. Dresselhaus 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 2007-12-13 with Science categories.
This concise, class-tested book was refined over the authors’ 30 years as instructors at MIT and the University Federal of Minas Gerais (UFMG) in Brazil. The approach centers on the conviction that teaching group theory along with applications helps students to learn, understand and use it for their own needs. Thus, the theoretical background is confined to introductory chapters. Subsequent chapters develop new theory alongside applications so that students can retain new concepts, build on concepts already learned, and see interrelations between topics. Essential problem sets between chapters aid retention of new material and consolidate material learned in previous chapters.
Visual Group Theory
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Author : Nathan Carter
language : en
Publisher: American Mathematical Soc.
Release Date : 2021-06-08
Visual Group Theory written by Nathan Carter and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-06-08 with Education categories.
Recipient of the Mathematical Association of America's Beckenbach Book Prize in 2012! Group theory is the branch of mathematics that studies symmetry, found in crystals, art, architecture, music and many other contexts, but its beauty is lost on students when it is taught in a technical style that is difficult to understand. Visual Group Theory assumes only a high school mathematics background and covers a typical undergraduate course in group theory from a thoroughly visual perspective. The more than 300 illustrations in Visual Group Theory bring groups, subgroups, homomorphisms, products, and quotients into clear view. Every topic and theorem is accompanied with a visual demonstration of its meaning and import, from the basics of groups and subgroups through advanced structural concepts such as semidirect products and Sylow theory.
Optimal Analysis Of Structures By Concepts Of Symmetry And Regularity
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Author : Ali Kaveh
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-05-16
Optimal Analysis Of Structures By Concepts Of Symmetry And Regularity written by Ali Kaveh 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 2013-05-16 with Science categories.
Optimal analysis is defined as an analysis that creates and uses sparse, well-structured and well-conditioned matrices. The focus is on efficient methods for eigensolution of matrices involved in static, dynamic and stability analyses of symmetric and regular structures, or those general structures containing such components. Powerful tools are also developed for configuration processing, which is an important issue in the analysis and design of space structures and finite element models. Different mathematical concepts are combined to make the optimal analysis of structures feasible. Canonical forms from matrix algebra, product graphs from graph theory and symmetry groups from group theory are some of the concepts involved in the variety of efficient methods and algorithms presented. The algorithms elucidated in this book enable analysts to handle large-scale structural systems by lowering their computational cost, thus fulfilling the requirement for faster analysis and design of future complex systems. The value of the presented methods becomes all the more evident in cases where the analysis needs to be repeated hundreds or even thousands of times, as for the optimal design of structures by different metaheuristic algorithms. The book is of interest to anyone engaged in computer-aided analysis and design and software developers in this field. Though the methods are demonstrated mainly through skeletal structures, continuum models have also been added to show the generality of the methods. The concepts presented are not only applicable to different types of structures but can also be used for the analysis of other systems such as hydraulic and electrical networks.
Applications Of Finite Groups
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Author : J. S. Lomont
language : en
Publisher: Academic Press
Release Date : 2014-05-12
Applications Of Finite Groups written by J. S. Lomont and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-12 with Mathematics categories.
Applications of Finite Groups focuses on the applications of finite groups to problems of physics, including representation theory, crystals, wave equations, and nuclear and molecular structures. The book first elaborates on matrices, groups, and representations. Topics include abstract properties, applications, matrix groups, key theorem of representation theory, properties of character tables, simply reducible groups, tensors and invariants, and representations generated by functions. The text then examines applications and subgroups and representations, as well as subduced and induced representations, fermion annihilation and creation operators, crystallographic point groups, proportionality tensors in crystals, and nonrelativistic wave equations. The publication takes a look at space group representations and energy bands, symmetric groups, and applications. Topics include molecular and nuclear structures, multiplet splitting in crystalline electric fields, construction of irreducible representations of the symmetric groups, and reality of representations. The manuscript is a dependable source of data for physicists and researchers interested in the applications of finite groups.
Chemical Applications Of Symmetry And Group Theory
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Author : Rakshit Ameta
language : en
Publisher: CRC Press
Release Date : 2016-11-03
Chemical Applications Of Symmetry And Group Theory written by Rakshit Ameta and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-11-03 with Science categories.
As the structure and behavior of molecules and crystals depend on their different symmetries, group theory becomes an essential tool in many important areas of chemistry. It is a quite powerful theoretical tool to predict many basic as well as some characteristic properties of molecules. Whereas quantum mechanics provide solutions of some chemical problems on the basis of complicated mathematics, group theory puts forward these solutions in a very simplified and fascinating manner. Group theory has been successfully applied to many chemical problems. Students and teachers of chemical sciences have an invisible fear from this subject due to the difficulty with the mathematical jugglery. An active sixth dimension is required to understand the concept as well as to apply it to solve the problems of chemistry. This book avoids mathematical complications and presents group theory so that it is accessible to students as well as faculty and researchers. Chemical Applications of Symmetry and Group Theory discusses different applications to chemical problems with suitable examples. The book develops the concept of symmetry and group theory, representation of group, its applications to I.R. and Raman spectroscopy, U.V spectroscopy, bonding theories like molecular orbital theory, ligand field theory, hybridization, and more. Figures are included so that reader can visualize the symmetry, symmetry elements, and operations.
Imperfect Bifurcation In Structures And Materials
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Author : Kiyohiro Ikeda
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Imperfect Bifurcation In Structures And Materials written by Kiyohiro Ikeda 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 2013-03-09 with Science categories.
Many physical systems lose or gain stability and pattern through bifurca tion behavior. Extensive research of this behavior is carried out in many fields of science and engineering. The study of dynamic bifurcation be havior, for example, has made clear the mechanism of dynamic instability and chaos. The group-theoretic bifurcation theory is an established means to deal with the formation and selection of patterns in association with symmetry-breaking bifurcation. Since all physical systems are "imperfect," in that they inevitably involve some initial imperfections, the study of im perfect bifurcation (bifurcation of imperfect systems) has drawn a keen mathematical interest to yield a series of important results, such as the universal unfolding. In structural mechanics, bifurcation behavior has been studied to model the buckling and failure of structural systems. The sharp reduction of the strength of structural systems by initial imperfections is formulated as im perfection sensitivity laws. A series of statistical studies has been conducted to make clear the dependence of the strength of structures on the statis tical variation of initial imperfections. A difficulty in these studies arises from the presence of a large number of initial imperfections. At this state, most of these studies are carried out based on the Monte Carlo simulation for a number of initial imperfections, or, on an imperfection sensitivity law against a single initial imperfection.
Steel And Composite Structures
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Author : Y. C. Wang
language : en
Publisher: Routledge
Release Date : 2018-05-08
Steel And Composite Structures written by Y. C. Wang and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-05-08 with Technology & Engineering categories.
Over 150 papers representing the most recent international research findings on steel and composite structures. Including steel constructions; buckling and stability; codes; composite; control; fatigue and fracture; fire; impact; joints; maintenance; plates and shells; retrofitting; seismic; space structures; steel; structural analysis; structural components and assemblies; thin-walled structures; vibrations, and wind. A special session is dedicated on codification. A valuable source of information to researchers and practitioners in the field of steel and composite structures.
Exploiting Symmetry In Applied And Numerical Analysis
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Author : Eugene L. Allgower
language : en
Publisher: American Mathematical Soc.
Release Date :
Exploiting Symmetry In Applied And Numerical Analysis written by Eugene L. Allgower and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on with Mathematics categories.
Symmetry plays an important role in theoretical physics, applied analysis, classical differential equations, and bifurcation theory. Although numerical analysis has incorporated aspects of symmetry on an ad hoc basis, there is now a growing collection of numerical analysts who are currently attempting to use symmetry groups and representation theory as fundamental tools in their work. This book contains the proceedings of an AMS-SIAM Summer Seminar in Applied Mathematics, held in 1992 at Colorado State University. The seminar, which drew about 100 scientists from around the world, was intended to stimulate the systematic incorporation of symmetry and group theoretical concepts into numerical methods. The papers in this volume have been refereed and will not be published elsewhere.
Group Theory And Symmetry In Chemistry
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Author : Gurdeep Raj; Ajay Bhagi; Vinod Jain
language : en
Publisher: Krishna Prakashan Media
Release Date :
Group Theory And Symmetry In Chemistry written by Gurdeep Raj; Ajay Bhagi; Vinod Jain and has been published by Krishna Prakashan Media this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.