The Fiber Bundle Model
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The Fiber Bundle Model
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Author : Alex Hansen
language : en
Publisher: John Wiley & Sons
Release Date : 2015-11-02
The Fiber Bundle Model written by Alex Hansen and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-11-02 with Science categories.
Gathering research from physics, mechanical engineering, and statistics in a single resource for the first time, this text presents the background to the model, its theoretical basis, and applications ranging from materials science to earth science. The authors start by explaining why disorder is important for fracture and then go on to introduce the fiber bundle model, backed by various different applications. Appendices present the necessary mathematical, computational and statistical background required. The structure of the book allows the reader to skip some material that is too specialized, making this topic accessible to the engineering, mechanics and materials science communities, in addition to providing further reading for graduate students in statistical physics.
The Fiber Bundle Model
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Author : Alex Hansen
language : en
Publisher:
Release Date : 2015
The Fiber Bundle Model written by Alex Hansen and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with MATHEMATICS categories.
Fibre Bundles
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Author : D. Husemöller
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Fibre Bundles written by D. Husemöller 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 2013-06-29 with Mathematics categories.
The notion of a fibre bundle first arose out of questions posed in the 1930s on the topology and geometry of manifolds. By the year 1950 the defini tion of fibre bundle had been clearly formulated, the homotopy classifica tion of fibre bundles achieved, and the theory of characteristic classes of fibre bundles developed by several mathematicians, Chern, Pontrjagin, Stiefel, and Whitney. Steenrod's book, which appeared in 1950, gave a coherent treatment of the subject up to that time. About 1955 Milnor gave a construction of a universal fibre bundle for any topological group. This construction is also included in Part I along with an elementary proof that the bundle is universal. During the five years from 1950 to 1955, Hirzebruch clarified the notion of characteristic class and used it to prove a general Riemann-Roch theorem for algebraic varieties. This was published in his Ergebnisse Monograph. A systematic development of characteristic classes and their applications to manifolds is given in Part III and is based on the approach of Hirze bruch as modified by Grothendieck.
The Fiber Bundle
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Author : Ferenc Kun
language : en
Publisher: Frontiers Media SA
Release Date : 2022-01-10
The Fiber Bundle written by Ferenc Kun and has been published by Frontiers Media SA this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-01-10 with Science categories.
Fiber Bundles And Homotopy
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Author : Dai Tamaki
language : en
Publisher:
Release Date : 2021
Fiber Bundles And Homotopy written by Dai Tamaki and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021 with Fiber bundles (Mathematics) categories.
This book is an introduction to fiber bundles and fibrations. But the ultimate goal is to make the reader feel comfortable with basic ideas in homotopy theory. The author found that the classification of principal fiber bundles is an ideal motivation for this purpose. The notion of homotopy appears naturally in the classification. Basic tools in homotopy theory such as homotopy groups and their long exact sequence need to be introduced. Furthermore, the notion of fibrations, which is one of three important classes of maps in homotopy theory, can be obtained by extracting the most essential properties of fiber bundles. The book begins with elementary examples and then gradually introduces abstract definitions when necessary. The reader is assumed to be familiar with point-set topology, but it is the only requirement for this book.
Topics In The Homology Theory Of Fibre Bundles
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Author : Armand Borel
language : en
Publisher: Springer
Release Date : 2006-11-14
Topics In The Homology Theory Of Fibre Bundles written by Armand Borel and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
The Topology Of Fibre Bundles
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Author : Norman Earl Steenrod
language : en
Publisher:
Release Date : 1951
The Topology Of Fibre Bundles written by Norman Earl Steenrod and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1951 with Mathematics categories.
Fibre bundles, now an integral part of differential geometry, are also of great importance in modern physics--such as in gauge theory. This book, a succinct introduction to the subject by renown mathematician Norman Steenrod, was the first to present the subject systematically. It begins with a general introduction to bundles, including such topics as differentiable manifolds and covering spaces. The author then provides brief surveys of advanced topics, such as homotopy theory and cohomology theory, before using them to study further properties of fibre bundles. The result is a classic and timeless work of great utility that will appeal to serious mathematicians and theoretical physicists alike.
Fiber Bundles
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Author : James U. Gleaton
language : en
Publisher: Springer Nature
Release Date : 2023-03-15
Fiber Bundles written by James U. Gleaton and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-03-15 with Mathematics categories.
This book presents a critical overview of statistical fiber bundle models, including existing models and potential new ones. The authors focus on both the physical and statistical aspects of a specific load-sharing example: the breakdown for circuits of capacitors and related dielectrics. In addition, they investigate some areas of open research. This book is designed for graduate students and researchers in statistics, materials science, engineering, physics, and related fields, as well as practitioners and technicians in materials science and mechanical engineering.
Slope Stability And Erosion Control Ecotechnological Solutions
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Author : Joanne E. Norris
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-02-29
Slope Stability And Erosion Control Ecotechnological Solutions written by Joanne E. Norris 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 2008-02-29 with Technology & Engineering categories.
This chapter describes the processes involved in the transport of material over hillslopes. Hillslopes provide the gradients enabling material to be transported from the slopes themselves towards the valley bottoms, directly by gravity alone, or by water flowing down over the surface. Gravity has the potential to transfer material downslope if the material resistance to counteact it is insufficient. Similarly, water and wind flowing along the surface exert a drag on soil particles and have the potential to entrain material. After the gradient has fallen below a critical threshold to keep the material in tra- port, deposition occurs. Conventionally, slope processes in which gravity alone is the dominant transporting agent are called mass movements (Brunsden 1984). Processes in which other agents dominate are called erosion, e.g. wind or water erosion. Flowing water is an important transporting agent on which the emphasis is placed here. Although mass wasting is a natural process its incidence and impact may be exacerbated by human activities (Crozier 1986; Morgan 2005). A situation may ultimately arise in which human interests become unsafe or unsustainable. This impact is not only directly felt in the areas where material is removed or deposited and indirectly mass wasting may have an effect on soil and water quality in areas located further downstream. In the following sections a brief overview is given of the mechanisms, morphology, causes and consequences of mass movements and erosion.
Computational Mechanics 95
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Author : S.N. Atluri
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-11
Computational Mechanics 95 written by S.N. Atluri 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 2013-11-11 with Technology & Engineering categories.
AI!, in the earlier conferences (Tokyo, 1986; Atlanta, 1988, Melbourne, 1991; and Hong Kong, 1992) the response to the call for presentations at ICES-95 in Hawaii has been overwhelming. A very careful screening of the extended abstracts resulted in about 500 paper being accepted for presentation. Out of these, written versions of about 480 papers reached the conference secretariat in Atlanta in time for inclusion in these proceedings. The topics covered at ICES-95 range over the broadest spectrum of computational engineering science. The editors thank the international scientific committee, for their advice and encouragement in making ICES-95 a successful scientific event. Special thanks are expressed to the International Association for Boundary Elements Methods for hosting IABEM-95 in conjunction with ICES-95. The editors here express their deepest gratitude to Ms. Stacy Morgan for her careful handling of a myriad of details of ICES-95, often times under severe time constraints. The editors hope that the readers of this proceedings will find a kaleidoscopic view of computational engineering in the year 1995, as practiced in various parts of the world. Satya N. Atluri Atlanta, Georgia, USA Genki Yagawa Tokyo,Japan Thomas A. Cruse Nashville, TN, USA Organizing Committee Professor Genki Yagawa, University of Tokyo, Japan, Chair Professor Satya Atluri, Georgia Institute of Technology, U.S.A.