The Fiber Bundle Model
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| Author | : Alex Hansen |
| Publisher | : John Wiley & Sons |
| Total Pages | : 254 |
| Release | : 2015-11-02 |
| Genre | : Science |
| ISBN | : 352741214X |
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.
| Author | : D. Husemöller |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 333 |
| Release | : 2013-06-29 |
| Genre | : Mathematics |
| ISBN | : 1475740085 |
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.
| Author | : Ferenc Kun |
| Publisher | : Frontiers Media SA |
| Total Pages | : 150 |
| Release | : 2022-01-10 |
| Genre | : Science |
| ISBN | : 2889740110 |
| Author | : Armand Borel |
| Publisher | : Springer |
| Total Pages | : 100 |
| Release | : 2006-11-14 |
| Genre | : Mathematics |
| ISBN | : 3540349758 |
| Author | : W. Drechsler |
| Publisher | : Springer |
| Total Pages | : 251 |
| Release | : 2014-03-12 |
| Genre | : Science |
| ISBN | : 9783662214657 |
| Author | : Dai Tamaki |
| Publisher | : |
| Total Pages | : 0 |
| Release | : 2021 |
| Genre | : Fiber bundles (Mathematics) |
| ISBN | : 9789811237997 |
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.
| Author | : Chris J. Isham |
| Publisher | : Allied Publishers |
| Total Pages | : 308 |
| Release | : 2002 |
| Genre | : Geometry, Differential |
| ISBN | : 9788177643169 |
| Author | : Steinar Johannesen |
| Publisher | : CRC Press |
| Total Pages | : 595 |
| Release | : 2016-12-08 |
| Genre | : Mathematics |
| ISBN | : 1315342626 |
This book provides a systematic presentation of the mathematical foundation of modern physics with applications particularly within classical mechanics and the theory of relativity. Written to be self-contained, Smooth Manifolds and Fibre Bundles with Applications to Theoretical Physics provides complete and rigorous proofs of all the results presented within. Among the themes illustrated in the book are differentiable manifolds, differential forms, fiber bundles and differential geometry with non-trivial applications especially within the general theory of relativity. The emphasis is upon a systematic and logical construction of the mathematical foundations. It can be used as a textbook for a pure mathematics course in differential geometry, assuming the reader has a good understanding of basic analysis, linear algebra and point set topology. The book will also appeal to students of theoretical physics interested in the mathematical foundation of the theories.
| Author | : James U. Gleaton |
| Publisher | : Springer Nature |
| Total Pages | : 164 |
| Release | : 2023-03-15 |
| Genre | : Mathematics |
| ISBN | : 3031147979 |
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.
| Author | : John Willard Milnor |
| Publisher | : Princeton University Press |
| Total Pages | : 342 |
| Release | : 1974 |
| Genre | : Mathematics |
| ISBN | : 9780691081229 |
The theory of characteristic classes provides a meeting ground for the various disciplines of differential topology, differential and algebraic geometry, cohomology, and fiber bundle theory. As such, it is a fundamental and an essential tool in the study of differentiable manifolds. In this volume, the authors provide a thorough introduction to characteristic classes, with detailed studies of Stiefel-Whitney classes, Chern classes, Pontrjagin classes, and the Euler class. Three appendices cover the basics of cohomology theory and the differential forms approach to characteristic classes, and provide an account of Bernoulli numbers. Based on lecture notes of John Milnor, which first appeared at Princeton University in 1957 and have been widely studied by graduate students of topology ever since, this published version has been completely revised and corrected.
