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Material Geometry Groupoids In Continuum Mechanics
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Book Synopsis Material Geometry: Groupoids In Continuum Mechanics by : Manuel De Leon
Download or read book Material Geometry: Groupoids In Continuum Mechanics written by Manuel De Leon and published by World Scientific. This book was released on 2021-04-23 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is the first in which the theory of groupoids and algebroids is applied to the study of the properties of uniformity and homogeneity of continuous media. It is a further step in the application of differential geometry to the mechanics of continua, initiated years ago with the introduction of the theory of G-structures, in which the group G denotes the group of material symmetries, to study smoothly uniform materials.The new approach presented in this book goes much further by being much more general. It is not a generalization per se, but rather a natural way of considering the algebraic-geometric structure induced by the so-called material isomorphisms. This approach has allowed us to encompass non-uniform materials and discover new properties of uniformity and homogeneity that certain material bodies can possess, thus opening a new area in the discipline.
Book Synopsis Geometric Continuum Mechanics by : Reuven Segev
Download or read book Geometric Continuum Mechanics written by Reuven Segev and published by Springer Nature. This book was released on 2020-05-13 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: This contributed volume explores the applications of various topics in modern differential geometry to the foundations of continuum mechanics. In particular, the contributors use notions from areas such as global analysis, algebraic topology, and geometric measure theory. Chapter authors are experts in their respective areas, and provide important insights from the most recent research. Organized into two parts, the book first covers kinematics, forces, and stress theory, and then addresses defects, uniformity, and homogeneity. Specific topics covered include: Global stress and hyper-stress theories Applications of de Rham currents to singular dislocations Manifolds of mappings for continuum mechanics Kinematics of defects in solid crystals Geometric Continuum Mechanics will appeal to graduate students and researchers in the fields of mechanics, physics, and engineering who seek a more rigorous mathematical understanding of the area. Mathematicians interested in applications of analysis and geometry will also find the topics covered here of interest.
Book Synopsis The Geometrical Language of Continuum Mechanics by : Marcelo Epstein
Download or read book The Geometrical Language of Continuum Mechanics written by Marcelo Epstein and published by Cambridge University Press. This book was released on 2010-07-26 with total page 325 pages. Available in PDF, EPUB and Kindle. Book excerpt: Epstein presents the fundamental concepts of modern differential geometry within the framework of continuum mechanics. Divided into three parts of roughly equal length, the book opens with a motivational chapter to impress upon the reader that differential geometry is indeed the natural language of continuum mechanics or, better still, that the latter is a prime example of the application and materialisation of the former. In the second part, the fundamental notions of differential geometry are presented with rigor using a writing style that is as informal as possible. Differentiable manifolds, tangent bundles, exterior derivatives, Lie derivatives, and Lie groups are illustrated in terms of their mechanical interpretations. The third part includes the theory of fiber bundles, G-structures, and groupoids, which are applicable to bodies with internal structure and to the description of material inhomogeneity. The abstract notions of differential geometry are thus illuminated by practical and intuitively meaningful engineering applications.
Book Synopsis Material Inhomogeneities and their Evolution by : Marcelo Epstein
Download or read book Material Inhomogeneities and their Evolution written by Marcelo Epstein and published by Springer Science & Business Media. This book was released on 2007-09-05 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: With its origins in the theories of continuous distributions of dislocations and ofmetalplasticity,inhomogeneitytheoryisarichandvibrant?eldofresearch. The recognition of the important role played by con?gurational or material forces in phenomena such as growth and remodelling is perhaps its greatest present-day impetus. While some excellent comprehensive works approa- ing the subject from di?erent angles have been published, the objective of this monograph is to present a point of view that emphasizes the di?erenti- geometric aspects of inhomogeneity theory. In so doing, we follow the general lines of thought that we have propounded in many publications and presen- tions over the last two decades. Although based on these sources, this book is a stand-alone entity and contains some new results and perspectives. At the same time, it does not intend to present either a historical account of the - velopment of the subject or a comprehensive picture of the various schools of thought that can be encountered by perusing scholarly journals and attending specialized symposia. The book is divided into three parts, the ?rst of which is entirely devoted to the formulation of the theory in the absence of evolution. In other words, time is conspicuously absent from Part I. It opens with the geometric ch- acterization of material inhomogeneity within the context of simple bodies in Chapter 1, followed by extensions to second-grade and Cosserat media in Chapters 2 and 3.
Book Synopsis Differential Geometry by : Marcelo Epstein
Download or read book Differential Geometry written by Marcelo Epstein and published by Springer. This book was released on 2014-07-02 with total page 147 pages. Available in PDF, EPUB and Kindle. Book excerpt: Differential Geometry offers a concise introduction to some basic notions of modern differential geometry and their applications to solid mechanics and physics. Concepts such as manifolds, groups, fibre bundles and groupoids are first introduced within a purely topological framework. They are shown to be relevant to the description of space-time, configuration spaces of mechanical systems, symmetries in general, microstructure and local and distant symmetries of the constitutive response of continuous media. Once these ideas have been grasped at the topological level, the differential structure needed for the description of physical fields is introduced in terms of differentiable manifolds and principal frame bundles. These mathematical concepts are then illustrated with examples from continuum kinematics, Lagrangian and Hamiltonian mechanics, Cauchy fluxes and dislocation theory. This book will be useful for researchers and graduate students in science and engineering.
Book Synopsis Topology and Groupoids by : Ronald Brown
Download or read book Topology and Groupoids written by Ronald Brown and published by Booksurge Llc. This book was released on 2006 with total page 512 pages. Available in PDF, EPUB and Kindle. Book excerpt: Annotation. The book is intended as a text for a two-semester course in topology and algebraic topology at the advanced undergraduate orbeginning graduate level. There are over 500 exercises, 114 figures, numerous diagrams. The general direction of the book is towardhomotopy theory with a geometric point of view. This book would providea more than adequate background for a standard algebraic topology coursethat begins with homology theory. For more information seewww.bangor.ac.uk/r.brown/topgpds.htmlThis version dated April 19, 2006, has a number of corrections made.
Book Synopsis Geometric Models for Noncommutative Algebras by : Ana Cannas da Silva
Download or read book Geometric Models for Noncommutative Algebras written by Ana Cannas da Silva and published by American Mathematical Soc.. This book was released on 1999 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: The volume is based on a course, ``Geometric Models for Noncommutative Algebras'' taught by Professor Weinstein at Berkeley. Noncommutative geometry is the study of noncommutative algebras as if they were algebras of functions on spaces, for example, the commutative algebras associated to affine algebraic varieties, differentiable manifolds, topological spaces, and measure spaces. In this work, the authors discuss several types of geometric objects (in the usual sense of sets with structure) that are closely related to noncommutative algebras. Central to the discussion are symplectic and Poisson manifolds, which arise when noncommutative algebras are obtained by deforming commutative algebras. The authors also give a detailed study of groupoids (whose role in noncommutative geometry has been stressed by Connes) as well as of Lie algebroids, the infinitesimal approximations to differentiable groupoids. Featured are many interesting examples, applications, and exercises. The book starts with basic definitions and builds to (still) open questions. It is suitable for use as a graduate text. An extensive bibliography and index are included.
Book Synopsis The Directory of Graduate Studies by :
Download or read book The Directory of Graduate Studies written by and published by . This book was released on 1999 with total page 1876 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Hamilton’s Principle in Continuum Mechanics by : Anthony Bedford
Download or read book Hamilton’s Principle in Continuum Mechanics written by Anthony Bedford and published by Springer Nature. This book was released on 2021-12-14 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt: This revised, updated edition provides a comprehensive and rigorous description of the application of Hamilton’s principle to continuous media. To introduce terminology and initial concepts, it begins with what is called the first problem of the calculus of variations. For both historical and pedagogical reasons, it first discusses the application of the principle to systems of particles, including conservative and non-conservative systems and systems with constraints. The foundations of mechanics of continua are introduced in the context of inner product spaces. With this basis, the application of Hamilton’s principle to the classical theories of fluid and solid mechanics are covered. Then recent developments are described, including materials with microstructure, mixtures, and continua with singular surfaces.
Book Synopsis Introduction to Foliations and Lie Groupoids by : Ieke Moerdijk
Download or read book Introduction to Foliations and Lie Groupoids written by Ieke Moerdijk and published by . This book was released on 2003 with total page 173 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives a quick introduction to the theory of foliations and Lie groupoids. It is based on the authors' extensive teaching experience and contains numerous examples and exercises making it ideal either for independent study or as the basis of a graduate course.
Book Synopsis Geometry, Mechanics, and Control in Action for the Falling Cat by : Toshihiro Iwai
Download or read book Geometry, Mechanics, and Control in Action for the Falling Cat written by Toshihiro Iwai and published by Springer Nature. This book was released on 2021-04-23 with total page 193 pages. Available in PDF, EPUB and Kindle. Book excerpt: The falling cat is an interesting theme to pursue, in which geometry, mechanics, and control are in action together. As is well known, cats can almost always land on their feet when tossed into the air in an upside-down attitude. If cats are not given a non-vanishing angular momentum at an initial instant, they cannot rotate during their motion, and the motion they can make in the air is vibration only. However, cats accomplish a half turn without rotation when landing on their feet. In order to solve this apparent mystery, one needs to thoroughly understand rotations and vibrations. The connection theory in differential geometry can provide rigorous definitions of rotation and vibration for many-body systems. Deformable bodies of cats are not easy to treat mechanically. A feasible way to approach the question of the falling cat is to start with many-body systems and then proceed to rigid bodies and, further, to jointed rigid bodies, which can approximate the body of a cat. In this book, the connection theory is applied first to a many-body system to show that vibrational motions of the many-body system can result in rotations without performing rotational motions and then to the cat model consisting of jointed rigid bodies. On the basis of this geometric setting, mechanics of many-body systems and of jointed rigid bodies must be set up. In order to take into account the fact that cats can deform their bodies, three torque inputs which may give a twist to the cat model are applied as control inputs under the condition of the vanishing angular momentum. Then, a control is designed according to the port-controlled Hamiltonian method for the model cat to perform a half turn and to halt the motion upon landing. The book also gives a brief review of control systems through simple examples to explain the role of control inputs.
Download or read book Industrial Research in Britain written by and published by . This book was released on 1976 with total page 886 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Current Research in Britain written by and published by . This book was released on 1991 with total page 1386 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Synthetic Geometry of Manifolds by : Anders Kock
Download or read book Synthetic Geometry of Manifolds written by Anders Kock and published by Cambridge University Press. This book was released on 2010 with total page 317 pages. Available in PDF, EPUB and Kindle. Book excerpt: This elegant book is sure to become the standard introduction to synthetic differential geometry. It deals with some classical spaces in differential geometry, namely 'prolongation spaces' or neighborhoods of the diagonal. These spaces enable a natural description of some of the basic constructions in local differential geometry and, in fact, form an inviting gateway to differential geometry, and also to some differential-geometric notions that exist in algebraic geometry. The presentation conveys the real strength of this approach to differential geometry. Concepts are clarified, proofs are streamlined, and the focus on infinitesimal spaces motivates the discussion well. Some of the specific differential-geometric theories dealt with are connection theory (notably affine connections), geometric distributions, differential forms, jet bundles, differentiable groupoids, differential operators, Riemannian metrics, and harmonic maps. Ideal for graduate students and researchers wishing to familiarize themselves with the field.
Book Synopsis Directory of Published Proceedings by :
Download or read book Directory of Published Proceedings written by and published by . This book was released on 2002 with total page 68 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Lectures on Field Theory and Topology by : Daniel S. Freed
Download or read book Lectures on Field Theory and Topology written by Daniel S. Freed and published by American Mathematical Soc.. This book was released on 2019-08-23 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: These lectures recount an application of stable homotopy theory to a concrete problem in low energy physics: the classification of special phases of matter. While the joint work of the author and Michael Hopkins is a focal point, a general geometric frame of reference on quantum field theory is emphasized. Early lectures describe the geometric axiom systems introduced by Graeme Segal and Michael Atiyah in the late 1980s, as well as subsequent extensions. This material provides an entry point for mathematicians to delve into quantum field theory. Classification theorems in low dimensions are proved to illustrate the framework. The later lectures turn to more specialized topics in field theory, including the relationship between invertible field theories and stable homotopy theory, extended unitarity, anomalies, and relativistic free fermion systems. The accompanying mathematical explanations touch upon (higher) category theory, duals to the sphere spectrum, equivariant spectra, differential cohomology, and Dirac operators. The outcome of computations made using the Adams spectral sequence is presented and compared to results in the condensed matter literature obtained by very different means. The general perspectives and specific applications fuse into a compelling story at the interface of contemporary mathematics and theoretical physics.
Book Synopsis Manifolds and Differential Geometry by : Jeffrey Marc Lee
Download or read book Manifolds and Differential Geometry written by Jeffrey Marc Lee and published by American Mathematical Soc.. This book was released on 2009 with total page 690 pages. Available in PDF, EPUB and Kindle. Book excerpt: Differential geometry began as the study of curves and surfaces using the methods of calculus. This book offers a graduate-level introduction to the tools and structures of modern differential geometry. It includes the topics usually found in a course on differentiable manifolds, such as vector bundles, tensors, and de Rham cohomology.
