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Author: Patrick Rabier Publisher: Springer ISBN: Category : Mathematics Languages : en Pages : 168
Book Description
This monograph is a mathematical study of steady-state motions of a spinning hyperelastic incompressible, homogenous and isotropic cylinder. So far there was very little quantitative information on this subject and no mathematical analysis. The authors developed mathematical tools that are not standard in this kind of bifurcation problems. Qualitative results independent of the stress-strain relation are obtained that are consistent with physical experiments. These phenomena are shown to be related to mathematical bifurcation. The spectral analysis is accomplished by a new method that combines techniques of the modern theory of partial differential equations and abstract functional analysis with Fourier decomposition and sharper results on Bessel functions. These techniques represent in their own right a contribution that will find application not only in the study of rotating bodies, but in other physical situations that can be characterized by non-compact bifurcation.
Author: Patrick Rabier Publisher: Springer ISBN: Category : Mathematics Languages : en Pages : 168
Book Description
This monograph is a mathematical study of steady-state motions of a spinning hyperelastic incompressible, homogenous and isotropic cylinder. So far there was very little quantitative information on this subject and no mathematical analysis. The authors developed mathematical tools that are not standard in this kind of bifurcation problems. Qualitative results independent of the stress-strain relation are obtained that are consistent with physical experiments. These phenomena are shown to be related to mathematical bifurcation. The spectral analysis is accomplished by a new method that combines techniques of the modern theory of partial differential equations and abstract functional analysis with Fourier decomposition and sharper results on Bessel functions. These techniques represent in their own right a contribution that will find application not only in the study of rotating bodies, but in other physical situations that can be characterized by non-compact bifurcation.
Author: G. Iooss Publisher: Springer Science & Business Media ISBN: 1468493361 Category : Science Languages : en Pages : 300
Book Description
In its most general form bifurcation theory is a theory of equilibrium solutions of nonlinear equations. By equilibrium solutions we mean, for example, steady solutions, time-periodic solutions, and quasi-periodic solutions. The purpose of this book is to teach the theory of bifurcation of equilibrium solutions of evolution problems governed by nonlinear differential equations. We have written this book for the broaqest audience of potentially interested learners: engineers, biologists, chemists, physicists, mathematicians, econom ists, and others whose work involves understanding equilibrium solutions of nonlinear differential equations. To accomplish our aims, we have thought it necessary to make the analysis 1. general enough to apply to the huge variety of applications which arise in science and technology, and 2. simple enough so that it can be understood by persons whose mathe matical training does not extend beyond the classical methods of analysis which were popular in the 19th Century. Of course, it is not possible to achieve generality and simplicity in a perfect union but, in fact, the general theory is simpler than the detailed theory required for particular applications. The general theory abstracts from the detailed problems only the essential features and provides the student with the skeleton on which detailed structures of the applications must rest. It is generally believed that the mathematical theory of bifurcation requires some functional analysis and some of the methods of topology and dynamics.
Author: Wayne Nagata Publisher: American Mathematical Soc. ISBN: 0821837257 Category : Mathematics Languages : en Pages : 186
Book Description
Nonlinear dynamical systems and the formation of spatio-temporal patterns play an important role in current research on partial differential equations. This book contains articles on topics of current interest in applications of dynamical systems theory to problems of pattern formation in space and time. Topics covered include aspects of lattice dynamical systems, convection in fluid layers with large aspect ratios, mixed mode oscillations and canards, bacterial remediation of waste, gyroscopic systems, data clustering, and the second part of Hilbert's 16th problem. Most of the book consists of expository survey material, and so can serve as a source of convenient entry points to current research topics in nonlinear dynamics and pattern formation. This volume arose from a workshop held at the Fields Institute in December of 2003, honoring Professor William F. Langford's fundamental work on the occasion of his sixtieth birthday. Information for our distributors: Titles in this series are copublished with the Fields Institute for Research in Mathematical Sciences (Toronto, Ontario, Canada).
Author: David D. Nolte Publisher: Oxford University Press ISBN: 0192528505 Category : Science Languages : en Pages : 384
Book Description
Galileo Unbound traces the journey that brought us from Galileo's law of free fall to today's geneticists measuring evolutionary drift, entangled quantum particles moving among many worlds, and our lives as trajectories traversing a health space with thousands of dimensions. Remarkably, common themes persist that predict the evolution of species as readily as the orbits of planets or the collapse of stars into black holes. This book tells the history of spaces of expanding dimension and increasing abstraction and how they continue today to give new insight into the physics of complex systems. Galileo published the first modern law of motion, the Law of Fall, that was ideal and simple, laying the foundation upon which Newton built the first theory of dynamics. Early in the twentieth century, geometry became the cause of motion rather than the result when Einstein envisioned the fabric of space-time warped by mass and energy, forcing light rays to bend past the Sun. Possibly more radical was Feynman's dilemma of quantum particles taking all paths at once — setting the stage for the modern fields of quantum field theory and quantum computing. Yet as concepts of motion have evolved, one thing has remained constant, the need to track ever more complex changes and to capture their essence, to find patterns in the chaos as we try to predict and control our world.
Author: Stuart Antman Publisher: Springer Science & Business Media ISBN: 0387276491 Category : Mathematics Languages : en Pages : 845
Book Description
Enlarged, updated, and extensively revised, this second edition illuminates specific problems of nonlinear elasticity, emphasizing the role of nonlinear material response. Opening chapters discuss strings, rods, and shells, and applications of bifurcation theory and the calculus of variations to problems for these bodies. Subsequent chapters cover tensors, three-dimensional continuum mechanics, three-dimensional elasticity , general theories of rods and shells, and dynamical problems. Each chapter includes interesting, challenging, and tractable exercises.
Author: Jean-Louis Tassoul Publisher: Princeton University Press ISBN: 140086898X Category : Science Languages : en Pages : 524
Book Description
Ever since the first observations of sunspots in the early seventeenth century, stellar rotation has been a major topic in astronomy and astrophysics. Jean-Louis Tassoul synthesizes a large number of theoretical investigations on rotating stars. Drawing upon his own research, Professor Tassoul also carefully critiques various competing ideas. In the first three chapters, the author provides a short historical sketch of stellar rotation, the main observational data on the Sun and other stars on which the subsequent theory is based, and the basic Newtonian hydrodynamics used to study rotating stars. Following a discussion of some general mechanical properties of stars in a state of permanent rotation, he reviews the main techniques for determining the structure of a rotating star and its stability with respect to infinitesimal disturbances. Since the actual distribution of angular momentum within stars is still unknown, Professor Tassoul considers various models of angular momentum as well as of meridional circulation. He devotes the rest of his study to the problems concerning various groups of stars and stages in stellar evolution. Originally published in 1979. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
Author: Chi-Sing Man Publisher: Springer Science & Business Media ISBN: 1402023081 Category : Science Languages : en Pages : 828
Book Description
Through his voluminous and in?uential writings, editorial activities, organi- tional leadership, intellectual acumen, and strong sense of history, Clifford - brose Truesdell III (1919–2000) was the main architect for the renaissance of - tional continuum mechanics since the middle of the twentieth century. The present collection of 42 essays and research papers pays tribute to this man of mathematics, science, and natural philosophy as well as to his legacy. The ?rst ?ve essays by B. D. Coleman, E. Giusti, W. Noll, J. Serrin, and D. Speiser were texts of addresses given by their authors at the Meeting in memory of Clifford Truesdell, which was held in Pisa in November 2000. In these essays the reader will ?nd personal reminiscences of Clifford Truesdell the man and of some of his activities as scientist, author, editor, historian of exact sciences, and principal founding member of the Society for Natural Philosophy. The bulk of the collection comprises 37 research papers which bear witness to the Truesdellian legacy. These papers cover a wide range of topics; what ties them together is the rational spirit. Clifford Truesdell, in his address upon receipt of a Birkhoff Prize in 1978, put the essence of modern continuum mechanics succinctly as “conceptual analysis, analysis not in the sense of the technical term but in the root meaning: logical criticism, dissection, and creative scrutiny.
Author: Patrick Rabier
Author: Patrick Rabier
Author: Patrick Rabier
Author: G. Iooss
Author: Wayne Nagata
Author: David D. Nolte
Author: Stuart Antman
Author: Jean-Louis Tassoul
Author: S. Böhme
Author: 
Author: Chi-Sing Man