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| Author | : C.P. Bruter |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 412 |
| Release | : 2001-11-30 |
| Genre | : Mathematics |
| ISBN | : 9781402003424 |
Download Bifurcation Theory, Mechanics and Physics Book in PDF, ePub and Kindle
This volume presents the proceedings of a colloquium inspired by the former President of the French Mathematical Society, Michel Herve. The aim was to promote the development of mathematics through applications. Since the ancient supports the new, it seemed appropriate to center the theoretical conferences on new subjects. Since the world is movement and creation, the theoretical conferences were planned on mechanics (movement) and bifurcation theory (creation). Five aspects of mechanics were to be presented, but, unfortunately, it has not been possible to include the statis tical mechanics aspect. So that only four aspects are presented: Classical mechanics (Hamiltonian, Lagrangian, Poisson) (W.N. Tulczyjew, J .E. l-lhite, C.M. MarIe). - Quantum mechanics (in particular the passage from the classi cal to the quantum approach and the problem of finding the explicit solution of Schrodinger's equation)(M. Cahen and S. Gutt, J. Leray). Fluid mechanics (meaning problems involving partial differ ential equations. One of the speakers we hoped would attend the conference was in Japan at the time, however his lecture is presented in these proceedings.) (J.F. Pommaret, H.I-l. Shi) - Mathematical "information" theory (S. Guiasll) Traditional physical arguments are characterized by their great homogeneity, and mathematically expressed by the compactness prop erty. In such cases, there is a kind of duality between locality and globality, which allows the use of the infinitesimal in global considerations.
| Author | : C.P. Bruter |
| Publisher | : Springer |
| Total Pages | : 0 |
| Release | : 2001-12-14 |
| Genre | : Mathematics |
| ISBN | : 9789400971929 |
Download Bifurcation Theory, Mechanics and Physics Book in PDF, ePub and Kindle
| Author | : M. Kubicek |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 253 |
| Release | : 2012-12-06 |
| Genre | : Science |
| ISBN | : 3642859577 |
Download Computational Methods in Bifurcation Theory and Dissipative Structures Book in PDF, ePub and Kindle
"Dissipative structures" is a concept which has recently been used in physics to discuss the formation of structures organized in space and/or time at the expense of the energy flowing into the system from the outside. The space-time structural organization of biological systems starting from the subcellular level up to the level of ecological systems, coherent structures in laser and of elastic stability in mechanics, instability in hydro plasma physics, problems dynamics leading to the development of turbulence, behavior of electrical networks and chemical reactors form just a short list of problems treated in this framework. Mathematical models constructed to describe these systems are usually nonlinear, often formed by complicated systems of algebraic, ordinary differ ential, or partial differential equations and include a number of character istic parameters. In problems of theoretical interest as well as engineering practice, we are concerned with the dependence of solutions on parameters and particularly with the values of parameters where qualitatively new types of solutions, e.g., oscillatory solutions, new stationary states, and chaotic attractors, appear (bifurcate). Numerical techniques to determine both bifurcation points and the depen dence of steady-state and oscillatory solutions on parameters are developed and discussed in detail in this text. The text is intended to serve as a working manual not only for students and research workers who are interested in dissipative structures, but also for practicing engineers who deal with the problems of constructing models and solving complicated nonlinear systems.
| Author | : Hans Troger |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 419 |
| Release | : 2012-12-06 |
| Genre | : Science |
| ISBN | : 3709191688 |
Download Nonlinear Stability and Bifurcation Theory Book in PDF, ePub and Kindle
Every student in engineering or in other fields of the applied sciences who has passed through his curriculum knows that the treatment of nonlin ear problems has been either avoided completely or is confined to special courses where a great number of different ad-hoc methods are presented. The wide-spread believe that no straightforward solution procedures for nonlinear problems are available prevails even today in engineering cir cles. Though in some courses it is indicated that in principle nonlinear problems are solveable by numerical methods the treatment of nonlinear problems, more or less, is considered to be an art or an intellectual game. A good example for this statement was the search for Ljapunov functions for nonlinear stability problems in the seventies. However things have changed. At the beginning of the seventies, start ing with the work of V.1. Arnold, R. Thom and many others, new ideas which, however, have their origin in the work of H. Poincare and A. A. Andronov, in the treatment of nonlinear problems appeared. These ideas gave birth to the term Bifurcation Theory. Bifurcation theory allows to solve a great class of nonlinear problems under variation of parameters in a straightforward manner.
| Author | : Michal Fečkan |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 387 |
| Release | : 2011-05-30 |
| Genre | : Science |
| ISBN | : 3642182690 |
Download Bifurcation and Chaos in Discontinuous and Continuous Systems Book in PDF, ePub and Kindle
"Bifurcation and Chaos in Discontinuous and Continuous Systems" provides rigorous mathematical functional-analytical tools for handling chaotic bifurcations along with precise and complete proofs together with concrete applications presented by many stimulating and illustrating examples. A broad variety of nonlinear problems are studied involving difference equations, ordinary and partial differential equations, differential equations with impulses, piecewise smooth differential equations, differential and difference inclusions, and differential equations on infinite lattices as well. This book is intended for mathematicians, physicists, theoretically inclined engineers and postgraduate students either studying oscillations of nonlinear mechanical systems or investigating vibrations of strings and beams, and electrical circuits by applying the modern theory of bifurcation methods in dynamical systems. Dr. Michal Fečkan is a Professor at the Department of Mathematical Analysis and Numerical Mathematics on the Faculty of Mathematics, Physics and Informatics at the Comenius University in Bratislava, Slovakia. He is working on nonlinear functional analysis, bifurcation theory and dynamical systems with applications to mechanics and vibrations.
| Author | : Yushu Chen |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 465 |
| Release | : 2012-12-06 |
| Genre | : Technology & Engineering |
| ISBN | : 1447115759 |
Download Bifurcation and Chaos in Engineering Book in PDF, ePub and Kindle
For the many different deterministic non-linear dynamic systems (physical, mechanical, technical, chemical, ecological, economic, and civil and structural engineering), the discovery of irregular vibrations in addition to periodic and almost periodic vibrations is one of the most significant achievements of modern science. An in-depth study of the theory and application of non-linear science will certainly change one's perception of numerous non-linear phenomena and laws considerably, together with its great effects on many areas of application. As the important subject matter of non-linear science, bifurcation theory, singularity theory and chaos theory have developed rapidly in the past two or three decades. They are now advancing vigorously in their applications to mathematics, physics, mechanics and many technical areas worldwide, and they will be the main subjects of our concern. This book is concerned with applications of the methods of dynamic systems and subharmonic bifurcation theory in the study of non-linear dynamics in engineering. It has grown out of the class notes for graduate courses on bifurcation theory, chaos and application theory of non-linear dynamic systems, supplemented with our latest results of scientific research and materials from literature in this field. The bifurcation and chaotic vibration of deterministic non-linear dynamic systems are studied from the viewpoint of non-linear vibration.
| Author | : V.I. Arnold |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 279 |
| Release | : 2013-12-01 |
| Genre | : Mathematics |
| ISBN | : 3642578845 |
Download Dynamical Systems V Book in PDF, ePub and Kindle
Bifurcation theory and catastrophe theory are two well-known areas within the field of dynamical systems. Both are studies of smooth systems, focusing on properties that seem to be manifestly non-smooth. Bifurcation theory is concerned with the sudden changes that occur in a system when one or more parameters are varied. Examples of such are familiar to students of differential equations, from phase portraits. Understanding the bifurcations of the differential equations that describe real physical systems provides important information about the behavior of the systems. Catastrophe theory became quite famous during the 1970's, mostly because of the sensation caused by the usually less than rigorous applications of its principal ideas to "hot topics", such as the characterization of personalities and the difference between a "genius" and a "maniac". Catastrophe theory is accurately described as singularity theory and its (genuine) applications. The authors of this book, previously published as Volume 5 of the Encyclopaedia, have given a masterly exposition of these two theories, with penetrating insight.
| Author | : Remco I. Leine |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 245 |
| Release | : 2013-03-19 |
| Genre | : Mathematics |
| ISBN | : 3540443983 |
Download Dynamics and Bifurcations of Non-Smooth Mechanical Systems Book in PDF, ePub and Kindle
This monograph combines the knowledge of both the field of nonlinear dynamics and non-smooth mechanics, presenting a framework for a class of non-smooth mechanical systems using techniques from both fields. The book reviews recent developments, and opens the field to the nonlinear dynamics community. This book addresses researchers and graduate students in engineering and mathematics interested in the modelling, simulation and dynamics of non-smooth systems and nonlinear dynamics.
| Author | : Q.S. Nguyen |
| Publisher | : Springer |
| Total Pages | : 296 |
| Release | : 2014-05-04 |
| Genre | : Science |
| ISBN | : 3709127122 |
Download Bifurcation and Stability of Dissipative Systems Book in PDF, ePub and Kindle
The first theme concerns the plastic buckling of structures in the spirit of Hill’s classical approach. Non-bifurcation and stability criteria are introduced and post-bifurcation analysis performed by asymptotic development method in relation with Hutchinson’s work. Some recent results on the generalized standard model are given and their connection to Hill’s general formulation is presented. Instability phenomena of inelastic flow processes such as strain localization and necking are discussed. The second theme concerns stability and bifurcation problems in internally damaged or cracked colids. In brittle fracture or brittle damage, the evolution law of crack lengths or damage parameters is time-independent like in plasticity and leads to a similar mathematical description of the quasi-static evolution. Stability and non-bifurcation criteria in the sense of Hill can be again obtained from the discussion of the rate response.
| Author | : George Exadaktylos |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 469 |
| Release | : 2007-04-27 |
| Genre | : Science |
| ISBN | : 3540493425 |
Download Bifurcations, Instabilities, Degradation in Geomechanics Book in PDF, ePub and Kindle
This is an up-to-date review of developments in the field of bifurcations and instabilities in geomechanics from some of the world’s leading experts. Leading international researchers and practitioners of the topics debate the developments and applications which have occurred over the last few decades. Beside fundamental research findings, applications in geotechnical, petroleum, mining, and bulk materials engineering are emphasised.
