Download or read book Nonlinear Oscillations of Hamiltonian PDEs written by Massimiliano Berti and published by Springer Science & Business Media. This book was released on 2007-10-01 with total page 191 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many partial differential equations (PDEs) that arise in physics can be viewed as infinite-dimensional Hamiltonian systems. This monograph presents recent existence results of nonlinear oscillations of Hamiltonian PDEs, particularly of periodic solutions for completely resonant nonlinear wave equations. The text serves as an introduction to research in this fascinating and rapidly growing field. Graduate students and researchers interested in variational techniques and nonlinear analysis applied to Hamiltonian PDEs will find inspiration in the book.
Download or read book Contributions to the Theory of Nonlinear Oscillations AM 41 Volume IV written by Solomon Lefschetz and published by Princeton University Press. This book was released on 2016-03-02 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: The description for this book, Contributions to the Theory of Nonlinear Oscillations (AM-41), Volume IV, will be forthcoming.
Download or read book Nonlinear Oscillations and Boundary Value Problems for Hamiltonian Systems written by Frank H. Clarke and published by . This book was released on 1979 with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt: Hamilton's differential equations are basic in the study of theoretical mechanics. A particular class of motions of interest for such systems of equations are the periodic ones, which correspond to oscillations (vibrations) of the underlying physical system; the absence of such motions is usually associated with resonance phenomena. In this paper we give conditions on the Hamiltonian function H which guarantee the existence of periodic orbits, as well as other more general types of motions. One distinction with previous work on the subject is that we consider forced vibrations arising from external driving forces; another is that the solutions in question are characterized directly as the solutions of a specific minimization problem (i.e., we obtain a 'variational principle'), a feature which could prove useful for computational purposes.
Download or read book Contributions to the Theory of Nonlinear Oscillations AM 29 Volume II written by Solomon Lefschetz and published by Princeton University Press. This book was released on 2016-03-02 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt: These two new collections, numbers 28 and 29 respectively in the Annals of Mathematics Studies, continue the high standard set by the earlier Annals Studies 20 and 24 by bringing together important contributions to the theories of games and of nonlinear differential equations.
Download or read book Nonlinear Oscillations and Waves in Dynamical Systems written by P.S Landa and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 550 pages. Available in PDF, EPUB and Kindle. Book excerpt: A rich variety of books devoted to dynamical chaos, solitons, self-organization has appeared in recent years. These problems were all considered independently of one another. Therefore many of readers of these books do not suspect that the problems discussed are divisions of a great generalizing science - the theory of oscillations and waves. This science is not some branch of physics or mechanics, it is a science in its own right. It is in some sense a meta-science. In this respect the theory of oscillations and waves is closest to mathematics. In this book we call the reader's attention to the present-day theory of non-linear oscillations and waves. Oscillatory and wave processes in the systems of diversified physical natures, both periodic and chaotic, are considered from a unified poin t of view . The relation between the theory of oscillations and waves, non-linear dynamics and synergetics is discussed. One of the purposes of this book is to convince reader of the necessity of a thorough study popular branches of of the theory of oscillat ions and waves, and to show that such science as non-linear dynamics, synergetics, soliton theory, and so on, are, in fact , constituent parts of this theory. The primary audiences for this book are researchers having to do with oscillatory and wave processes, and both students and post-graduate students interested in a deep study of the general laws and applications of the theory of oscillations and waves.
Download or read book Hamiltonian Dynamical Systems and Applications written by Walter Craig and published by Springer Science & Business Media. This book was released on 2008-02-17 with total page 450 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is the collected and extended notes from the lectures on Hamiltonian dynamical systems and their applications that were given at the NATO Advanced Study Institute in Montreal in 2007. Many aspects of the modern theory of the subject were covered at this event, including low dimensional problems. Applications are also presented to several important areas of research, including problems in classical mechanics, continuum mechanics, and partial differential equations.
Download or read book Numerical Continuation and Bifurcation in Nonlinear PDEs written by Hannes Uecker and published by SIAM. This book was released on 2021-08-19 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a hands-on approach to numerical continuation and bifurcation for nonlinear PDEs in 1D, 2D, and 3D. Partial differential equations (PDEs) are the main tool to describe spatially and temporally extended systems in nature. PDEs usually come with parameters, and the study of the parameter dependence of their solutions is an important task. Letting one parameter vary typically yields a branch of solutions, and at special parameter values, new branches may bifurcate. After a concise review of some analytical background and numerical methods, the author explains the free MATLAB package pde2path by using a large variety of examples with demo codes that can be easily adapted to the reader's given problem. Numerical Continuation and Bifurcation in Nonlinear PDEs will appeal to applied mathematicians and scientists from physics, chemistry, biology, and economics interested in the numerical solution of nonlinear PDEs, particularly the parameter dependence of solutions. It can be used as a supplemental text in courses on nonlinear PDEs and modeling and bifurcation.
Download or read book Contributions to the Theory of Nonlinear Oscillations AM 45 Volume V written by Lamberto Cesari and published by Princeton University Press. This book was released on 2016-03-02 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: The description for this book, Contributions to the Theory of Nonlinear Oscillations (AM-45), Volume V, will be forthcoming.
Download or read book Perturbation Method in the Theory of Nonlinear Oscillations written by Ahmed Aly Kamel and published by . This book was released on 1970 with total page 60 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Nonlinear Equations for Beams and Degenerate Plates with Piers written by Maurizio Garrione and published by Springer Nature. This book was released on 2019-10-31 with total page 115 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book develops a full theory for hinged beams and degenerate plates with multiple intermediate piers with the final purpose of understanding the stability of suspension bridges. New models are proposed and new tools are provided for the stability analysis. The book opens by deriving the PDE’s based on the physical models and by introducing the basic framework for the linear stationary problem. The linear analysis, in particular the behavior of the eigenvalues as the position of the piers varies, enables the authors to tackle the stability issue for some nonlinear evolution beam equations, with the aim of determining the “best position” of the piers within the beam in order to maximize its stability. The study continues with the analysis of a class of degenerate plate models. The torsional instability of the structure is investigated, and again, the optimal position of the piers in terms of stability is discussed. The stability analysis is carried out by means of both analytical tools and numerical experiments. Several open problems and possible future developments are presented. The qualitative analysis provided in the book should be seen as the starting point for a precise quantitative study of more complete models, taking into account the action of aerodynamic forces. This book is intended for a two-fold audience. It is addressed both to mathematicians working in the field of Differential Equations, Nonlinear Analysis and Mathematical Physics, due to the rich number of challenging mathematical questions which are discussed and left as open problems, and to Engineers interested in mechanical structures, since it provides the theoretical basis to deal with models for the dynamics of suspension bridges with intermediate piers. More generally, it may be enjoyable for readers who are interested in the application of Mathematics to real life problems.
Download or read book Nonlinear Analysis and Semilinear Elliptic Problems written by Antonio Ambrosetti and published by Cambridge University Press. This book was released on 2007-01-04 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt: A graduate text explaining how methods of nonlinear analysis can be used to tackle nonlinear differential equations. Suitable for mathematicians, physicists and engineers, topics covered range from elementary tools of bifurcation theory and analysis to critical point theory and elliptic partial differential equations. The book is amply illustrated with many exercises.
Download or read book Lectures On Quantum Mechanics And Attractors written by Alexander Komech and published by World Scientific. This book was released on 2022-02-18 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives a concise introduction to Quantum Mechanics with a systematic, coherent, and in-depth explanation of related mathematical methods from the scattering theory and the theory of Partial Differential Equations.The book is aimed at graduate and advanced undergraduate students in mathematics, physics, and chemistry, as well as at the readers specializing in quantum mechanics, theoretical physics and quantum chemistry, and applications to solid state physics, optics, superconductivity, and quantum and high-frequency electronic devices.The book utilizes elementary mathematical derivations. The presentation assumes only basic knowledge of the origin of Hamiltonian mechanics, Maxwell equations, calculus, Ordinary Differential Equations and basic PDEs. Key topics include the Schrödinger, Pauli, and Dirac equations, the corresponding conservation laws, spin, the hydrogen spectrum, and the Zeeman effect, scattering of light and particles, photoelectric effect, electron diffraction, and relations of quantum postulates with attractors of nonlinear Hamiltonian PDEs. Featuring problem sets and accompanied by extensive contemporary and historical references, this book could be used for the course on Quantum Mechanics and is also suitable for individual study.
Download or read book Variational Methods written by Maïtine Bergounioux and published by Walter de Gruyter GmbH & Co KG. This book was released on 2017-01-11 with total page 621 pages. Available in PDF, EPUB and Kindle. Book excerpt: With a focus on the interplay between mathematics and applications of imaging, the first part covers topics from optimization, inverse problems and shape spaces to computer vision and computational anatomy. The second part is geared towards geometric control and related topics, including Riemannian geometry, celestial mechanics and quantum control. Contents: Part I Second-order decomposition model for image processing: numerical experimentation Optimizing spatial and tonal data for PDE-based inpainting Image registration using phase・amplitude separation Rotation invariance in exemplar-based image inpainting Convective regularization for optical flow A variational method for quantitative photoacoustic tomography with piecewise constant coefficients On optical flow models for variational motion estimation Bilevel approaches for learning of variational imaging models Part II Non-degenerate forms of the generalized Euler・Lagrange condition for state-constrained optimal control problems The Purcell three-link swimmer: some geometric and numerical aspects related to periodic optimal controls Controllability of Keplerian motion with low-thrust control systems Higher variational equation techniques for the integrability of homogeneous potentials Introduction to KAM theory with a view to celestial mechanics Invariants of contact sub-pseudo-Riemannian structures and Einstein・Weyl geometry Time-optimal control for a perturbed Brockett integrator Twist maps and Arnold diffusion for diffeomorphisms A Hamiltonian approach to sufficiency in optimal control with minimal regularity conditions: Part I Index
Download or read book Quasi Periodic Solutions of Nonlinear Wave Equations on the D Dimensional Torus written by Massimiliano Berti and published by . This book was released on 2020 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Advanced Topics in Nonsmooth Dynamics written by Remco Leine and published by Springer. This book was released on 2018-06-07 with total page 462 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses emerging topics in the area of nonsmooth dynamics research, such as numerical methods for nonsmooth systems, impact laws for multi-collisions, nonlinear vibrations and control of nonsmooth systems. It documents original work of researchers at the European Network for NonSmooth Dynamics (ENNSD), which provides a cooperation platform for researchers in the field and promotes research focused on nonsmooth dynamics and its applications. Since the establishment of the network in 2012, six ENNSD symposia have been organized at different European locations. The network brings together 40 specialists from 9 different countries in and outside Europe and a wealth of scientific knowledge has been gathered and developed by this group of experts in recent years. The book is of interest to both new and experienced researchers in the field of nonsmooth dynamics. Each chapter is written in such a way as to provide an introduction to the topic for researchers from other fields.
Download or read book Nonlinear Oscillations Dynamical Systems and Bifurcations of Vector Fields written by John Guckenheimer and published by Springer Science & Business Media. This book was released on 2013-11-21 with total page 475 pages. Available in PDF, EPUB and Kindle. Book excerpt: An application of the techniques of dynamical systems and bifurcation theories to the study of nonlinear oscillations. Taking their cue from Poincare, the authors stress the geometrical and topological properties of solutions of differential equations and iterated maps. Numerous exercises, some of which require nontrivial algebraic manipulations and computer work, convey the important analytical underpinnings of problems in dynamical systems and help readers develop an intuitive feel for the properties involved.
Download or read book The Parameterization Method for Invariant Manifolds written by Àlex Haro and published by Springer. This book was released on 2016-04-18 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents some theoretical and computational aspects of the parameterization method for invariant manifolds, focusing on the following contexts: invariant manifolds associated with fixed points, invariant tori in quasi-periodically forced systems, invariant tori in Hamiltonian systems and normally hyperbolic invariant manifolds. This book provides algorithms of computation and some practical details of their implementation. The methodology is illustrated with 12 detailed examples, many of them well known in the literature of numerical computation in dynamical systems. A public version of the software used for some of the examples is available online. The book is aimed at mathematicians, scientists and engineers interested in the theory and applications of computational dynamical systems.
