Download or read book Theory of Nonlinear Lattices written by Morikazu Toda and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 233 pages. Available in PDF, EPUB and Kindle. Book excerpt: Soliton theory, the theory of nonlinear waves in lattices composed of particles interacting by nonlinear forces, is treated rigorously in this book. The presentation is coherent and self-contained, starting with pioneering work and extending to the most recent advances in the field. Special attention is focused on exact methods of solution of nonlinear problems and on the exact mathematical treatment of nonlinear lattice vibrations. This new edition updates the material to take account of important new advances.
Download or read book Theory and Applications of Coupled Map Lattices written by K. Kaneko and published by . This book was released on 1993-04-13 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: The technique of the coupled map lattice (CML) is a rapidly developing field in nonlinear dynamics at present. This book gives a fully illustrative overview of current research in the field. A CML is a dynamical system in which there is some interaction ('coupled') between continuous state elements, which evolve in discrete time ('map') and are distributed on a discrete space ('lattice'). This book investigates both the theoretical aspects and applications of CMLs to spatially extended systems in nonlinear dynamical systems.
Download or read book Dynamics of Lattice Materials written by A. Srikantha Phani and published by John Wiley & Sons. This book was released on 2017-09-25 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides a comprehensive introduction to the dynamic response of lattice materials, covering the fundamental theory and applications in engineering practice Offers comprehensive treatment of dynamics of lattice materials and periodic materials in general, including phononic crystals and elastic metamaterials Provides an in depth introduction to elastostatics and elastodynamics of lattice materials Covers advanced topics such as damping, nonlinearity, instability, impact and nanoscale systems Introduces contemporary concepts including pentamodes, local resonance and inertial amplification Includes chapters on fast computation and design optimization tools Topics are introduced using simple systems and generalized to more complex structures with a focus on dispersion characteristics
Download or read book Jacobi Operators and Completely Integrable Nonlinear Lattices written by Gerald Teschl and published by American Mathematical Soc.. This book was released on 2000 with total page 373 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume serves as an introduction and reference source on spectral and inverse theory of Jacobi operators and applications of these theories to the Toda and Kac-van Moerbeke hierarchy.
Download or read book Nonlinear Periodic Waves and Their Modulations written by Anatoli? Mikha?lovich Kamchatnov and published by World Scientific. This book was released on 2000 with total page 399 pages. Available in PDF, EPUB and Kindle. Book excerpt: Although the mathematical theory of nonlinear waves and solitons has made great progress, its applications to concrete physical problems are rather poor, especially when compared with the classical theory of linear dispersive waves and nonlinear fluid motion. The Whitham method, which describes the combining action of the dispersive and nonlinear effects as modulations of periodic waves, is not widely used by applied mathematicians and physicists, though it provides a direct and natural way to treat various problems in nonlinear wave theory. Therefore it is topical to describe recent developments of the Whitham theory in a clear and simple form suitable for applications in various branches of physics.This book develops the techniques of the theory of nonlinear periodic waves at elementary level and in great pedagogical detail. It provides an introduction to a Whitham's theory of modulation in a form suitable for applications. The exposition is based on a thorough analysis of representative examples taken from fluid mechanics, nonlinear optics and plasma physics rather than on the formulation and study of a mathematical theory. Much attention is paid to physical motivations of the mathematical methods developed in the book. The main applications considered include the theory of collisionless shock waves in dispersive systems and the nonlinear theory of soliton formation in modulationally unstable systems. Exercises are provided to amplify the discussion of important topics such as singular perturbation theory, Riemann invariants, the finite gap integration method, and Whitham equations and their solutions.
Download or read book Non Linear Lattice written by Ignazio Licata and Sauro Succi and published by MDPI. This book was released on 2018-07-17 with total page 291 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a printed edition of the Special Issue "Non-Linear Lattice" that was published in Entropy
Download or read book The Discrete Nonlinear Schr dinger Equation written by Panayotis G. Kevrekidis and published by Springer Science & Business Media. This book was released on 2009-07-07 with total page 417 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the first effort to summarize a large volume of results obtained over the past 20 years in the context of the Discrete Nonlinear Schrödinger equation and the physical settings that it describes.
Download or read book Nonlinearity and Disorder Theory and Applications written by Fatkhulla Abdullaev and published by Springer Science & Business Media. This book was released on 2002-01-31 with total page 488 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proceedings of the NATO Advanced Research Workshop, Tashkent, Uzbekistan, 2-6 October 2001
Download or read book Theory of Nonlinear Lattices written by Morikazu Toda and published by Springer. This book was released on 1981 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with waves in lattices composed of particles interacting by nonlinear forces. Since motion in a lattice with exponential interac tion between nearest neighbors can be analyzed rigorously, it is treated as the central subject to be discussed. From the idea that the fundamentals of the mathematical methods for nonlinear lattices would be elucidated by rigorous results, I was led in 1966 to the lattice with exponential interaction, which has since proved to be a subject of intensive investigation by many researchers. Therefore I have tried to describe the development of the study of this lattice. The presentation is intended to be coherent and self-contained. Chapter 1 starts with a rather historical exposition, and deals with the motion in the lattices and in continuous systems in general. Funda mental concepts necessary for later chapters, including the partic1elike behavior of stable pulses (solitons), the most characteristic entities of the nonlinear waves, are introduced. The dual transformation, which exchanges the roles of particles and interaction, is described for devel opment in the next chapter.
Download or read book Nonlinear Waves Solitons and Chaos written by Eryk Infeld and published by Cambridge University Press. This book was released on 2000-07-13 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: The second edition of a highly successful book on nonlinear waves, solitons and chaos.
Download or read book Advanced Synergetics written by Hermann Haken and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 371 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text on the interdisciplinary field of synergetics will be of interest to students and scientists in physics, chemistry, mathematics, biology, electrical, civil and mechanical engineering, and other fields. It continues the outline of basic con cepts and methods presented in my book Synergetics. An Introduction, which has by now appeared in English, Russian, J apanese, Chinese, and German. I have written the present book in such a way that most of it can be read in dependently of my previous book, though occasionally some knowledge of that book might be useful. But why do these books address such a wide audience? Why are instabilities such a common feature, and what do devices and self-organizing systems have in common? Self-organizing systems acquire their structures or functions without specific interference from outside. The differentiation of cells in biology, and the process of evolution are both examples of self-organization. Devices such as the electronic oscillators used in radio transmitters, on the other hand, are man made. But we often forget that in many cases devices function by means of pro cesses which are also based on self-organization. In an electronic oscillator the motion of electrons becomes coherent without any coherent driving force from the outside; the device is constructed in such a way as to permit specific collective motions of the electrons. Quite evidently the dividing line between self-organiz ing systems and man-made devices is not at all rigid.
Download or read book Synergetics From Microscopic to Macroscopic Order written by E. Frehland and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the papers presented at the International Symposium on "Synergetics - From Microscopic to Macroscopic Order", held at the Wissenschafts kolleg z~ Berlin (Institute for Advanced Study Berlin), on July 4-8, 1983. Further more, it contains a contribution of T. Ohta, who unfortunately could not partici pate in this meeting, on the evolution of mUltigene families. The papers discuss the evolution and the function of ordered structures from small microscopic scales up to large macroscopic dimensions. On the one hand, these structures derive from physical or biological systems; on the other hand, they also affect economic, sociological and philosophical questions. I would like to thank the Wissenschaftskolleg zu Berlin for the extraordinary support and hospitality during my one year's stay there as a fellow, which made the planning, preparation and organization of this symposium possible. I would also like to acknowledge the work of B. Fritsch and D. Dorner who actively participated in this undertaking. I am grateful to Professor Haken, the founder of synergetics, whose participation in the planning and styling of the concept of the conference was essential. I am especially thankful to Mrs. U. Monigatti for her indefatigable help with the prep aration and organization of the conference. The financial support was provided by the "Deutsche Forschungsgemeinschaft". Berlin, November 1983 E. Frehland Contents Some Introductory Remarks on Synergetics By H. Haken ...
Download or read book The Many body Problem written by Daniel Charles Mattis and published by World Scientific. This book was released on 1993 with total page 992 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book differs from its predecessor, Lieb & Mattis Mathematical Physics in One Dimension, in a number of important ways. Classic discoveries which once had to be omitted owing to lack of space ? such as the seminal paper by Fermi, Pasta and Ulam on lack of ergodicity of the linear chain, or Bethe's original paper on the Bethe ansatz ? can now be incorporated. Many applications which did not even exist in 1966 (some of which were originally spawned by the publication of Lieb & Mattis) are newly included. Among these, this new book contains critical surveys of a number of important developments: the exact solution of the Hubbard model, the concept of spinons, the Haldane gap in magnetic spin-one chains, bosonization and fermionization, solitions and the approach to thermodynamic equilibrium, quantum statistical mechanics, localization of normal modes and eigenstates in disordered chains, and a number of other contemporary concerns.
Download or read book Jacobi Matrices and the Moment Problem written by Yurij M. Berezansky and published by Springer Nature. This book was released on 2024-01-06 with total page 489 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents the solution of the classical moment problem, the construction of Jacobi matrices and corresponding polynomials. The cases of strongly,trigonometric, complex and real two-dimensional moment problems are discussed, and the Jacobi-type matrices corresponding to the trigonometric moment problem are shown. The Berezansky theory of the expansion in generalized eigenvectors for corresponding set of commuting operators plays the key role in the proof of results. The book is recommended for researchers in fields of functional analysis, operator theory, mathematical physics, and engineers who deal with problems of coupled pendulums.
Download or read book Nonlinear Time Series Analysis written by Holger Kantz and published by Cambridge University Press. This book was released on 2004 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt: The paradigm of deterministic chaos has influenced thinking in many fields of science. Chaotic systems show rich and surprising mathematical structures. In the applied sciences, deterministic chaos provides a striking explanation for irregular behaviour and anomalies in systems which do not seem to be inherently stochastic. The most direct link between chaos theory and the real world is the analysis of time series from real systems in terms of nonlinear dynamics. Experimental technique and data analysis have seen such dramatic progress that, by now, most fundamental properties of nonlinear dynamical systems have been observed in the laboratory. Great efforts are being made to exploit ideas from chaos theory wherever the data displays more structure than can be captured by traditional methods. Problems of this kind are typical in biology and physiology but also in geophysics, economics, and many other sciences.
Download or read book Encyclopedia of Nonlinear Science written by Alwyn Scott and published by Routledge. This book was released on 2006-05-17 with total page 2881 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 438 alphabetically-arranged essays, this work provides a useful overview of the core mathematical background for nonlinear science, as well as its applications to key problems in ecology and biological systems, chemical reaction-diffusion problems, geophysics, economics, electrical and mechanical oscillations in engineering systems, lasers and nonlinear optics, fluid mechanics and turbulence, and condensed matter physics, among others.
Download or read book Modern Perspectives in Theoretical Physics written by K. S. Sreelatha and published by Springer Nature. This book was released on 2021-04-12 with total page 182 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book highlights the review of articles in theoretical physics by the students of Professor K. Babu Joseph, as a Festschrift for his 80th Birthday. This book is divided into four sections based on the contributions of Babu Joseph and his students. The four sections are Cosmology, High Energy Physics, Mathematical Physics and Non-linear Dynamics and its applications.
