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Author : Ignazio Licata and Sauro Succi
Publisher : MDPI
Page : 291 pages
File Size : 52,7 Mb
Release : 2018-07-17
Category : Electronic books
ISBN : 9783038423065
This book is a printed edition of the Special Issue "Non-Linear Lattice" that was published in Entropy
Author : Morikazu Toda
Publisher : Springer Science & Business Media
Page : 233 pages
File Size : 45,6 Mb
Release : 2012-12-06
Category : Science
ISBN : 9783642832192
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.
Author : Ignazio Licata,Sauro Succi
Publisher : Unknown
Page : 128 pages
File Size : 51,5 Mb
Release : 2016
Category : Physics
ISBN : 3038423076
The development of mathematical techniques, combined with new possibilities of computational simulation, have greatly broadened the study of non-linear lattices, a theme among the most refined and interdisciplinary-oriented in the field of mathematical physics. This Special Issue mainly focuses on state-of-the-art advancements concerning the many facets of non-linear lattices, from the theoretical ones to more applied ones. The non-linear and discrete systems play a key role in all ranges of physical experience, from macrophenomena to condensed matter, up to some models of space discrete space-time
Author : Morikazu Toda
Publisher : Springer
Page : 0 pages
File Size : 52,8 Mb
Release : 1981
Category : Science
ISBN : 3642965857
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.
Author : John D. Clayton
Publisher : Springer Science & Business Media
Page : 700 pages
File Size : 43,9 Mb
Release : 2010-11-01
Category : Science
ISBN : 9789400703506
This book describes behavior of crystalline solids primarily via methods of modern continuum mechanics. Emphasis is given to geometrically nonlinear descriptions, i.e., finite deformations. Primary topics include anisotropic crystal elasticity, plasticity, and methods for representing effects of defects in the solid on the material's mechanical response. Defects include crystal dislocations, point defects, twins, voids or pores, and micro-cracks. Thermoelastic, dielectric, and piezoelectric behaviors are addressed. Traditional and higher-order gradient theories of mechanical behavior of crystalline solids are discussed. Differential-geometric representations of kinematics of finite deformations and lattice defect distributions are presented. Multi-scale modeling concepts are described in the context of elastic and plastic material behavior. Representative substances towards which modeling techniques may be applied are single- and poly- crystalline metals and alloys, ceramics, and minerals. This book is intended for use by scientists and engineers involved in advanced constitutive modeling of nonlinear mechanical behavior of solid crystalline materials. Knowledge of fundamentals of continuum mechanics and tensor calculus is a prerequisite for accessing much of the text. This book could be used as supplemental material for graduate courses on continuum mechanics, elasticity, plasticity, micromechanics, or dislocation mechanics, for students in various disciplines of engineering, materials science, applied mathematics, and condensed matter physics.
Author : E. Atlee Jackson
Publisher : CUP Archive
Page : 532 pages
File Size : 50,9 Mb
Release : 1989
Category : Mathematics
ISBN : 0521426324
The dynamics of physical, chemical, biological, or fluid systems generally must be described by nonlinear models, whose detailed mathematical solutions are not obtainable. To understand some aspects of such dynamics, various complementary methods and viewpoints are of crucial importance. In this book the perspectives generated by analytical, topological and computational methods, and interplays between them, are developed in a variety of contexts. This book is a comprehensive introduction to this field, suited to a broad readership, and reflecting a wide range of applications. Some of the concepts considered are: topological equivalence; embeddings; dimensions and fractals; Poincaré maps and map-dynamics; empirical computational sciences vis-á-vis mathematics; Ulam's synergetics; Turing's instability and dissipative structures; chaos; dynamic entropies; Lorenz and Rossler models; predator-prey and replicator models; FPU and KAM phenomena; solitons and nonsolitons; coupled maps and pattern dynamics; cellular automata.
Author : Mikhail D. Starostenkov,Pavel V. Zakharov,Artem V. Markidonov,Pavel Y. Tabakov
Publisher : Materials Research Forum LLC
Page : 129 pages
File Size : 47,5 Mb
Release : 2024-02-10
Category : Technology & Engineering
ISBN : 9781644902882
The book presents an overview of nonlinear effects arising in discrete lattices of metals. Topics covered include discrete breathers, quasi-breathers, soliton waves, and shock waves. Keywords: Soliton, Discrete Breathers, Quasi-Breathers, Shock Waves, Supersonic Waves, Molecular Dynamics, Self-Organization, Nonlinearity, Dislocation Extraction Algorithm, Frenkel Pairs, Stacking Fault Tetrahedra.
Author : M.D.S. Aliyu
Publisher : CRC Press
Page : 405 pages
File Size : 45,8 Mb
Release : 2017-12-19
Category : Mathematics
ISBN : 9781439854853
A comprehensive overview of nonlinear H∞ control theory for both continuous-time and discrete-time systems, Nonlinear H∞-Control, Hamiltonian Systems and Hamilton-Jacobi Equations covers topics as diverse as singular nonlinear H∞-control, nonlinear H∞ -filtering, mixed H2/ H∞-nonlinear control and filtering, nonlinear H∞-almost-disturbance-decoupling, and algorithms for solving the ubiquitous Hamilton-Jacobi-Isaacs equations. The link between the subject and analytical mechanics as well as the theory of partial differential equations is also elegantly summarized in a single chapter. Recent progress in developing computational schemes for solving the Hamilton-Jacobi equation (HJE) has facilitated the application of Hamilton-Jacobi theory in both mechanics and control. As there is currently no efficient systematic analytical or numerical approach for solving them, the biggest bottle-neck to the practical application of the nonlinear equivalent of the H∞-control theory has been the difficulty in solving the Hamilton-Jacobi-Isaacs partial differential-equations (or inequalities). In light of this challenge, the author hopes to inspire continuing research and discussion on this topic via examples and simulations, as well as helpful notes and a rich bibliography. Nonlinear H∞-Control, Hamiltonian Systems and Hamilton-Jacobi Equations was written for practicing professionals, educators, researchers and graduate students in electrical, computer, mechanical, aeronautical, chemical, instrumentation, industrial and systems engineering, as well as applied mathematics, economics and management.
Author : Xianfeng Chen,Guoquan Zhang,Heping Zeng,Qi Guo,Weilong She
Publisher : Walter de Gruyter GmbH & Co KG
Page : 381 pages
File Size : 42,7 Mb
Release : 2015-01-01
Category : Science
ISBN : 9783110382822
This book presents an overview of the state of the art of nonlinear optics from weak light nonlinear optics, ultrafast nonlinear optics to electro-optical theory and applications. Topics range from the fundamental studies of the interaction between matter and radiation to the development of devices, components, and systems of tremendous commercial interest for widespread applications in optical telecommunications, medicine, and biotechnology.
Author : Zene Horii
Publisher : Unknown
Page : 264 pages
File Size : 53,7 Mb
Release : 2007
Category : Lattice dynamics
ISBN : CORNELL:31924095843953
Author : Gérard A. Maugin
Publisher : Unknown
Page : 328 pages
File Size : 54,7 Mb
Release : 1999
Category : Mathematics
ISBN : 0198534841
The mathematical modelling of changing structures in materials is of increasing importance to industry where applications of the theory are found in subjects as diverse as aerospace and medicine. This book deals with aspects of the nonlinear dynamics of deformable ordered solids (known as elastic crystals) where the nonlinear effects combine or compete with each other. Physical and mathematical models are discused and computational aspects are also included. Different models are considered - on discrete as well as continuum scales - applying heat, electricity, or magnetism to the crystal structure and these are analysed using the equations of rational mechanics. Students are introduced to the important equations of nonlinear science that describe shock waves, solitons and chaos and also the non-exactly integrable systems or partial differential equations. A large number of problems and examples are included, many taken from recent research and involving both one-dimensional and two-dimensional problems as well as some coupled degress of freedom.
Author : Robert Sinclair MacKay,Luis V zquez,Mar¡a Paz Zorzano
Publisher : World Scientific
Page : 372 pages
File Size : 41,5 Mb
Release : 2003
Category : Mathematics
ISBN : 9812704620
This conference was the third meeting organized in the framework of the European LOCNET project. The main topics discussed by this international research collaboration were localization by nonlinearity and spatial discreteness, and energy transfer (in crystals, biomolecules and Josephson arrays).
Author : Juan F. R. Archilla,Faustino Palmero,M. Carmen Lemos,Bernardo Sánchez-Rey,Jesús Casado-Pascual
Publisher : Springer
Page : 340 pages
File Size : 41,7 Mb
Release : 2017-12-21
Category : Science
ISBN : 9783319722184
This book presents an overview of the most recent advances in nonlinear science. It provides a unified view of nonlinear properties in many different systems and highlights many new developments. While volume 1 concentrates on mathematical theory and computational techniques and challenges, which are essential for the study of nonlinear science, this second volume deals with nonlinear excitations in several fields. These excitations can be localized and transport energy and matter in the form of breathers, solitons, kinks or quodons with very different characteristics, which are discussed in the book. They can also transport electric charge, in which case they are known as polarobreathers or solectrons. Nonlinear excitations can influence function and structure in biology, as for example, protein folding. In crystals and other condensed matter, they can modify transport properties, reaction kinetics and interact with defects. There are also engineering applications in electric lattices, Josephson junction arrays, waveguide arrays, photonic crystals and optical fibers. Nonlinear excitations are inherent to Bose-Einstein Condensates, constituting an excellent benchmark for testing their properties and providing a pathway for future discoveries in fundamental physics.
Author : Fatkhulla Abdullaev,Ole Bang,Mads Peter Sørensen
Publisher : Springer Science & Business Media
Page : 488 pages
File Size : 47,8 Mb
Release : 2002-01-31
Category : Mathematics
ISBN : 1402001916
Proceedings of the NATO Advanced Research Workshop, Tashkent, Uzbekistan, 2-6 October 2001
Author : Michael Shats,Horst Punzmann
Publisher : World Scientific
Page : 397 pages
File Size : 52,5 Mb
Release : 2006
Category : Science
ISBN : 9789812566980
This book is based on the lectures delivered at the 19th Canberra International Physics Summer School held at the Australian National University in Canberra (Australia) in January 2006.The problem of turbulence and coherent structures is of key importance in many fields of science and engineering. It is an area which is vigorously researched across a diverse range of disciplines such as theoretical physics, oceanography, atmospheric science, magnetically confined plasma, nonlinear optics, etc. Modern studies in turbulence and coherent structures are based on a variety of theoretical concepts, numerical simulation techniques and experimental methods, which cannot be reviewed effectively by a single expert.The main goal of these lecture notes is to introduce state-of-the-art turbulence research in a variety of approaches (theoretical, numerical simulations and experiments) and applications (fluids, plasmas, geophysics, nonlinear optical media) by several experts. A smooth introduction is presented to readers who are not familiar with the field, while reviewing the most recent advances in the area. This collection of lectures will provide a useful review for both postgraduate students and researchers new to the advancements in this field, as well as specialists seeking to expand their knowledge across different areas of turbulence research.
