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Theory of Nonlinear Lattices

Author: Morikazu Toda

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 233

ISBN-13: 3642832199

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.

Non-Linear Lattice

Author: Ignazio Licata and Sauro Succi

Publisher: MDPI

Published: 2018-07-17

Total Pages: 291

ISBN-13: 3038423068

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This book is a printed edition of the Special Issue "Non-Linear Lattice" that was published in Entropy

Dynamics of Lattice Materials

Author: A. Srikantha Phani

Publisher: John Wiley & Sons

Published: 2017-09-25

Total Pages: 312

ISBN-13: 1118729595

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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

Non-linear Lattice

Author: Ignazio Licata

Publisher:

Published: 2016

Total Pages:

ISBN-13: 9783038423072

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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

Nonlinear Mechanics of Crystals

Author: John D. Clayton

Publisher: Springer Science & Business Media

Published: 2010-11-01

Total Pages: 709

ISBN-13: 9400703503

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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.

Theory of Nonlinear Lattices

Author: Morikazu Toda

Publisher: Springer

Published: 1981

Total Pages: 0

ISBN-13: 9783642965852

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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.

Jacobi Operators and Completely Integrable Nonlinear Lattices

Author: Gerald Teschl

Publisher: American Mathematical Soc.

Published: 2000

Total Pages: 373

ISBN-13: 0821819402

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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.

Linear and Nonlinear Waves in Microstructured Solids

Author: Igor V. Andrianov

Publisher: CRC Press

Published: 2021-04-22

Total Pages: 322

ISBN-13: 1000372219

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This book uses asymptotic methods to obtain simple approximate analytic solutions to various problems within mechanics, notably wave processes in heterogeneous materials. Presenting original solutions to common issues within mechanics, this book builds upon years of research to demonstrate the benefits of implementing asymptotic techniques within mechanical engineering and material science. Focusing on linear and nonlinear wave phenomena in complex micro-structured solids, the book determines their global characteristics through analysis of their internal structure, using homogenization and asymptotic procedures, in line with the latest thinking within the field. The book’s cutting-edge methodology can be applied to optimal design, non-destructive control and in deep seismic sounding, providing a valuable alternative to widely used numerical methods. Using case studies, the book covers topics such as elastic waves in nonhomogeneous materials, regular and chaotic dynamics based on continualisation and discretization and vibration localization in 1D Linear and Nonlinear lattices. The book will be of interest to students, research engineers, and professionals specialising in mathematics and physics as well as mechanical and civil engineering.

Perspectives of Nonlinear Dynamics: Volume 1

Author: E. Atlee Jackson

Publisher: CUP Archive

Published: 1989

Total Pages: 532

ISBN-13: 9780521426329

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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.

Nonlinear Effects in Model Lattices of Metals

Author: Mikhail D. Starostenkov

Publisher: Materials Research Forum LLC

Published: 2024-02-10

Total Pages: 129

ISBN-13: 1644902885

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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.