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Nonlinear Waves and Pattern Dynamics
by Efim Pelinovsky Nizar Abcha Innocent MutabaziThis book addresses the fascinating phenomena associated with nonlinear waves and spatio-temporal patterns. These appear almost everywhere in nature from sand bed forms to brain patterns, and yet their understanding still presents fundamental scientific challenges. The reader will learn here, in particular, about the current state-of-the art and new results in: Nonlinear water waves: resonance, solitons, focusing, Bose-Einstein condensation, as well as and their relevance for the sea environment (sea-wind interaction, sand bed forms, fiber clustering) Pattern formation in non-equilibrium media: soap films, chimera patterns in oscillating media, viscoelastic Couette-Taylor flow, flow in the wake behind a heated cylinder, other pattern formation. The editors and authors dedicate this book to the memory of Alexander Ezersky, Professor of Fluid Mechanics at the University of Caen Normandie (France) from September 2007 to July 2016. Before 2007, he had served as a Senior Scientist at the Institute of Applied Physics of the Russian Academy of Sciences in Nizhny Novgorod (Russia). The chapters have been written by leading scientists in Nonlinear Physics, and the topics chosen so as to cover all the fields to which Prof. Ezersky himself contributed, by means of experimental, theoretical and numerical approaches. The volume will appeal to advanced students and researchers studying nonlinear waves and pattern dynamics, as well as other scientists interested in their applications in various natural media.
Nonlinear Waves and Solitons on Contours and Closed Surfaces
by Andrei LuduThis volume is an introduction to nonlinear waves and soliton theory in the special environment of compact spaces such a closed curves and surfaces and other domain contours. It assumes familiarity with basic soliton theory and nonlinear dynamical systems. The first part of the book introduces the mathematical concept required for treating the manifolds considered, providing relevant notions from topology and differential geometry. An introduction to the theory of motion of curves and surfaces - as part of the emerging field of contour dynamics - is given. The second and third parts discuss the modeling of various physical solitons on compact systems, such as filaments, loops and drops made of almost incompressible materials thereby intersecting with a large number of physical disciplines from hydrodynamics to compact object astrophysics. This book is intended for graduate students and researchers in mathematics, physics and engineering. This new edition has been thoroughly revised, expanded and updated.
Nonlinear Waves in Elastic Media
by A.G. Kulikovskii Elena I. SveshnikovaNonlinear Waves in Elastic Media explores the theoretical results of one-dimensional nonlinear waves, including shock waves, in elastic media. It is the first book to provide an in-depth and comprehensive presentation of the nonlinear wave theory while taking anisotropy effects into account. The theory is completely worked out and draws on 15 years of research by the authors, one of whom also wrote the 1965 classic Magnetohydrodynamics. Nonlinear Waves in Elastic Media emphasizes the behavior of quasitransverse waves and analyzes arbitrary discontinuity disintegration problems, illustrating that the solution can be non-unique - a surprising result. The solution is shown to be especially interesting when anisotropy and nonlinearity effects interact, even in small-amplitude waves. In addition, the text contains an independent mathematical chapter describing general methods to study hyperbolic systems expressing the conservation laws. The theoretical results described in Nonlinear Waves in Elastic Media allow, for the first time, discovery and interpretation of many new peculiarities inherent to the general problem of discontinuous solutions and so provide a valuable resource for advanced students and researchers involved with continuum mechanics and partial differential equations.
Nonlinear Waves: From Dissipative Solitons to Magnetic Solitons
by Emmanuel Kengne WuMing LiuThis book highlights the methods to engineer dissipative and magnetic nonlinear waves propagating in nonlinear systems. In the first part of the book, the authors present methodologically mathematical models of nonlinear waves propagating in one- and two-dimensional nonlinear transmission networks without/with dissipative elements. Based on these models, the authors investigate the generation and the transmission of nonlinear modulated waves, in general, and solitary waves, in particular, in networks under consideration. In the second part of the book, the authors develop basic theoretical results for the dynamics matter-wave and magnetic-wave solitons of nonlinear systems and of Bose–Einstein condensates trapped in external potentials, combined with the time-modulated nonlinearity. The models treated here are based on one-, two-, and three-component non-autonomous Gross–Pitaevskii equations. Based on the Heisenberg model of spin–spin interactions, the authors also investigate the dynamics of magnetization in ferromagnet with or without spin-transfer torque. This research book is suitable for physicists, mathematicians, engineers, and graduate students in physics, mathematics, and network and information engineering.
Nonlinear X-Ray Spectroscopy for Materials Science (Springer Series in Optical Sciences #246)
by Iwao Matsuda Ryuichi ArafuneX-ray experiments have been used widely in materials science, and conventional spectroscopy has been based on linear responses in light–matter interactions. Recent development of ultrafast light sources of tabletop lasers and X-ray free electron lasers reveals nonlinear optical phenomena in the X-ray region, and the measurement signals have been found to carry a further wealth of information on materials. This book overviews such nonlinear X-ray spectroscopy and its related issues for materials science. Each chapter is written by pioneers in the field and skillfully reviews the topics of nonlinear spectroscopy including X-ray multi-photon absorption and X-ray second harmonic generation. The chapters are divided depending on photon wavelength, ranging from extreme ultraviolet to (soft) X-ray. To facilitate readers’ comprehensive understanding, some of the chapters cover the conventional linear X-ray spectroscopy and basic principles of the non-linear responses. The book is mainly accessible as a primer for junior/senior- or graduate-level readers, and it also serves as a useful reference or guide even for established researchers in optical spectroscopy. The book offers readers opportunities to benefit from cutting-edge research in this new area of nonlinear X-ray spectroscopy.
Nonlinear and Complex Dynamics
by Albert C. Luo José António Machado Dumitru BaleanuNonlinear Dynamics of Complex Systems describes chaos, fractal and stochasticities within celestial mechanics, financial systems and biochemical systems. Part I discusses methods and applications in celestial systems and new results in such areas as low energy impact dynamics, low-thrust planar trajectories to the moon and earth-to-halo transfers in the sun, earth and moon. Part II presents the dynamics of complex systems including bio-systems, neural systems, chemical systems and hydro-dynamical systems. Finally, Part III covers economic and financial systems including market uncertainty, inflation, economic activity and foreign competition and the role of nonlinear dynamics in each.
Nonlinear and Modern Mathematical Physics: NMMP-2022, Tallahassee, Florida, USA (Virtual), June 17–19 (Springer Proceedings in Mathematics & Statistics #459)
by Solomon Manukure Wen-Xiu MaThis book gathers peer-reviewed, selected contributions from participants of the 6th International Workshop on Nonlinear and Modern Mathematical Physics (NMMP-2022), hosted virtually from June 17–19, 2022. Works contained in this volume cover topics like nonlinear differential equations, integrable systems, Hamiltonian systems, inverse scattering transform, Painleve's analysis, nonlinear wave phenomena and applications, numerical methods of nonlinear wave equations, quantum integrable systems, and more. In this book, researchers and graduate students in mathematics and related areas will find new methods and tools that only recently have been developed to solve nonlinear problems. The sixth edition of the NMMP workshop was organized by Florida A&M University in Tallahassee, Florida, USA, with support from the University of South Florida, Florida State University, Embry-Riddle Aeronautical University, Savannah State University, Prairie View A&M University, and Beijing Jiaotong University. The aim was to bring together researchers from around the world to present their findings and foster collaboration for future research.
Nonlinear, Nonlocal and Fractional Turbulence: Alternative Recipes for the Modeling of Turbulence
by Kolumban Hutter Peter William EgolfExperts of fluid dynamics agree that turbulence is nonlinear and nonlocal. Because of a direct correspondence, nonlocality also implies fractionality. Fractional dynamics is the physics related to fractal (geometrical) systems and is described by fractional calculus. Up-to-present, numerous criticisms of linear and local theories of turbulence have been published. Nonlinearity has established itself quite well, but so far only a very small number of general nonlocal concepts and no concrete nonlocal turbulent flow solutions were available. This book presents the first analytical and numerical solutions of elementary turbulent flow problems, mainly based on a nonlocal closure. Considerations involve anomalous diffusion (Lévy flights), fractal geometry (fractal-β, bi-fractal and multi-fractal model) and fractional dynamics. Examples include a new ‘law of the wall’ and a generalization of Kraichnan’s energy-enstrophy spectrum that is in harmony with non-extensive and non-equilibrium thermodynamics (Tsallis thermodynamics) and experiments. Furthermore, the presented theories of turbulence reveal critical and cooperative phenomena in analogy with phase transitions in other physical systems, e.g., binary fluids, para-ferromagnetic materials, etc.; the two phases of turbulence identifying the laminar streaks and coherent vorticity-rich structures. This book is intended, apart from fluids specialists, for researchers in physics, as well as applied and numerical mathematics, who would like to acquire knowledge about alternative approaches involved in the analytical and numerical treatment of turbulence.
Nonlinearity in Energy Harvesting Systems
by Abdelali El Aroudi Dimitri Galayko Elena Blokhina Eduard AlarconThis book is a single-source guide to nonlinearity and nonlinear techniques in energy harvesting, with a focus on vibration energy harvesters for micro and nanoscale applications. The authors demonstrate that whereas nonlinearity was avoided as an undesirable phenomenon in early energy harvesters, now it can be used as an essential part of these systems. Readers will benefit from an overview of nonlinear techniques and applications, as well as deeper insight into methods of analysis and modeling of energy harvesters, employing different nonlinearities. The role of nonlinearity due to different aspects of an energy harvester is discussed, including nonlinearity due to mechanical-to-electrical conversion, nonlinearity due to conditioning electronic circuits, nonlinearity due to novel materials (e. g. , graphene), etc. Coverage includes tutorial introductions to MEMS and NEMS technology, as well as a wide range of applications, such as nonlinear oscillators and transducers for energy harvesters and electronic conditioning circuits for effective energy processing.
Nonlinearity in Structural Dynamics: Detection, Identification and Modelling
by K WordenMany types of engineering structures exhibit nonlinear behavior under real operating conditions. Sometimes the unpredicted nonlinear behavior of a system results in catastrophic failure. In civil engineering, grandstands at sporting events and concerts may be prone to nonlinear oscillations due to looseness of joints, friction, and crowd movements.
Nonlinearity, Bounded Rationality, and Heterogeneity: Some Aspects of Market Economies as Complex Systems
by Tamotsu OnozakiThis book follows a nonlinear approach in considering both chaotic dynamical models and agent-based simulation models of economics as well as their dynamical behaviors. Three key words arising in this context are "nonlinearity", "bounded rationality" and "heterogeneity", which make up the title of the book. Nonlinearity is the warp that runs throughout all models because systems that exhibit chaotic or other complex behavior in the absence of any exogenous disturbances are absolutely nonlinear. Bounded rationality constitutes the woof because economic systems do not exhibit complex behavior if all agents are perfectly rational as is usually assumed in neoclassical economics. Agents who are boundedly rational have to struggle to do their best under informational restriction and tend to adapt themselves to the economic environment without knowing what is the best. Furthermore, heterogeneity of firms or consumers dyes the fabric of complex dynamics woven from the warp and woof.
Nonlocal Euler–Bernoulli Beam Theories: A Comparative Study (SpringerBriefs in Applied Sciences and Technology)
by Jingkai ChenThis book presents a comparative study on the static responses of the Euler-Bernoulli beam governed by nonlocal theories, including the Eringen’s stress-gradient beam theory, the Mindlin’s strain-gradient beam theory, the higher-order beam theory and the peridynamic beam theory. Benchmark examples are solved analytically and numerically using these nonlocal beam equations, including the simply-supported beam, the clamped-clamped beam and the cantilever beam. Results show that beam deformations governed by different nonlocal theories at different boundary conditions show complex behaviors. Specifically, the Eringen’s stress-gradient beam equation and the peridynamic beam equation yield a much softer beam deformation for simply-supported beam and clamped-clamped beam, while the beam governed by the Mindlin’s strain-gradient beam equation is much stiffer. The cantilever beam exhibits a completely different behavior. The higher-order beam equation can be stiffer or softer depending on the values of the two nonlocal parameters. Moreover, the deformation fluctuation of the truncated order peridynamic beam equation is observed and explained from the singularity aspect of the solution expression. This research casts light on the fundamental explanation of nonlocal beam theories in nano-electromechanical systems.
Nonnitrogenous Organocatalysis (Organocatalysis Series)
by Andrew HarnedSince the 1990s the synthetic community has shown a growing interest in the development of catalytic reactions that employ entirely organic catalysts – so-called ‘organocatalysts’. With the current emphasis on green chemistry throughout the chemical industry, organocatalysis has become indispensible. In spite of this growth and recognition, there can be a misconception that organocatalysts are only based on nitrogen-containing functional groups (amines, ureas, and quaternary ammonium salts, for example), and are only useful for asymmetric reactions. <P><P> Nonnitrogenous Organocatalysis shows that the umbrella of organocatalysis covers other main group elements besides nitrogen, and the coverage is not just limited to asymmetric methods. Many of the catalysts and mechanisms discussed may not have a viable asymmetric variant or cannot be rendered asymmetric at all. This does not make them any less useful, as illustrated in this book.
Nonparametric Bayesian Inference in Biostatistics
by Peter Müller Riten MitraAs chapters in this book demonstrate, BNP has important uses in clinical sciences and inference for issues like unknown partitions in genomics. Nonparametric Bayesian approaches (BNP) play an ever expanding role in biostatistical inference from use in proteomics to clinical trials. Many research problems involve an abundance of data and require flexible and complex probability models beyond the traditional parametric approaches. As this book's expert contributors show, BNP approaches can be the answer. Survival Analysis, in particular survival regression, has traditionally used BNP, but BNP's potential is now very broad. This applies to important tasks like arrangement of patients into clinically meaningful subpopulations and segmenting the genome into functionally distinct regions. This book is designed to both review and introduce application areas for BNP. While existing books provide theoretical foundations, this book connects theory to practice through engaging examples and research questions. Chapters cover: clinical trials, spatial inference, proteomics, genomics, clustering, survival analysis and ROC curve.
Nonperturbative Topological Phenomena in QCD and Related Theories (Lecture Notes in Physics #977)
by Edward ShuryakThis book introduces a variety of aspects in nonperturbative Quantum Chromodynamics (QCD), focusing on the topological objects present in gauge theories. These objects, like magnetic monopoles, instantons, instanto-dysons, sphalerons, QCD flux tubes, etc, are first introduced individually and, later, treated collectively. As ensembles, they produce various phenomena that can be modeled numerically in lattice gauge theories and such collective effects, produced on the lattice, are extensively discussed in some chapters. In turn, the notion of duality, which is crucial in modern field/string theories, is elucidated by taking into consideration the electric-magnetic duality, the Poisson duality, and the AdS/CFT duality. This monograph is based on various lectures given by Edward Shuryak at Stony Brook during the last three decades and it is meant for advanced graduate students and young researchers in theoretical and mathematical physics who are willing to consolidate their knowledge in the topological phenomena encountered in fundamental QCD research.
Nonplussed!: Mathematical Proof of Implausible Ideas
by Julian HavilMath—the application of reasonable logic to reasonable assumptions—usually produces reasonable results. But sometimes math generates astonishing paradoxes—conclusions that seem completely unreasonable or just plain impossible but that are nevertheless demonstrably true. Did you know that a losing sports team can become a winning one by adding worse players than its opponents? Or that the thirteenth of the month is more likely to be a Friday than any other day? Or that cones can roll unaided uphill? In Nonplussed!—a delightfully eclectic collection of paradoxes from many different areas of math—popular-math writer Julian Havil reveals the math that shows the truth of these and many other unbelievable ideas.Nonplussed! pays special attention to problems from probability and statistics, areas where intuition can easily be wrong. These problems include the vagaries of tennis scoring, what can be deduced from tossing a needle, and disadvantageous games that form winning combinations. Other chapters address everything from the historically important Torricelli's Trumpet to the mind-warping implications of objects that live on high dimensions. Readers learn about the colorful history and people associated with many of these problems in addition to their mathematical proofs.Nonplussed! will appeal to anyone with a calculus background who enjoys popular math books or puzzles.
Nonrelativistic Quantum X-Ray Physics
by Stefan P. Hau-RiegeProviding a solid theoretical background in photon-matter interaction, Nonrelativistic Quantum X-Ray Physics enables readers to understand experiments performed at XFEL-facilities and x-ray synchrotrons. As a result, after reading this book, scientists and students will be able to outline and perform calculations of some important x-ray-matter interaction processes. Key features of the contents are that the scope reaches beyond the dipole approximation when necessary and that it includes short-pulse interactions. To aid the reader in this transition, some relevant examples are discussed in detail, while non-relativistic quantum electrodynamics help readers to obtain an in-depth understanding of the formalisms and processes. The text presupposes a basic (undergraduate-level) understanding of mechanics, electrodynamics, and quantum mechanics. However, more specialized concepts in these fields are introduced and the reader is directed to appropriate references. While primarily benefiting users of x-ray light-sources, the material is equally of relevance to researchers in various disciplines, such as life sciences, biology, materials science, physics, and chemistry that plan on applying these new facilities in their respective fields.
Nonribosomal Peptide and Polyketide Biosynthesis
by Bradley S. EvansThis volume presents an overview of nonribosomal peptide synthetase (NRPS) and polyketide synthase (PKS) structure and function. It then continues with methods for the analysis of these pathways including conventional enzymological assays, contemporary mass spectrometric analysis techniques, specialized molecular biological approaches applicable to NRPSs and PKSs, and small molecule analysis tools tailored to this very special class of natural products, and concludes by examining bioinformatics tools for the analysis of these enzymes, pathways, and molecules. Written for the highly successful Methods in Molecular Biology series, chapters include introductions to their respective topics, lists of the necessary materials and reagents, step-by-step, readily reproducible laboratory protocols, and tips on troubleshooting and avoiding known pitfalls. Authoritative and practical, Nonribosomal Peptide and Polyketide Biosynthesis: Methods and Protocols serves as a valuable reference for those experienced in studying NRPS and PKS enzymes, pathways, and natural products as well as a gateway for those just entering the field.
Nonsense on Stilts: How To Tell Science From Bunk
by Massimo PigliucciRecent polls suggest that fewer than 40 percent of Americans believe in Darwin’s theory of evolution, despite it being one of science’s best-established findings. Parents still refuse to vaccinate their children for fear it causes autism, though this link has been consistently disproved. And about 40 percent of Americans believe that the threat of global warming is exaggerated, including many political leaders. In this era of fake news and alternative facts, there is more bunk than ever. But why do people believe in it? And what causes them to embrace such pseudoscientific beliefs and practices? In this fully revised second edition, noted skeptic Massimo Pigliucci sets out to separate the fact from the fantasy in an entertaining exploration of the nature of science, the borderlands of fringe science, and—borrowing a famous phrase from philosopher Jeremy Bentham—the nonsense on stilts. Presenting case studies on a number of controversial topics, Pigliucci cuts through the ambiguity surrounding science to look more closely at how science is conducted, how it is disseminated, how it is interpreted, and what it means to our society. The result is in many ways a “taxonomy of bunk” that explores the intersection of science and culture at large. No one—neither the public intellectuals in the culture wars between defenders and detractors of science nor the believers of pseudoscience themselves—is spared Pigliucci’s incisive analysis in this timely reminder of the need to maintain a line between expertise and assumption. Broad in scope and implication, Nonsense on Stilts is a captivating guide for the intelligent citizen who wishes to make up her own mind while navigating the perilous debates that will shape the future of our planet.
Nonsense on Stilts: How to Tell Science from Bunk
by Massimo PigliucciNonsense on Stilts is a timely reminder of the need to maintain a line between expertise and assumption. Broad in scope and implication, it is also ultimately a captivating guide for the intelligent citizen who wishes to make up her own mind while navigating the perilous debates that will affect the future of our planet.
Nonsense-Mediated mRNA Decay
by Lynne E. MaquatNonsense-Mediated mRNA Decay is the first book devoted to nonsense-mediated mRNA decay (NMD). The rationale for such a book is the enormous information that studies of NMD have provided on the intricacies of post-transcriptional gene expression. The first five sections of the book are divided according to organism and begin with chapters on S. cere
Nonsmooth Lyapunov Analysis in Finite and Infinite Dimensions (Communications and Control Engineering)
by Yury OrlovNonsmooth Lyapunov Analysis in Finite and Infinite Dimensions provides helpful tools for the treatment of a broad class of dynamical systems that are governed, not only by ordinary differential equations but also by partial and functional differential equations. Existing Lyapunov constructions are extended to discontinuous systems—those with variable structure and impact—by the involvement of nonsmooth Lyapunov functions. The general theoretical presentation is illustrated by control-related applications; the nonsmooth Lyapunov construction is particularly applied to the tuning of sliding-mode controllers in the presence of mismatched disturbances and to orbital stabilization of the bipedal gate. The nonsmooth construction is readily extendible to the control and identification of distributed-parameter and time-delay systems.The first part of the book outlines the relevant fundamentals of benchmark models and mathematical basics. The second concentrates on the construction of nonsmooth Lyapunov functions. Part III covers design and applications material.This book will benefit the academic research and graduate student interested in the mathematics of Lyapunov equations and variable-structure control, stability analysis and robust feedback design for discontinuous systems. It will also serve the practitioner working with applications of such systems. The reader should have some knowledge of dynamical systems theory, but no background in discontinuous systems is required—they are thoroughly introduced in both finite- and infinite-dimensional settings.
Nonsmooth Mechanics
by Bernard BrogliatoNow in its third edition, this standard reference is a comprehensive treatment of nonsmooth mechanical systems refocused to give more prominence to issues connected with control and modelling. It covers Lagrangian and Newton-Euler systems, detailing mathematical tools such as convex analysis and complementarity theory. The ways in which nonsmooth mechanics influence and are influenced by well-posedness analysis, numerical analysis and simulation, modelling and control are explained. Contact/impact laws, stability theory and trajectory-tracking control are given detailed exposition connected by a mathematical framework formed from complementarity systems and measure-differential inclusions. Links are established with electrical circuits with set-valued nonsmooth elements as well as with other nonsmooth dynamical systems like impulsive and piecewise linear systems. Nonsmooth Mechanics (third edition) retains the topical structure familiar from its predecessors but has been substantially rewritten, edited and updated to account for the significant body of results that have emerged in the twenty-first century--including developments in: the existence and uniqueness of solutions; impact models; extension of the Lagrange-Dirichlet theorem and trajectory tracking; and well-posedness of contact complementarity problems with and without friction. Many figures (both new and redrawn to improve the clarity of the presentation) and examples are used to illustrate the theoretical developments. Material introducing the mathematics of nonsmooth mechanics has been improved to reflect the broad range of applications interest that has developed since publication of the second edition. The detail of some mathematical essentials is provided in four appendices. With its improved bibliography of over 1,300 references and wide-ranging coverage, Nonsmooth Mechanics (third edition) is sure to be an invaluable resource for researchers and postgraduates studying the control of mechanical systems, robotics, granular matter and relevant fields of applied mathematics. "The book's two best features, in my view are its detailed survey of the literature. . . and its detailed presentation of many examples illustrating both the techniques and their limitations. . . For readers interested in the field, this book will serve as an excellent introductory survey. " Andrew Lewis in Automatica "It is written with clarity, contains the latest research results in the area of impact problems for rigid bodies and is recommended for both applied mathematicians and engineers. " Panagiotis D. Panagiotopoulos in Mathematical Reviews "The presentation is excellent in combining rigorous mathematics with a great number of examples. . . allowing the reader to understand the basic concepts. " Hans Troger in Mathematical Abstracts
Nonsmooth Mechanics and Convex Optimization
by Yoshihiro Kanno"This book concerns matter that is intrinsically difficult: convex optimization, complementarity and duality, nonsmooth analysis, linear and nonlinear programming, etc. The author has skillfully introduced these and many more concepts, and woven them into a seamless whole by retaining an easy and consistent style throughout. The book is not all the
Nonstationary Resonant Dynamics of Oscillatory Chains and Nanostructures
by Leonid I. Manevitch Agnessa Kovaleva Valeri Smirnov Yuli StarosvetskyThis book suggests a new common approach to the study of resonance energy transport based on the recently developed concept of Limiting Phase Trajectories (LPTs), presenting applications of the approach to significant nonlinear problems from different fields of physics and mechanics. In order to highlight the novelty and perspectives of the developed approach, it places the LPT concept in the context of dynamical phenomena related to the energy transfer problems and applies the theory to numerous problems of practical importance. This approach leads to the conclusion that strongly nonstationary resonance processes in nonlinear oscillator arrays and nanostructures are characterized either by maximum possible energy exchange between the clusters of oscillators (coherence domains) or by maximum energy transfer from an external source of energy to the chain. The trajectories corresponding to these processes are referred to as LPTs. The development and the use of the LPTs concept are motivated by the fact that non-stationary processes in a broad variety of finite-dimensional physical models are beyond the well-known paradigm of nonlinear normal modes (NNMs), which is fully justified either for stationary processes or for nonstationary non-resonance processes described exactly or approximately by the combinations of the non-resonant normal modes. Thus, the role of LPTs in understanding and analyzing of intense resonance energy transfer is similar to the role of NNMs for the stationary processes. The book is a valuable resource for engineers needing to deal effectively with the problems arising in the fields of mechanical and physical applications, when the natural physical model is quite complicated. At the same time, the mathematical analysis means that it is of interest to researchers working on the theory and numerical investigation of nonlinear oscillations.