This introductory text presents the basic aspects and most important features of various types of resonances and anti-resonances in dynamical systems. In particular, for each resonance, it covers the theoretical concepts, illustrates them with case studies, and reviews the available information on mechanisms, characterization, numerical simulations, experimental realizations, possible quantum analogues, applications and significant advances made over the years. Resonances are one of the most fundamental phenomena exhibited by nonlinear systems and refer to specific realizations of maximum response of a system due to the ability of that system to store and transfer energy received from an external forcing source. Resonances are of particular importance in physical, engineering and biological systems - they can prove to be advantageous in many applications, while leading to instability and even disasters in others. The book is self-contained, providing the details of mathematical derivations and techniques involved in numerical simulations. Though primarily intended for graduate students, it can also be considered a reference book for any researcher interested in the dynamics of resonant phenomena.

The method of multiple scales has been used to analyze the motion of rolling reentry bodies under the influence of nonlinear pitch, damping, and Magnus moments. Each of these moments is assumed to be a cubic function of angle of attack.

Nonlinear resonance analysis is a unique mathematical tool that can be used to study resonances in relation to, but independently of, any single area of application. This is the first book to present the theory of nonlinear resonances as a new scientific field, with its own theory, computational methods, applications and open questions. The book includes several worked examples, mostly taken from fluid dynamics, to explain the concepts discussed. Each chapter demonstrates how nonlinear resonance analysis can be applied to real systems, including large-scale phenomena in the Earth's atmosphere and novel wave turbulent regimes, and explains a range of laboratory experiments. The book also contains a detailed description of the latest computer software in the field. It is suitable for graduate students and researchers in nonlinear science and wave turbulence, along with fluid mechanics and number theory. Colour versions of a selection of the figures are available at www.cambridge.org/9780521763608.

One of the most important features of nonlinear systems with several degrees of freedom is the presence of internal resonances at certain relations between natural frequencies of different modes. This monograph is the first book devoted predominantly to internal resonances in different mechanical systems including those of practical importance.The main purpose is to consider the internal resonances from the general point of view and to elucidate their role in applied nonlinear dynamics by using an efficient approach based on introducing the complex representation of equations of motion (together with the multiple scale method). Considered here are autonomous and nonautonomous discrete two-degree-of-freedom systems, infinite chains of particles, and continuous systems, including circular rings and cylindrical shells. Specific attention is paid to the case of one-to-one internal resonance in systems with cubic nonlinearities. Steady-state and nonstationary regimes of motion, interaction of the internal and external resonances at forced oscillations, and bifurcations of steady-state modes and their stability are systematically studied.

This unique book aims to treat a class of nonlinear waves that are reflected from the boundaries of media of finite extent. It involves both standing (unforced) waves and resonant oscillations due to external periodic forcing. The waves are both hyperbolic and dispersive. To achieve this aim, the book develops the necessary understanding of linear waves and the mathematical techniques of nonlinear waves before dealing with nonlinear waves in bounded media. The examples used come mainly from gas dynamics, water waves and viscoelastic waves.

This unique book explores both theoretical and experimental aspects of nonlinear vibrations and stability of shells and plates. It is ideal for researchers, professionals, students, and instructors. Expert researchers will find the most recent progresses in nonlinear vibrations and stability of shells and plates, including advanced problems of shells with fluid-structure interaction. Professionals will find many practical concepts, diagrams, and numerical results, useful for the design of shells and plates made of traditional and advanced materials. They will be able to understand complex phenomena such as dynamic instability, bifurcations, and chaos, without needing an extensive mathematical background. Graduate students will find (i) a complete text on nonlinear mechanics of shells and plates, collecting almost all the available theories in a simple form, (ii) an introduction to nonlinear dynamics, and (iii) the state of art on the nonlinear vibrations and stability of shells and plates, including fluid-structure interaction problems.

The theory of waves is generalized on cases of strongly nonlinear waves, multivalued waves, and particle–waves. The appearance of these waves in various continuous media and physical fields is explained by resonances and nonlinearity effects. Extreme waves emerging in different artificial and natural systems from atom scale to the Universe are explored. Vast amounts of experimental data and comparisons of them with the results of the developed theory are presented. The book was written for graduate students as well as for researchers and engineers in the fields of geophysics, nonlinear wave studies, cosmology, physical oceanography, and ocean and coastal engineering. It is designed as a professional reference for those working in the wave analysis and modeling fields.

It is a source of great pleasure to help launch the new Springer Series in Solid-State Sciences. Some years aga I wrote my book, Principles of Magnetic Resonance. I have been eager to publish a new book concerned with spin temperature, double resonance, and spin-flip line narrowing, topics basic to important trends in present-day magnetic resonance which were not treated in my earlier book. Invitations to lecture in Osaka, Japan, in Leuven, Belgium, and Lausanne, Switzerland, had provided occasion to prepare first drafts of the new topics and to get student feedback. My plans were changed, however, when I learned that Principles of M agnetic Resonance was no longer available. Dr. Lotsch, Physics Editor of Springer-Verlag, and I decided it made sense to combine the new book with a modified old one, thereby continuing to make available a complete text in basic magnetic resonance written with a philosophy of presenting a thorough treatment of a small number of concepts which are key to large areas of magnetic res on an ce. In addition to adding three new chapters, I have added new material to the original chapters, have added two new appendices-one on the use of Bloch equations to describe rate processes, the other on the effect of diffusion on spin echoes-and have augmented the collection of homework problems.

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The first nonlinear optical effect was observed in the 19th century by John Kerr. Nonlinear optics, however, started to grow up only after the invention of the laser, when intense light sources became easily available. The seminal studies by Peter Franken and Nicolaas Bloembergen, in the 1960s, paved the way for the development of today’s nonlinear photonics, the field of research that encompasses all the studies, designs, and implementations of nonlinear optical devices that can be used for the generation, communication, and processing of information. This field has attracted significant attention, partly due to the great potential of exploiting the optical nonlinearities of new or advanced materials to induce new phenomena and achieve new functions. According to Clarivate Web of Science, almost 200,000 papers were published that refer to the topic “nonlinear optic*”. Over 36,000 papers were published in the last four years (2015–2018) with the same keyword, and over 17,000 used the keyword “nonlinear photonic*”. The present Special Issue of Micromachines aims at reviewing the current state of the art and presenting perspectives of further development. Fundamental and applicative aspects are considered, with special attention paid to hot topics that may lead to technological and scientific breakthroughs.