Exact Solutions and Invariant Subspaces of Nonlinear Partial Differential Equations in Mechanics and Physics is the first book to provide a systematic construction of exact solutions via linear invariant subspaces for nonlinear differential operators. Acting as a guide to nonlinear evolution equations and models from physics and mechanics, the book focuses on the existence of new exact solutions on linear invariant subspaces for nonlinear operators and their crucial new properties. This practical reference deals with various partial differential equations (PDEs) and models that exhibit some common nonlinear invariant features. It begins with classical as well as more recent examples of solutions on invariant subspaces. In the remainder of the book, the authors develop several techniques for constructing exact solutions of various nonlinear PDEs, including reaction-diffusion and gas dynamics models, thin-film and Kuramoto-Sivashinsky equations, nonlinear dispersion (compacton) equations, KdV-type and Harry Dym models, quasilinear magma equations, and Green-Naghdi equations. Using exact solutions, they describe the evolution properties of blow-up or extinction phenomena, finite interface propagation, and the oscillatory, changing sign behavior of weak solutions near interfaces for nonlinear PDEs of various types and orders. The techniques surveyed in Exact Solutions and Invariant Subspaces of Nonlinear Partial Differential Equations in Mechanics and Physics serve as a preliminary introduction to the general theory of nonlinear evolution PDEs of different orders and types.
Deals with the theoretical, analytical and advanced numerical study of the structure and dynamics of one-dimensional as well as two- and three-dimensional solitons and nonlinear waves described by Korteweg-de Vries (KdV), Kadomtsev-Petviashvili (KP), nonlinear Schrodinger (NLS) and derivative NLS (DNLS) classes of equations.
Wave Turbulence refers to the statistical theory of weakly nonlinear dispersive waves. There is a wide and growing spectrum of physical applications, ranging from sea waves, to plasma waves, to superfluid turbulence, to nonlinear optics and Bose-Einstein condensates. Beyond the fundamentals the book thus also covers new developments such as the interaction of random waves with coherent structures (vortices, solitons, wave breaks), inverse cascades leading to condensation and the transitions between weak and strong turbulence, turbulence intermittency as well as finite system size effects, such as “frozen” turbulence, discrete wave resonances and avalanche-type energy cascades. This book is an outgrow of several lectures courses held by the author and, as a result, written and structured rather as a graduate text than a monograph, with many exercises and solutions offered along the way. The present compact description primarily addresses students and non-specialist researchers wishing to enter and work in this field.
This monograph systematically develops and considers the so-called "dressing method" for solving differential equations (both linear and nonlinear), a means to generate new non-trivial solutions for a given equation from the (perhaps trivial) solution of the same or related equation. Throughout, the text exploits the "linear experience" of presentation, with special attention given to the algebraic aspects of the main mathematical constructions and to practical rules of obtaining new solutions.
Modulational Interactions in Plasmas is the first book to present all the basic considerations relevant to the topic. It adopts a simple and universal approach, based on new methods developed for the description of modulation interactions in arbitrary media. Emphasis is given to the role of modulational interactions in fundamental topics, such as laser acceleration, the generation of strong magnetic fields, r.f. plasma heating and current drive, physical phenomena in active geophysical and space experiments, interactions of r.f. radiation with the ionosphere, etc. The methods employed can also be applied to other areas of physics. Audience: Researchers in plasma and laser physics, and nonlinear optics.
For the first time, exact analytical solutions are available for some of the most interesting types of problems arising in physics and applied mathematics. Hydrodynamics of Unstable Media outlines the theory of "quasi-gaseous" unstable media, and demonstrates how the theory can be used to obtain analytical solutions. Until now, the solutions to many of the examples considered in this new book have been numerical or partial solutions. By developing a new theory of hydrodynamics for unstable media, the authors provide a means for scientists and mathematicians to solve problems exactly and analytically. Solutions to some 50 problems are provided! Hydrodynamics of Unstable Media features interdisciplinary discussions by internationally recognized authors.
This volume collects for the first time in English the most representative and enlightening of Prokofiev's letters, including some previously suppressed missives that have never before been published. Expertly translated and annotated by Harlow Robinson, the correspondence presented here covers Prokofiev's earliest years at St. Petersburg Conservatory, his extensive worldwide travels, and his return to Moscow. Among the correspondents are childhood friend Vera Alpers, harpist Eleonora Damskaya, ballet impresario Sergei Diaghilev, theatrical director Vsevolod Meyerhold, Soviet critic Boris Asafiev, composers Vernon Duke and Nikolai Miaskovsky, soprano Nina Koshetz, musicologist Nicolas Slonimsky, violinist Jascha Heifetz, conductor Serge Koussevitsky, and film director Sergei Eisenstein. Prokofiev vividly describes, often with dramatic flair and a quirky sense of humor, concerts, performances, his compositions, political events, and meetings with other musicians and composers. His observations are peppered with musical gossip as well as eccentric, original, and disarmingly apolitical insights.
This book addresses the peculiarities of nonlinear wave propagation in waveguides and explains how the stratification depends on the waveguide and confinement. An example of this is an optical fibre that does not allow light to pass through a density jump. The book also discusses propagation in the nonlinear regime, which is characterized by a specific waveform and amplitude, to demonstrate so-called solitonic behaviour. In this case, a wave may be strongly localized, and propagates with a weak change in shape. In the waveguide case there are additional contributions of dispersion originating from boundary or asymptotic conditions. Offering concrete guidance on solving application problems, this essentially (more than twice) expanded second edition includes various aspects of guided propagation of nonlinear waves as well as new topics like solitonic behaviour of one-mode and multi-mode excitation and propagation and plasma waveguides, propagation peculiarities of electromagnetic waves in metamaterials, new types of dispersion, dissipation, electromagnetic waveguides, planetary waves and plasma waves interaction.The key feature of the solitonic behaviour is based on Coupled KdV and Coupled NS systems. The systems are derived in this book and solved numerically with the proof of stability and convergence. The domain wall dynamics of ferromagnetic microwaveguides and Bloch waves in nano-waveguides are also included with some problems of magnetic momentum and charge transport.
What would it feel like To Run the World? Soviet rulers spent the Cold War trying desperately to find out. Perennial insecurities, delusions of grandeur, and desire for recognition propelled Moscow on a headlong quest for global power, with dire consequences and painful legacies that continue to shape our world.
Discover the latest advances in ferroelectric and piezoelectric material sciences with this comprehensive monograph, divided into six chapters, each offering unique insights into the field.Chapter 1 delves into the manufacture and study of new ceramic materials, focusing on complex oxides of various metals (Aurivillius phases). The authors explore layered bismuth titanates and niobates, known for their high Curie temperature, and discuss how varying their chemical composition can lead to significant changes in their electrophysical properties. Chapter 2 explores the fascinating world of ferroelectrics — dielectrics with spontaneous polarization. Mathematical models and approaches of fractional calculus are used to understand the process of polarization switching in these materials, shedding light on the fractality of electrical responses. In Chapter 3, readers gain valuable insights into the inhomogeneous polarization process of polycrystalline ferroelectrics, a crucial stage in creating piezoceramic samples for energy converters. The authors present a comprehensive mathematical model that allows the determination of various characteristics, including dielectric and piezoelectric hysteresis loops and the effect of attenuation processes.Chapter 4 focuses on state-of-the-art piezoelectric energy harvesting, discussing theoretical, experimental, and computer modelling approaches. The authors discuss piezoelectric generators (PEGs) of different types (cantilever, stack and axis) and nonlinear effects arising at their operation. Chapter 5 presents expanded test and finite element models for cantilever-type and axial-type PEGs with active elements. The studies cover various structural and electric schemes of the PEGs with proof mass, bimorph and cylindrical piezoelectric elements, and excitation loads. Finally, Chapter 6 reviews some results in the last five years, obtained in modelling the vibration of devices from piezoactive materials, including five important effects: piezoelectric, flexoelectric, pyroelectric, piezomagnetic and flexomagnetic.As a diverse addition to the literature, this book is a relevant resource for researchers, engineers, and students seeking to expand their knowledge of cutting-edge developments in this exciting field.
2010. After graduating from university in Moscow, a native of Argentina, Agata Garcia Lopez, should return to her homeland. Before leaving home, she decides to visit Yemen, where her good university friend Andrey Zorin serves at the Russian embassy. However, a few days after her arrival in the Yemeni capital, a war begins in the strife-torn country. To return to Moscow, the girl will have to take part in an operation to evacuate Russian citizens. And at the same time to sort out her feelings for the friend who invited her... The story is an artistic, not a documentary-historical work. All her characters and the events described are completely fictional. The book may be of interest to fans of adventure prose and fiction about the Arab Middle East. Translated from Russian.
This book presents a 360-degree picture of the world of insects and explores how their existence affects our lives: the "good, bad, and ugly" aspects of their interactions with humankind. It provides a lucid introductory text for beginning undergraduate students in the life sciences, particularly those pursuing beginner courses in entomology, agriculture, and botany.
This book presents new approaches to R&D of piezoelectric actuators and generators of different types based on established, original constructions and contemporary research into framework of theoretical, experimental, and numerical methods of physics, mechanics, and materials science. Improved technical solutions incorporated into the devices demonstrate high output values of voltage and power, allowing application of the goods in various areas of energy harvesting. The book is divided into seven chapters, each presenting main results of the chapter, along with a brief exposition of novel findings from around the world proving context for the author’s results. It presents particular results of the Soviet and Russian schools of Mechanics and Material Sciences not previously available outside of Russia.
This is the first book on synthetic data for deep learning, and its breadth of coverage may render this book as the default reference on synthetic data for years to come. The book can also serve as an introduction to several other important subfields of machine learning that are seldom touched upon in other books. Machine learning as a discipline would not be possible without the inner workings of optimization at hand. The book includes the necessary sinews of optimization though the crux of the discussion centers on the increasingly popular tool for training deep learning models, namely synthetic data. It is expected that the field of synthetic data will undergo exponential growth in the near future. This book serves as a comprehensive survey of the field. In the simplest case, synthetic data refers to computer-generated graphics used to train computer vision models. There are many more facets of synthetic data to consider. In the section on basic computer vision, the book discusses fundamental computer vision problems, both low-level (e.g., optical flow estimation) and high-level (e.g., object detection and semantic segmentation), synthetic environments and datasets for outdoor and urban scenes (autonomous driving), indoor scenes (indoor navigation), aerial navigation, and simulation environments for robotics. Additionally, it touches upon applications of synthetic data outside computer vision (in neural programming, bioinformatics, NLP, and more). It also surveys the work on improving synthetic data development and alternative ways to produce it such as GANs. The book introduces and reviews several different approaches to synthetic data in various domains of machine learning, most notably the following fields: domain adaptation for making synthetic data more realistic and/or adapting the models to be trained on synthetic data and differential privacy for generating synthetic data with privacy guarantees. This discussion is accompanied by an introduction into generative adversarial networks (GAN) and an introduction to differential privacy.
This IBM® Redbooks® publication captures several of the preferred practices and describes the performance gains that can be achieved by implementing the IBM System Storage® SAN Volume Controller and IBM Storwize® V7000 powered by IBM Spectrum VirtualizeTM V8.2.1. These practices are based on field experience. This book highlights configuration guidelines and preferred practices for the storage area network (SAN) topology, clustered system, back-end storage, storage pools and managed disks, volumes, remote copy services, and hosts. Then it provides performance guidelines for SAN Volume Controller, back-end storage, and applications. It explains how you can optimize disk performance with the IBM System Storage Easy Tier® function. It also provides preferred practices for monitoring, maintaining, and troubleshooting SAN Volume Controller and Storwize V7000. This book is intended for experienced storage, SAN, and SAN Volume Controller administrators and technicians. Understanding his book requires advanced knowledge of the SAN Volume Controller and Storwize V7000 and SAN environments. Important: On 11th February 2020 IBM announced the arrival of SAN Volume Controller SA2 and SV2, and IBM FlashSystem® 7200 to the family. This book was written specifically for prior versions of SVC and Storwize V7000; however, most of the general principles will apply. If you are in any doubt as to their applicability then you should work with your local IBM representative. This book will be updated to comprehensively include SAN Volume Controller SA2 and SV2 and FlashSystem 7200 in due course.
The dynamical projectors method proves to reduce a multicomponent problem to the simplest one-component problem with its solution determined by specific initial or boundary conditions. Its universality and application in many different physical problems make it particularly useful in hydrodynamics, electrodynamics, plasma physics, and boundary layer problems. A great variety of underlying mechanisms are included making this book useful for those working in wave theory, hydrodynamics, electromagnetism, and applications. "The authors developed a universal and elegant tool – dynamical projector method. Using this method for very complicated hydro-thermodynamic and electrodynamics problem settings, they were able to get a lot of interesting analytical results in areas where before often just numerical methods were applicable." —L. A. Bordag, University of Applied Sciences Zittau/Görlitz, Zittau, Germany "The book is intended for professionals working in various fields of linear and nonlinear mathematical physics, partial differential equations and theoretical physics. The book is written clearly, and in my opinion, its material will be useful and easy to understand for professionals and for students familiar with ordinary and partial differential equations." —Sergey Dobrokhotov, Russian Academy of Sciences, Moscow, Russia
This book presents the theory and results of experimental studies of the propagation of infrasound waves in a real atmosphere with its inherent fine-scale layered structure of wind speed and temperature. It is motivated by the fact that the statistical characteristics of anisotropic (or layered) fluctuations of meteorological fields, the horizontal scales of which significantly exceed their vertical scales, have been very poorly studied compared to those of locally isotropic turbulence in the inertial range of scales. This book addresses this lacuna by developing a theory of the formation of anisotropic inhomogeneities of the atmosphere in a random field of internal gravity waves and vortex structures. Using theory, it explains numerous experimental data depicting the influence of the fine structure of the atmosphere on the propagation of infrasound waves from pulsed sources. The text will appeal to specialists in the fields of acoustics and optics of the atmosphere, remote sensing of the atmosphere, the dynamics of internal waves, nonlinear acoustics, and infrasound monitoring of explosions and natural hazards.
This book summarizes the main advances in the field of nonlinear evolution and pattern formation caused by longwave instabilities in fluids. It will allow readers to master the multiscale asymptotic methods and become familiar with applications of these methods in a variety of physical problems. Longwave instabilities are inherent to a variety of systems in fluid dynamics, geophysics, electrodynamics, biophysics, and many others. The techniques of the derivation of longwave amplitude equations, as well as the analysis of numerous nonlinear equations, are discussed throughout. This book will be of value to researchers and graduate students in applied mathematics, physics, and engineering, in particular within the fields of fluid mechanics, heat and mass transfer theory, and nonlinear dynamics.
This book examines the deterioration of relations between the USSR and China in the 1960s, whereby once powerful allies became estranged, competitive, and increasingly hostile neighbors. It shows how the intrinsic inequality of the Sino-Soviet alliance - seen as entirely natural by the Russians but bitterly resented by the Chinese - resulted in its ultimate collapse.
One of the main goals of investigations of shock-wave phenomena in condensed matter is to develop methods for predicting effects of explosions, high-velocity collisions, and other kinds of intense dynamic loading of materials and structures. Based on the results of international research conducted over the past 30 years, this book is addressed not only to experts in shock-wave physics, but also to interested representatives from adjacent fields of activity and to students who seek an introduction to the current issues. With that goal in mind, the book opens with a brief account of the theoretical background and a short description of experimental techniques. The authors then progress to a systematic treatment of special topics, some of which have not been fully addressed in the literature to date.
Volume 2 offers three in-depth articles covering significant areas in applied mathematics research. Chapters feature numerous illustrations, extensive background material and technical details, and abundant examples. The authors analyze nonlinear front propagation for a large class of semilinear partial differential equations using probabilistic methods; examine wave localization phenomena in one-dimensional random media; and offer an extensive introduction to certain model equations for nonlinear wave phenomena.
This is the second volume of Nonlinear Equations with Small Parameter containing new methods of construction of global asymptotics of solutions to nonlinear equations with small parameter. They allow one to match asymptotics of various properties with each other in transition regions and to get unified formulas for connection of characteristic parameters of approximate solutions. This approach underlies modern asymptotic methods and gives a deep insight into crucial nonlinear phenomena. These are beginnings of chaos in dynamical systems, incipient solitary and shock waves, oscillatory processes in crystals, engineering constructions and quantum systems. Apart from independent interest the approximate solutions serve as a foolproof basis for testing numerical algorithms. The second volume will be related to partial differential equations.
This book explores non-standard processes in complex electrochemical systems, covering the structure and phase composition of modified alloys, saturation kinetics, and properties of surface layers. It also investigates the plasma electrolytic polishing of many alloys. The book presents the physicist with conditions of heating metals up to 1000 °C inside a solution, the chemist with reactions in vapour-gaseous media and on the surface of an electrode, and the metal scientist with the diffusion saturation of metals with nitrogen, carbon and boron. It will also appeal to engineers, university and college professors, and other researchers in related fields.
There are more than 200 examples and problems supplemented by answers and solutions in this book. In this textbook, the authors primarily propose the problems, the physical content of which is rather transparent, and the process of solving allows the reader to see all the beauty of hydrodynamics. The authors have deliberately excluded problems whose solution might require rigorous mathematical proofs of different theorems and statements. A useful and unique publication.
This monograph systematically develops and considers the so-called "dressing method" for solving differential equations (both linear and nonlinear), a means to generate new non-trivial solutions for a given equation from the (perhaps trivial) solution of the same or related equation. Throughout, the text exploits the "linear experience" of presentation, with special attention given to the algebraic aspects of the main mathematical constructions and to practical rules of obtaining new solutions.
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