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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.
A discussion of the fundamental changes that occur when dynamical systems from the fields of nonlinear optics, solids, hydrodynamics and biophysics are scaled down to nanosize. The authors are leading scientists in the field and each of their contributions provides a broader introduction to the specific area of research. In so doing, they include both the experimental and theoretical point of view, focusing especially on the effects on the nonlinear dynamical behavior of scaling, stochasticity and quantum mechanics. For everybody working on the synthesis and integration of nanoscopic devices who sooner or later will have to learn how to deal with nonlinear effects.
Wave evolution on a falling film is a classical hydrodynamic instability whose rich wave dynamics have been carefully recorded in the last fifty years. Such waves are known to profoundly affect the mass and heat transfer of multi-phase industrial units.This book describes the collective effort of both authors and their students in constructing a comprehensive theory to describe the complex wave evolution from nearly harmonic waves at the inlet to complex spatio-temporal patterns involving solitary waves downstream. The mathematical theory represents a significant breakthrough from classical linear stability theories, which can only describe the inlet harmonic waves and also extends classical soliton theory for integrable systems to real solitrary wave dynamics with dissipation. One unique feature of falling-film solitary wave dynamics, which drives much of the spatio-temporal wave evolution, is the irreversible coalescence of such localized wave structures. It represents the first full description of a hydrodynamic instability from inception to developed chaos. This approach should prove useful for other complex hydrodynamic instabilities and would allow industrial engineers to better design their multi-phase apparati by exploiting the deciphered wave dynamics. This publication gives a comprehensive review of all experimental records and existing theories and significantly advances state of the art on the subject and are complimented by complex and attractive graphics from computational fluid mechanics.
Nonlinear partial differential equations abound in modern physics. The problems arising in these fields lead to fascinating questions and, at the same time, progress in understanding the mathematical structures is of great importance to the models. Nevertheless, activity in one of the approaches is not always sufficiently in touch with developments in the other field. The book presents the joint efforts of mathematicians and physicists involved in modelling reactive flows, in particular superconductivity and superfluidity. Certain contributions are fundamental to an understanding of such cutting-edge research topics as rotating Bose-Einstein condensates, Kolmogorov-Zakharov solutions for weak turbulence equations, and the propagation of fronts in heterogeneous media.
Nonlinear partial differential equations abound in modern physics. The problems arising in these fields lead to fascinating questions and, at the same time, progress in understanding the mathematical structures is of great importance to the models. Nevertheless, activity in one of the approaches is not always sufficiently in touch with developments in the other field. The book presents the joint efforts of mathematicians and physicists involved in modelling reactive flows, in particular superconductivity and superfluidity. Certain contributions are fundamental to an understanding of such cutting-edge research topics as rotating Bose-Einstein condensates, Kolmogorov-Zakharov solutions for weak turbulence equations, and the propagation of fronts in heterogeneous media.
The revolution is well underway. Our understanding and utilization of microelectromechanical systems (MEMS) are growing at an explosive rate with a worldwide market approaching billions of dollars. In time, microdevices will fill the niches of our lives as pervasively as electronics do right now. But if these miniature devices are to fulfill their mammoth potential, today's engineers need a thorough grounding in the underlying physics, modeling techniques, fabrication methods, and materials of MEMS. The MEMS Handbook delivers all of this and more. Its team of authors-unsurpassed in their experience and standing in the scientific community- explore various aspects of MEMS: their design, fabrication, and applications as well as the physical modeling of their operations. Designed for maximum readability without compromising rigor, it provides a current and essential overview of this fledgling discipline.
Thoroughly revised and updated, the new edition of the best-selling MEMS Handbook is now presented as a three-volume set that offers state-of-the-art coverage of microelectromechanical systems. The first volume, MEMS: Introduction and Fundamentals builds the required background and explores various physical considerations of MEMS. Topics include scaling, simulation models, the basics of control theory, and the physics of materials flow, thin liquid films, and bubble/drop transport. New chapters in this edition address lattice Boltzmann simulations and microscale hydrodynamics. Standing well on its own, this books builds an outstanding foundation for further exploration of MEMS and their applications.
Lists citations with abstracts for aerospace related reports obtained from world wide sources and announces documents that have recently been entered into the NASA Scientific and Technical Information Database.
This volume contains nearly all the papers presented at the AMS-IMS-SIAM Joint Summer Research Conference on Biofluiddynamics, held in July 1991, at the University of Washington, Seattle. The lead paper, by Sir James Lighthill, presents a comprehensive review of external flows in biology. The other papers on external and internal flows illuminate developments in the protean field of biofluiddynamics from diverse viewpoints, reflecting the field's multidisciplinary nature. For this reason, the work should be useful to mathematicians, biologists, engineers, physiologists, cardiologists and oceanographers alike. The papers highlight a number of problems that have remained largely unexplored due to the difficulty of addressing biological flow motions, which are often governed by large systems of nonlinear differential equations and involve complex geometries. However, recent advances in computational fluid dynamics have expanded opportunities to solve such problems. These developments have increased interest in areas such as the mechanisms of blood and air flow in humans, the dynamic ecology of the oceans, animal swimming and flight, to name a few.
Zusammenfassung: This volume aims to present the latest advancements in experimental, analytical, and numerical methodologies aimed at exploring the nonlinear dynamics of diverse systems across varying length and time scales. It delves into the following topics: Methodologies for nonlinear dynamic analysis (harmonic balance, asymptotic techniques, enhanced time integration) Data-driven dynamics, machine learning techniques Exploration of bifurcations and nonsmooth systems Nonlinear phenomena in mechanical systems and structures Experimental dynamics, system identification, and monitoring techniques Fluid-structure interaction Dynamics of multibody systems Turning processes, rotating systems, and systems with time delays