Instability of flows and their transition to turbulence are widespread phenomena in engineering and the natural environment. They are important in applied mathematics, astrophysics, biology, geophysics, meteorology, oceanography, physics, and engineering. This is a graduate-level textbook to introduce these phenomena by modeling them mathematically, and describing numerical simulations and laboratory experiments. The visualization of instabilities is emphasized with many figures. Many worked examples and exercises for students illustrate the ideas of the text. Readers are assumed to be fluent...

Jon Lee focuses on key mathematical ideas leading to useful models and algorithms, rather than on data structures and implementation details, in this introductory graduate-level text for students of operations research, mathematics, and computer science. The viewpoint is polyhedral, and Lee also uses matroids as a unifying idea. Topics include linear and integer programming, polytopes, matroids and matroid optimization, shortest paths, and network flows. Problems and exercises are included throughout as well as references for further study.

Kostrov and Das present a general theoretical model summarizing our current knowledge of fracture mechanics as applied to earthquakes and earthquake source processes. Part I explains continuum and fracture mechanics, providing the reader with some background and context. Part II continues with a discussion of the inverse problem of earthquake source theory and a description of the seismic moment tensor. Part III presents specific earthquake source models. Although data processing and acquisition techniques are discussed only in simplified form for illustrative purposes, the material in this...

Kostrov and Das present a general theoretical model summarizing our current knowledge of fracture mechanics as applied to earthquakes and earthquake source processes. Part I explains continuum and fracture mechanics, providing the reader with some background and context. Part II continues with a discussion of the inverse problem of earthquake source theory and a description of the seismic moment tensor. Part III presents specific earthquake source models. Although data processing and acquisition techniques are discussed only in simplified form for illustrative purposes, the material in this...

This book provides a unified account of the theory required to establish upper and lower bounds.

Professor Ottino presents a unified and systematic account of the kinematics of mixing fluids. He suggests that fluid mixing be regarded, in some respects, as the efficent stretching and folding of material lines and surfaces. This corresponds to analyzing a particular type of dynamical system, and Ottino explores the connection. The work is heavily illustrated with line diagrams, and black-and-white and color plates. The graphics aid the reader in developing a more systematic and intuitive picture, complementing the scientific presentation given in the text itself.

Professor Bennett's work explores the potential for inverse theory, emphasizing possibilities rather than expedient or rudimentary applications. In addition to interpolating the data and adding realism to the model solutions, the methods can yield estimates for unobserved flow variables, forcing fields, and model parameters. Inverse formulations can resolve ill-posed modeling problems, lead to design criteria for oceanic observing systems, and enable the testing of models as scientific hypothesis. Ocean models considered range from linear, finite-dimensional systems of equality and inequality...

This book reviews and interrelates a large number of theoretical and experimental contributions to the research on finite plastic deformation of single crystals and polycrystalline metals made during the past quarter century. An overall theoretical framework for investigation of large strains in crystalline materials is presented that enables the blending of contemporary and earlier experimental research with modern concepts in solid mechanics. Professor Havner has provided a historical perspective throughout including accurate attribution of ideas and emphasis on pioneering studies,...

The investigation of nonlinear phenomena in acoustics has a rich history stretching back to the mechanical physical sciences in the nineteenth century. The study of nonlinear phenomena, such as explosions and jet engines, prompted the sharp growth of interest in nonlinear acoustic phenomena. In this book, the authors consider models of different "acoustic" media as well as equations and behavior of finite-amplitude waves. The authors also consider the effects of nonlinearity, dissipation, dispersion, and for two- and three-dimensional problems, reflection and diffraction on the evolution and...

A coherent treatment of nonlinear systems covering chaos, fractals, and bifurcation, as well as equilibrium, stability, and nonlinear oscillations. The systems treated are mostly of difference and differential equations. The author introduces the mathematical properties of nonlinear systems as an integrated theory, rather than simply presenting isolated fashionable topics. The topics are discussed in as concrete a way as possible, worked examples and problems are used to motivate and illustrate the general principles. More advanced parts of the text are denoted by asterisks, thus making it...