This book is an introduction to the application of nonlinear dynamics to problems of stability, chaos and turbulence arising in continuous media and their connection to dynamical systems. With an emphasis on the understanding of basic concepts, it should be of interest to nearly any science-oriented undergraduate and potentially to anyone who wants to learn about recent advances in the field of applied nonlinear dynamics. Technicalities are, however, not completely avoided. They are instead explained as simply as possible using heuristic arguments and specific worked examples.
The aim of this book is to develop a unified approach to nonlinear science, which does justice to its multiple facets and to the diversity and richness of the concepts and tools developed in this field over the years. Nonlinear science emerged in its present form following a series of closely related and decisive analytic, numerical and experimental developments that took place over the past three decades. It appeals to an extremely large variety of subject areas, but, at the same time, introduces into science a new way of thinking based on a subtle interplay between qualitative and quantitative techniques, topological and metric considerations and deterministic and statistical views. Special effort has been made throughout the book to illustrate both the development of the subject and the mathematical techniques, by reference to simple models. Each chapter concludes with a set of problems. This book will be of great value to graduate students in physics, applied mathematics, chemistry, engineering and biology taking courses in nonlinear science and its applications.
The impact of Benard's discovery on 20th century physics is crucial to any modern research area such as fluid dynamics, nonlinear dynamics, and non-equilibrium thermodynamics, just to name a few. This centenary review shows the broad scope and development including modern applications, edited and written by experts in the field.
Symmetry is a property which occurs throughout nature and it is therefore natural that symmetry should be considered when attempting to model nature. In many cases, these models are also nonlinear and it is the study of nonlinear symmetric models that has been the basis of much recent work. Although systematic studies of nonlinear problems may be traced back at least to the pioneering contributions of Poincare, this remains an area with challenging problems for mathematicians and scientists. Phenomena whose models exhibit both symmetry and nonlinearity lead to problems which are challenging and rich in complexity, beauty and utility. In recent years, the tools provided by group theory and representation theory have proven to be highly effective in treating nonlinear problems involving symmetry. By these means, highly complex situations may be decomposed into a number of simpler ones which are already understood or are at least easier to handle. In the realm of numerical approximations, the systematic exploitation of symmetry via group repre sentation theory is even more recent. In the hope of stimulating interaction and acquaintance with results and problems in the various fields of applications, bifurcation theory and numerical analysis, we organized the conference and workshop Bifurcation and Symmetry: Cross Influences between Mathematics and Applications during June 2-7,8-14, 1991 at the Philipps University of Marburg, Germany.
Most environmental statutes passed since 1970 have endorsed a pragmatic or 'precautionary' principle under which the existence of a significant risk is enough to trigger regulation. At the same time, targets of such regulation have often argued on grounds of inefficiency that the associated costs outweigh any potential benefits. In this work, Jason Johnston unpacks and critiques the legal, economic, and scientific basis for precautionary climate policies pursued in the United States and in doing so sheds light on why the global warming policy debate has become increasingly bitter and disconnected from both climate science and economics. Johnston analyzes the most influential international climate science assessment organizations, the US electric power industry, and land management and renewable energy policies. Bridging sound economics and climate science, this pathbreaking book shows how the United States can efficiently adapt to a changing climate while radically reducing greenhouse gas emissions.
A rich variety of books devoted to dynamical chaos, solitons, self-organization has appeared in recent years. These problems were all considered independently of one another. Therefore many of readers of these books do not suspect that the problems discussed are divisions of a great generalizing science - the theory of oscillations and waves. This science is not some branch of physics or mechanics, it is a science in its own right. It is in some sense a meta-science. In this respect the theory of oscillations and waves is closest to mathematics. In this book we call the reader's attention to the present-day theory of non-linear oscillations and waves. Oscillatory and wave processes in the systems of diversified physical natures, both periodic and chaotic, are considered from a unified poin t of view . The relation between the theory of oscillations and waves, non-linear dynamics and synergetics is discussed. One of the purposes of this book is to convince reader of the necessity of a thorough study popular branches of of the theory of oscillat ions and waves, and to show that such science as non-linear dynamics, synergetics, soliton theory, and so on, are, in fact , constituent parts of this theory. The primary audiences for this book are researchers having to do with oscillatory and wave processes, and both students and post-graduate students interested in a deep study of the general laws and applications of the theory of oscillations and waves.
Proceedings of a symposium co-sponsored by the Air Force Historical Foundation and the Air Force History and Museums Program. The symposium covered relevant Air Force technologies ranging from the turbo-jet revolution of the 1930s to the stealth revolution of the 1990s. Illustrations.
This textbook presents a modern account of turbulence, one of the greatest challenges in physics. The state-of-the-art is put into historical perspective five centuries after the first studies of Leonardo and half a century after the first attempt by A. N. Kolmogorov to predict the properties of flow at very high Reynolds numbers. Such 'fully developed turbulence' is ubiquitous in both cosmical and natural environments, in engineering applications and in everyday life. The intended readership for the book ranges from first-year graduate students in mathematics, physics, astrophysics, geosciences and engineering, to professional scientists and engineers. Elementary presentations of dynamical systems ideas, of probabilistic methods (including the theory of large deviations) and of fractal geometry make this a self-contained textbook.
This book makes a significant contribution to a hitherto much neglected area. The book brings together a wide range of papers on a scale rarely seen with a geographic spread that enhances our understanding of the complex journey undertaken by those who aspire to become teachers of teachers. The authors, from more than ten countries, use a variety of approaches including narrative/life history, self-study and empirical research to demonstrate the complexity of the transformative search by individuals to establish their professional identity as teacher educators. The book offers fundamental and thoughtful critiques of current policy, practice and examples of established structures specifically supporting the professional development of teacher educators that may well have a wider applicability. Many of the authors are active and leading persons in the international fields of teacher education and of professional development. The book considers: novice teacher educators, issues of transition; identity development including research identity; the facilitation and mentoring of teacher educators; self-study research including collaborative writing, use of stories; professional development within the context of curriculum and structural reform. Becoming a teacher is recognised as a transformative search by individuals for their teaching identities. Becoming a teacher educator often involves a more complex and longer journey but, according to the many travel stories told here, one that can be a deeply satisfying experience. This book was published as a special issue of Professional Development in Education.
