The classical concept of turbulence is most often associated with fluid dynamics. However, it is in fact a dominant feature of most systems having a large or infinite number of degrees of freedom. In demonstration of this fact, the current volume covers topics such as acoustics, optics, and Jupiter's red spot, as wen as traditional hydrodynamics. The emphasis of the volume is on applications of the relatively new theory of weak turbulence. 'nis theory, which has been developed largely in the last twenty five years, anows for the existence of a multiplicity of linearly unstable modes interacting in a nonlinear "soup." It makes many intriguing connections to such topics as Hamiltonian mechanics, nonlinear parties, equations and integrable systems, stochastic analysis, and methods developed in quantum field theory. Most of the contributions in this book aim at finding and applying the proper mathematical and statistical tools to describe fully developed turbulence. These diverse applications serve to illustrate the power of a unified approach based for the most part on a Hamiltonian formulation. A few chapters address a class of stochastic nonlinear nondispersive waves known as Burger:e turbulence. Set into historical context by V. E. Zakharov's opening chapter, the contributions to this book will be of interest to research workers and graduate students in pure and applied mathematics, theoretical physics, fluid mechanics, oceanography, and various areas of engineering.
The series Advances in Industrial Control aims to report and encourage technology transfer in control engineering. The rapid development of control technology has an impact on all areas of the control discipline. New theory, new controllers, actuators, sensors, new industrial processes, computer methods, new applications, new philosophies, new challenges. Much of this development work resides in industrial reports, feasibility study papers and the reports of advanced collaborative projects. The series offers an opportunity for researchers to present an extended exposition of such new work in all aspects of industrial control for wider and rapid dissemination. Almost all physical systems are nonlinear and the success of linear control techniques depends on the extent of the nonlinear system behaviour and the careful attention given to switching linear controllers through the range of nonlinear system operations. In many industrial and process-control applications, good engineering practice, linear control systems and classical PID control can give satisfactory performance because the process nonlinearity is mild and the control system performance specification is not particularly demanding; however, there are other industrial system applications where the requirement for high-performance control can only be achieved if nonlinear control design techniques are used. Thus, in some industrial and technological domains there is a strong justification for more applications of nonlinear methods. One prevailing difficulty with nonlinear control methods is that they are not so easily understood nor are they easy to reduce to formulaic algorithms for routine application.
A systematic and comprehensive introduction to the study of nonlinear dynamical systems, in both discrete and continuous time, for nonmathematical students and researchers working in applied fields. An understanding of linear systems and the classical theory of stability are essential although basic reviews of the relevant material are provided. Further chapters are devoted to the stability of invariant sets, bifurcation theory, chaotic dynamics and the transition to chaos. In the final two chapters the authors approach the subject from a measure-theoretical point of view and compare results to those given for the geometrical or topological approach of the first eight chapters. Includes about one hundred exercises. A Windows-compatible software programme called DMC, provided free of charge through a website dedicated to the book, allows readers to perform numerical and graphical analysis of dynamical systems. Also available on the website are computer exercises and solutions to selected book exercises. See www.cambridge.org/economics/resources