Scaling Laws In Dynamical Systems

Scaling Laws in Dynamical Systems

Scaling Laws in Dynamical Systems

This book discusses many of the common scaling properties observed in some nonlinear dynamical systems mostly described by mappings. The unpredictability of the time evolution of two nearby initial conditions in the phase space together with the exponential divergence from each other as time goes by lead to the concept of chaos. Some of the observables in nonlinear systems exhibit characteristics of scaling invariance being then described via scaling laws. From the variation of control parameters, physical observables in the phase space may be characterized by using power laws that many times yield into universal behavior. The application of such a formalism has been well accepted in the scientific community of nonlinear dynamics. Therefore I had in mind when writing this book was to bring together few of the research results in nonlinear systems using scaling formalism that could treated either in under-graduation as well as in the post graduation in the several exact programs but no earlier requirements were needed from the students unless the basic physics and mathematics. At the same time, the book must be original enough to contribute to the existing literature but with no excessive superposition of the topics already dealt with in other text books. The majority of the Chapters present a list of exercises. Some of them are analytic and others are numeric with few presenting some degree of computational complexity.

Atmospheric Turbulence and Air Pollution Modelling

The study of turbulence in the atmosphere has seen considerable progress in the last decade. To put it briefly: boundary-layer meteorology, the branch of atmospheric science that concentrates on turbulence in the lower atmosphere, has moved from the surface layer into the boundary layer itself. The progress has been made on all fronts: theoretical, numerical and observational. On the other hand, air pollution modeling has not seen such a rapid evolution. It has not benefited as much as it should have from the increasing knowledge in the field of atmospheric turbulence. Air pollution modeling is still in many ways based on observations and theories of the surface layer only. This book aims to bring the reader up to date on recent advances in boundary-layer meteorology and to pave the path for applications in air pollution dispersion problems. The text originates from the material presented during a short course on Atmospheric Turbulence and Air Pollution Modeling held in The Hague during September 1981. This course was sponsored and organized by the Royal Netherlands Meteorological Institute, xi xii PREFACE to which both editors are affiliated. The Netherlands Government Ministry of Health and Environmental Protection and the Council of Europe also gave support.