Dynamik og statik

This reference work provides an authoritative single source for understanding and applying the concepts of complexity theory together with the tools and measures for analyzing complex systems in all fields of science and engineering. The science and tools of complexity and systems science include theories of self-organization, complex systems, synergetics, dynamical systems, turbulence, catastrophes, instabilities, nonlinearity, stochastic processes, chaos, neural networks, cellular automata, adaptive systems, and genetic algorithms. Examples of near-term problems and major unknowns that can be approached through complexity and systems science include: The structure, history and future of the universe; the biological basis of consciousness; the integration of genomics, proteomics and bioinformatics as systems biology; human longevity limits; the limits of computing; sustainability of life on earth; predictability, dynamics and extent of earthquakes, hurricanes, tsunamis, and other natural disasters; the dynamics of turbulent flows; lasers or fluids in physics, microprocessor design; macromolecular assembly in chemistry and biophysics; brain functions in cognitive neuroscience; climate change; ecosystem management; traffic management; and business cycles. All these seemingly quite different kinds of structure formation have a number of important features and underlying structures in common. These deep structural similarities can be exploited to transfer analytical methods and understanding from one field to another. This unique work will extend the influence of complexity and system science to a much wider audience than has been possible to date.

Statistical methods have a long history in the analysis of hydrological data for de-signing, planning, infilling, forecasting, and specifying better models to assess scenarios of land use and climate change in catchments. The effectiveness of statistical descriptions of hydrological processes reflects the enormous complexity of hydrological systems, which makes a purely deterministic description ineffective. This book hosts 11 papers devoted to statistics in hydrology, summarizing the recent advancement in statistical methods for hydrological studies such as statistical analysis of changes in hydrometeorological variables, forecasting and prediction of hydrological elements, hydrological forecasting uncertainty analysis, the use of new statistical methodologies for engineering hydrological design under stationary/nonstationary conditions, and so on. In general, the book will contribute to the promotion of the application of statistical methods in hydrology.

This is the 2nd edition of the book, Flow Visualization: Techniques and Examples, which was published by Imperial College Press in 2000. Many of the chapters have been revised and updated to take into consideration recent changes in a number of flow visualization and measurement techniques, including an updated high quality flow gallery. Unique among similar publications, this book focuses on the practical rather than theoretical aspects. Obtaining high quality flow visualization results is, in many ways, more of an art than a science, and experience plays a key deciding role. The depth and breadth of the material will make this book invaluable to readers of all levels of experience in the field.

This encyclopedia provides an authoritative single source for understanding and applying the concepts of complexity theory together with the tools and measures for analyzing complex systems in all fields of science and engineering. It links fundamental concepts of mathematics and computational sciences to applications in the physical sciences, engineering, biomedicine, economics and the social sciences.

Modern notions and important tools of classical mechanics are used in the study of concrete examples that model physically significant molecular and atomic systems. The parametric nature of these examples leads naturally to the study of the major qualitative changes of such systems (metamorphoses) as the parameters are varied. The symmetries of these systems, discrete or continuous, exact or approximate, are used to simplify the problem through a number of mathematical tools and techniques like normalization and reduction. The book moves gradually from finding relative equilibria using symmetry, to the Hamiltonian Hopf bifurcation and its relation to monodromy and, finally, to generalizations of monodromy.

Centered around the natural phenomena of relaxations and fluctuations, this monograph provides readers with a solid foundation in the linear and nonlinear Fokker-Planck equations that describe the evolution of distribution functions. It emphasizes principles and notions of the theory (e.g. self-organization, stochastic feedback, free energy, and Markov processes), while also illustrating the wide applicability (e.g. collective behavior, multistability, front dynamics, and quantum particle distribution). The focus is on relaxation processes in homogeneous many-body systems describable by nonlinear Fokker-Planck equations. Also treated are Langevin equations and correlation functions. Since these phenomena are exhibited by a diverse spectrum of systems, examples and applications span the fields of physics, biology and neurophysics, mathematics, psychology, and biomechanics.

Intended for beginners in ergodic theory, this introductory textbook addresses students as well as researchers in mathematical physics. The main novelty is the systematic treatment of characteristic problems in ergodic theory by a unified method in terms of convergent power series and renormalization group methods, in particular. Basic concepts of ergodicity, like Gibbs states, are developed and applied to, e.g., Asonov systems or KAM Theroy. Many examples illustrate the ideas and, in addition, a substantial number of interesting topics are treated in the form of guided problems.

This is the first monograph devoted to investigation of the most complex physical processes of soft systems, including a wide class of solutions. It blends modern theoretical understanding and experimental results, proposing new methods and models for the description of several soft systems.