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The Lorenz Equations
The equations which we are going to study in these notes were first presented in 1963 by E. N. Lorenz. They define a three-dimensional system of ordinary differential equations that depends on three real positive parameters. As we vary the parameters, we change the behaviour of the flow determined by the equations. For some parameter values, numerically computed solutions of the equations oscillate, apparently forever, in the pseudo-random way we now call "chaotic"; this is the main reason for the immense amount of interest generated by the equations in the eighteen years since Lorenz first presented them. In addition, there are some parameter values for which we see "preturbulence", a pheno...
50th Anniversary of the Metaphorical Butterfly Effect since Lorenz (1972)
Celebrate the 50th anniversary of the metaphorical butterfly effect, born from Edward Lorenz's 1963 work on initial condition sensitivity. In 1972, it became a metaphor for illustrating how minor changes could yield an organized system. Lorenz Models: Chaos & Regime Changes Explore Lorenz models' 1960-2008 evolution, chaos theory, and attractors. Unraveling High-dimensional Instability Challenge norms in "Butterfly Effect without Chaos?" as non-chaotic elements contribute uniquely. Modeling Atmospheric Dynamics Delve into atmospheric dynamics via "Storm Sensitivity Study." Navigating Data Assimilation Explore data assimilation's dance in chaotic and nonchaotic settings via the observabili...
Public Finance
Featuring a general equilibrium framework that is both cohesive and versatile, the Second Edition of Public Finance: A Normative Theory brings new and updated information to this classic text. Through its concentration on the microeconomic theory of the public sector in the context of capitalist market economics it addresses the subjects traditionally at the heart of public sector economics, including public good theory, theory of taxation, welfare analysis, externalities, tax incidence, cost benefit analysis, and fiscal federalism. Its goal of providing a foundation, rather than attempting to present the most recent scholarship in detail, makes this Second Edition both a valuable text and a resource for professionals. * Second edition provides new and updated information * Focuses on the heart of public sector economics, including public expenditure theory and policy, tax theory and policy, cost benefit-analysis, and fiscal federalism * Features a cohesive and versatile general equilibrium framework
Geology and Geomorphology of Alluvial and Fluvial Fans
Alluvial and fluvial fans are the most widespread depositional landform bordering the margins of highland regions and actively subsiding continental basins, across a broad spectrum of tectonic and climatic settings. They are significant to the local morphodynamics of mountain regions and also to the evolution of sediment-routing systems, affecting the propagation and preservation of stratigraphic signals of environmental change over vast areas. The volume presents case studies discussing the geology and geomorphology of alluvial and fluvial fans from both active systems and ancient ones preserved in the stratigraphic record. It brings together case studies from a range of continents, climatic and tectonic settings, some introducing innovative monitoring and analysis techniques, and it provides an overview of current debates in the field. This volume will be of particular interest to geologists, geomorphologists, sedimentologists and the general reader with an interest in Earth science.
Stochastic Models in Reliability, Network Security and System Safety
This book is dedicated to Jinhua Cao on the occasion of his 80th birthday. Jinhua Cao is one of the most famous reliability theorists. His main contributions include: published over 100 influential scientific papers; published an interesting reliability book in Chinese in 1986, which has greatly influenced the reliability of education, academic research and engineering applications in China; initiated and organized Reliability Professional Society of China (the first part of Operations Research Society of China) since 1981. The high admiration that Professor Cao enjoys in the reliability community all over the world was witnessed by the enthusiastic response of each contributor in this book....
Planetary Astrobiology
Are we alone in the universe? How did life arise on our planet? How do we search for life beyond Earth? These profound questions excite and intrigue broad cross sections of science and society. Answering these questions is the province of the emerging, strongly interdisciplinary field of astrobiology. Life is inextricably tied to the formation, chemistry, and evolution of its host world, and multidisciplinary studies of solar system worlds can provide key insights into processes that govern planetary habitability, informing the search for life in our solar system and beyond. Planetary Astrobiology brings together current knowledge across astronomy, biology, geology, physics, chemistry, and r...
