This advanced-level treatment describes the mathematics of catastrophe theory and its applications to problems in mathematics, physics, chemistry and engineering. 28 tables. 397 black-and-white illustrations. 1981 edition.

The new edition of this non-mathematical review of catastrophe theory contains updated results and many new or expanded topics including delayed loss of stability, shock waves, and interior scattering. Three new sections offer the history of singularity and its applications from da Vinci to today, a discussion of perestroika in terms of the theory of metamorphosis, and a list of 93 problems touching on most of the subject matter in the book.

This book aims to provide a straightforward introduction to chemical applications of the catastrophe theory. It is primarily intended for chemists interested in placing chemical reactions in the broader context of non-linear science, but it has a practical relevance for scientists in general. Catastrophe theory deals with those non-linear phenomena in which a continuous change in the control parameters results in a discontinuous alteration of a characteristic quantity of the system. The author discusses the origins of catastrophe theory, giving examples of occurrences in the areas of physics, chemistry and biology. Elementary theory and non-chemical applications are also described. The chemical kinetics and methods of analysis of chemical kinetic equations arising from elementary and generalized catastrophe theories are reviewed. Finally, the theory is applied to analyse and classify phenomena associated with the stability loss that may occur in chemical reactions. The book contains over 100 figures and an extensive subject index.

The history and science behind efforts to predict major disasters, from tsunamis to stock market crashes Can we predict cataclysmic disasters such as earthquakes, volcanic eruptions, or stock market crashes? The Indian Ocean tsunami of 2004 claimed more than 200,000 lives. Hurricane Katrina killed over 1,800 people and devastated the city of New Orleans. The recent global financial crisis has cost corporations and ordinary people around the world billions of dollars. Megadisasters is a book that asks why catastrophes such as these catch us by surprise, and reveals the history and groundbreaking science behind efforts to forecast major disasters and minimize their destruction. Each chapter of this exciting and eye-opening book explores a particular type of cataclysmic event and the research surrounding it, including earthquakes, tsunamis, volcanic eruptions, hurricanes, rapid climate change, collisions with asteroids or comets, pandemics, and financial crashes. Florin Diacu tells the harrowing true stories of people impacted by these terrible events, and of the scientists racing against time to predict when the next big disaster will strike. He describes the mathematical models that are so critical to understanding the laws of nature and foretelling potentially lethal phenomena, the history of modeling and its prospects for success in the future, and the enormous challenges to scientific prediction posed by the chaos phenomenon, which is the high instability that underlies many processes around us. Yielding new insights into the perils that can touch every one of us, Megadisasters shows how the science of predicting disasters holds the promise of a safer and brighter tomorrow.

Catastrophe Theory was introduced in the 1960s by the renowned Fields Medal mathematician René Thom as a part of the general theory of local singularities. Since then it has found applications across many areas, including biology, economics, and chemical kinetics. By investigating the phenomena of bifurcation and chaos, Catastrophe Theory proved to

This is a unique book about natural catastrophes, focusing on the mathematical aspects of these phenomena. Although academic in style and didactic in purpose, it is practical in the treatment of the diverse issues covered, which range from hazard warning and forecasting to engineering design criteria and insurance loss estimation. Addressing as it does many mathematical topics not found together in a single volume, the book should be of value to all those with a quantitative educational interest in or professional concern for natural catastrophes.

Mathematical Models of Life Support Systems is a component of Encyclopedia of Mathematical Sciences in which is part of the global Encyclopedia of Life Support Systems (EOLSS), an integrated compendium of twenty one Encyclopedias. The Theme is organized into several topics which represent the main scientific areas of the theme: The first topic, Introduction to Mathematical Modeling discusses the foundations of mathematical modeling and computational experiments, which are formed to support new methodologies of scientific research. The succeeding topics are Mathematical Models in - Water Sciences; Climate; Environmental Pollution and Degradation; Energy Sciences; Food and Agricultural Sciences; Population; Immunology; Medical Sciences; and Control of Catastrophic Processes. These two volumes are aimed at the following five major target audiences: University and College students Educators, Professional practitioners, Research personnel and Policy analysts, managers, and decision makers and NGOs.

Graduate students receive a stimulating introduction to analytical approximation techniques for solving differential equations in this text, which introduces scientifically significant problems and indicates useful solutions. 1966 edition.

This book reports on cutting-edge concepts related to Bourbaki’s notion of structures mères. It merges perspectives from logic, philosophy, linguistics and cognitive science, suggesting how they can be combined with Bourbaki’s mathematical structuralism in order to solve foundational, ontological and epistemological problems using a novel category-theoretic approach. By offering a comprehensive account of Bourbaki’s structuralism and answers to several important questions that have arisen in connection with it, the book provides readers with a unique source of information and inspiration for future research on this topic.

Useful guide covers two major subdivisions of combinatorics — enumeration and graph theory — with emphasis on conceptual needs of computer science. Each part is divided into a "basic concepts" chapter emphasizing intuitive needs of the subject, followed by four "topics" chapters that explore these ideas in depth. Invaluable practical resource for graduate students, advanced undergraduates, and professionals with an interest in algorithm design and other aspects of computer science and combinatorics. References for Linear Order & for Graphs, Trees, and Recursions. 219 figures.