Time Reversibility, Computer Simulation, and Chaos

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World Scientific, 1999 - Computers - 262 pages
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A small army of physicists, chemists, mathematicians, and engineers has joined forces to attack a classic problem, the "reversibility paradox", with modern tools. This book describes their work from the perspective of computer simulation, emphasizing the author's approach to the problem -- understanding the compatibility, and even inevitability, of the irreversible second law of thermodynamics with an underlying time-reversible mechanics. Computer simulation has made it possible to probe reversibility from a variety of directions and "chaos theory" or "nonlinear dynamics" has supplied a useful vocabulary and set of concepts, which allow a fuller explanation of irreversibility than that available to Boltzmann or to Green and Kubo and Onsager. Clear illustration of concepts is emphasized throughout, and reinforced with a glossary of technical terms from the specialized fields which have been combined here to focus on a common theme.

The book begins with a discussion on the idealized reversibility of basic physics and the pragmatic irreversibility of real life. Computer models, and simulation, are next discussed and illustrated. Simulations provide the means to assimilate concepts through worked-out examples. State-of-the-art analyses, from the point of view of dynamical systems, are applied to many-body examples from nonequilibrium molecular dynamics and to chaotic irreversible flows from finite-difference, finite-element, and particle-based continuum simulations. Two necessary concepts from dynamical-systems theory -- fractals and Lyapunov instability -- are fundamental to the approach.

Undergraduate-level physics, calculus, and ordinary differential equations are sufficientbackground for a full appreciation of this book, which is intended for advanced undergraduates, graduates, and research workers. The generous assortment of examples worked out in the text will stimulate readers to explore the rich and fruitful field of study which links fundamental reversible laws of physics to the irreversibility surrounding us all.

 

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Contents

TimeReversibility in Physics and Computation
29
Gibbs Statistical Mechanics
61
Irreversibility in Real Life
89
Microscopic Computer Simulation
111
Macroscopic Computer Simulation
141
Chaos Lyapunov Instability Fractals
163
Resolving the Reversibility Paradox
199
Afterworda Research Perspective
229
Glossary of Technical Terms
249
Copyright

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About the author (1999)

Tim Barmettler, author, and Bill Hoover, illustrator, grew up in the same neighborhood in Omaha, Nebraska. They met on their first day of kindergarten and have been friends ever since. Bill and Tim grew up fishing, playing soccer and basketball together. They shared dreams of being rock stars, professional soccer players, and world travelers. Bill would swing by Tim's house every morning so they could walk to school together. They dreamed of adventures and traveling the world. Neither one of them could have imagined that one day they would write a book about such travels. In high school, they both played on the varsity soccer team and continued to be good friends. After high school, they parted ways when Bill stayed in Omaha to attend Creighton University while Tim ventured to Northern Arizona University in Flagstaff. Today, Bill is enjoying a successful career as an artist in Omaha where he lives with his wife, Stacia. Hoover Studios is very well known in the Omaha art community. Tim is living in Gilbert Arizona with his wife, Barb and children, Will and Ally. He enjoys teaching English and coaching soccer. Tim wrote the The Contagious Yawn while living in Sedona, Arizona and teaching in the Verde Valley. It was years later when attending their 25th high school reunion, that Tim and Bill decided to collaborate on The Contagious Yawn.

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