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Title 
Time reversibility, computer simulation, algorithms, chaos 
Creator 
Hoover, William G. (William Graham), 1936 
Contributors 
Hoover, Carol Griswold. World Scientific (Firm) 
DescriptionAbstract 
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 authors' approach to the problem of understanding the compatibility, and even inevitability, of the irreversible second law of thermodynamics with an underlying timereversible 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 a set of concepts, which allow a fuller explanation of irreversibility than that available to Boltzmann or to Green, 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, contrasting the idealized reversibility of basic physics against the pragmatic irreversibility of real life. Computer models, and simulation, are next discussed and illustrated. Simulations provide the means to assimilate concepts through workedout examples. Stateoftheart analyses, from the point of view of dynamical systems, are applied to manybody examples from nonequilibrium molecular dynamics and to chaotic irreversible flows from finitedifference, finiteelement, and particlebased continuum simulations. Two necessary concepts from dynamicalsystems theory  fractals and Lyapunov instability  are fundamental to the approach. Undergraduatelevel physics, calculus, and ordinary differential equations are sufficient background 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. This expanded edition stresses and illustrates computer algorithms with many new workedout examples, and includes considerable new material on shockwaves, Lyapunov instability and fluctuations. 
DescriptionTable Of Contents 
1. Time reversibility, computer simulation, algorithms, chaos. 1.1. Microscopic reversibility; macroscopic irreversibility. 1.2. Time reversibility of irreversible processes. 1.3. Classical microscopic and macroscopic simulation. 1.4. Continuity, information, and bit reversibility. 1.5. Instability and chaos. 1.6. Simple explanations of complex phenomena. 1.7. The paradox: irreversibility from reversible dynamics. 1.8. Algorithm: fourthorder RungeKutta integrator. 1.9. Example problems. 1.10. Summary and notes  2. Timereversibility in physics and computation. 2.1. Introduction. 2.2. Time reversibility. 2.3. Levesque and Verlet's bitreversible algorithm. 2.4. Lagrangian and Hamiltonian mechanics. 2.5. Liouville's incompressible theorem. 2.6. What is macroscopic thermodynamics? 2.7. First and second laws of thermodynamics. 2.8. Temperature, Zeroth law, reservoirs, thermostats. 2.9. Irreversibility from stochastic irreversible equations. 2.10. Irreversibility from timereversible equations? 2.11. An algorithm implementing bitreversible dynamics. 2.12. Example problems. 2.13. Summary  3. Gibbs' statistical mechanics. 3.1. Scope and History. 3.2. Formal structure of Gibbs' statistical mechanics. 3.3. Initial conditions, boundary conditions, ergodicity. 3.4. From Hamiltonian dynamics to Gibbs' probability. 3.5. From Gibbs' probability to thermodynamics. 3.6. Pressure and energy from Gibbs' canonical ensemble. 3.7. Gibbs' entropy versus Boltzmann's entropy. 3.8. Numberdependence and thermodynamic fluctuations. 3.9. Green and Kubo's linearresponse theory. 3.10. An algorithm for local smoothparticle averages. 3.11. Example problems. 3.12. Summary  4. Irreversibility in real life. 4.1. Introduction. 4.2. Phenomenology  the linear dissipative laws. 4.3. Microscopic basis of the irreversible linear laws. 4.4. Solving the linear macroscopic equations. 4.5. Nonequilibrium entropy changes. 4.6. Fluctuations and nonequilibrium states. 4.7. Deviations from the phenomenological linear laws. 4.8. Causes of irreversibility a la Boltzmann and Lyapunov. 4.9. RayleighBenard algorithm with atomistic flow. 4.10. RayleighBenard algorithm for a continuum. 4.11. Three RayleighBenard example problems. 4.12. Summary  5. Microscopic computer simulation. 5.1. Introduction. 5.2. Integrating the motion equations. 5.3. Interpretation of results. 5.4. Control of a falling particle. 5.5. Second law of thermodynamics. 5.6. Simulating shear flow and heat flow. 5.7. Shockwaves. 5.8. Algorithm for periodic shear flow with doll's tensor. 5.9. Example problems. 5.10. Summary. ; 8 6. Shockwaves revisited. 6.1. Introduction. 6.2. Equation of state information from shockwaves. 6.3. Shockwave conditions for molecular dynamics. 6.4. Shockwave stability. 6.5. Thermodynamic variables. 6.6. Shockwave profiles from continuum mechanics 6.7. Comparing model profiles with molecular dynamics. 6.8. Lyapunov instability in strong shockwaves. 6.9. Summary  7. Macroscopic computer simulation. 7.1. Introduction. 7.2. Continuity and coordinate systems. 7.3. Macroscopic flow variables. 7.4. Finitedifference methods. 7.5. Finiteelement methods. 7.6. Smooth particle applied mechanics [SPAM]. 7.7. A SPAM algorithm for RayleighBenard convection. 7.8. Applications of SPAM to RayleighBenard flows. 7.9. Summary  8. Chaos, Lyapunov instability, fractals. 8.1. Introduction.{esc}{dollar}1 
Publisher 
World Scientific Pub. Co. 
Subject 
Statistical mechanics. Time reversal  Computer simulation. 
Identifier (Full text) 
http://www.worldscientific.com/worldscibooks/10.1142/8344#t=toc 
ISBN 
9789814383172 (electronic bk.) ; 9814383163 ; 9789814383165 
Language 
eng 
Type 
Text 
FormatExtent 
xxiv, 401 p. : ill. (some col.) 
Date 
c2012. 
RelationIs Part Of 
Advanced series in nonlinear dynamics v. 13 
OCLC number 
874502270 
CONTENTdm number 
1651 