Time Reversibility, Computer Simulation, Algorithms, Chaos (2nd Edition)

COMPUTER SIMULATION

By: Carol Griswold Hoover, William Graham Hoover

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Hardcover | 22 June 2012 | Edition Number 2

At a Glance

Hardcover
428 Pages

Edition Type
Revised

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22.9 x 16.4 x 2.8

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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 authors' approach to the problem of 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 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 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 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 worked-out examples, and includes considerable new material on shockwaves, Lyapunov instability and fluctuations.

Industry Reviews

Bill and Carol Hoover have teamed up to produce this greatly expanded new edition of Bill's earlier book grappling with one of the oldest problems in physics - reconciling the irreversibility of thermodynamics with the reversibility of Newtonian mechanics. -- Julien Clinton Sprott "Emeritus Professor of Physics, University of Wisconsin - Madison, Author of Chaos and Time-Series Analysis and Elegant Chaos"
The second edition with over 100 pages of new material, gives an up-to-date and distinctive treatment of physical issues, emphasizing the need for a holistic view incorporating theory, simulation and experiment. I -- Dr Carl Dettmann "University of Bristol"

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Non-Fiction Science Science in General Philosophy of Science Physics Thermodynamics & Heat Astronomy, Space & Time Time & Chronology Mathematics Applied Mathematics Nonlinear Science Statistical Physics

Calculus & Mathematical Analysis Numerical Analysis Booktopia Publisher Services World Scientific Publishing

Preface	p. vii
Preface to the First Edition	p. xi
Glossary of Technical Terms	p. xxi
Time Reversibility, Computer Simulation, Algorithms, Chaos	p. 1
Microscopic Reversibility; Macroscopic Irreversibility	p. 1
Time Reversibility of Irreversible Processes	p. 6
Classical Microscopic and Macroscopic Simulation	p. 8
Continuity, Information, and Bit Reversibility	p. 10
Instability and Chaos	p. 11
Simple Explanations of Complex Phenomena	p. 13
The Paradox: Irreversibility from Reversible Dynamics	p. 15
Algorithm: Fourth-Order Runge-Kutta Integrator	p. 16
Example Problems	p. 20
Equilibrium Baker Map	p. 21
Equilibrium Galton Board	p. 25
Equilibrium Hookean Pendulum	p. 29
Nosé-Hoover Oscillator with a Temperature Gradient	p. 32
Summary and Notes	p. 36
Notes and References	p. 37
Time-Reversibility in Physics and Computation	p. 39
Introduction	p. 39
Time Reversibility	p. 41
Levesque and Verlet's Bit-Reversible Algorithm	p. 44
Lagrangian and Hamiltonian Mechanics	p. 46
Liouville's Incompressible Theorem	p. 49
What is Macroscopic Thermodynamics?	p. 50
First and Second Laws of Thermodynamics	p. 52
Temperature, Zeroth Law, Reservoirs, Thermostats	p. 54
Irreversibility from Stochastic Irreversible Equations	p. 58
Irreversibility from Time-Reversible Equations?	p. 60
An Algorithm Implementing Bit-Reversible Dynamics	p. 61
Example Problems	p. 67
Time-Reversible Dissipative Map	p. 68
A Smooth-Potential Galton Board	p. 73
Summary	p. 77
Notes and References	p. 78
Gibbs' Statistical Mechanics	p. 81
Scope and History	p. 81
Formal Structure of Gibbs' Statistical Mechanics	p. 83
Initial Conditions, Boundary Conditions, Ergodicity	p. 86
From Hamiltonian Dynamics to Gibbs' Probability	p. 89
From Gibbs' Probability to Thermodynamics	p. 90
Pressure and Energy from Gibbs' Canonical Ensemble	p. 92
Gibbs' Entropy versus Boltzmann's Entropy	p. 93
Number-Dependence and Thermodynamics Fluctuations	p. 96
Green and Kubo's Linear-Response Theory	p. 97
An Algorithm for Local Smooth-Particle Averages	p. 99
Example Problems	p. 103
Quasiharmonic Thermodynamics	p. 104
Hard-Disk and Hard-Sphere Thermodynamics	p. 106
Time-Reversible Confined Free Expansion	p. 108
Summary	p. 111
Notes and References	p. 112
Irreversibility in Real Life	p. 113
Introduction	p. 113
Phenomenology - the Linear Dissipative Laws	p. 116
Microscopic Basis of the Irreversible Linear Laws	p. 117
Solving the Linear Macroscopic Equations	p. 119
Nonequilibrium Entropy Changes	p. 120
Fluctuations and Nonequilibrium States	p. 123
Deviations from the Phenomenological Linear Laws	p. 124
Causes of Irreversibility à la Boltzmann and Lyapunov	p. 126
Rayleigh-Bénard Algorithm with Atomistic Flow	p. 128
Rayleigh-Bénard Algorithm for a Continuum	p. 135
Three Rayleigh-Bénard Example Problems	p. 140
Rayleigh-Bénard Flow via Lorenz' Attractor	p. 142
Rayleigh-Bénard Flow with Continuum Mechanics	p. 144
Rayleigh-Bénard Flow with Molecular Dynamics	p. 154
Summary	p. 159
Notes and References	p. 160
Microscopic Computer Simulation	p. 163
Introduction	p. 163
Integrating the Motion Equations	p. 164
Interpretation of Results	p. 165
Control of a Falling Particle	p. 168
Second Law of Thermodynamics	p. 176
Simulating Shear Flow and Heat Flow	p. 177
Shockwaves	p. 181
Algorithm for Periodic Shear Flow with Doll's Tensor	p. 184
Example Problems	p. 188
Isokinetic Nonequilibrium Galton Board	p. 189
Heat-Conducting One-Dimensional Oscillator	p. 192
Many-Body Heat Flow	p. 195
Summary	p. 196
Notes and References	p. 197
Shockwaves Revisited	p. 199
Introduction	p. 199
Equation of State Information from Shockwaves	p. 201
Shockwave Conditions for Molecular Dynamics	p. 203
Shockwave Stability	p. 206
Thermodynamic Variables	p. 214
Shockwave Profiles from Continuum Mechanics	p. 215
Shockwave Profile with Shear Viscosity	p. 217
Shockwave Profile with Viscosity and Conductivity	p. 220
Shockwave Profiles with Tensor Temperatures	p. 222
Flow Algorithm with Maxwell-Cattaneo Time Delays	p. 223
Comparing Model Profiles with Molecular Dynamics	p. 229
Lyapunov Instability in Strong Shockwaves	p. 232
Summary	p. 238
Notes and References	p. 238
Macroscopic Computer Simulation	p. 241
Introduction	p. 241
Continuity and Coordinate Systems	p. 243
Macroscopic Flow Variables	p. 245
Finite-Difference Methods	p. 246
Finite-Element Methods	p. 248
Smooth Particle Applied Mechanics [SPAM]	p. 251
A SPAM Algorithm for Rayleigh-Bénard Convection	p. 255
Initial Conditions	p. 255
SPAM Evaluation of the Particle Densities	p. 257
SPAM Evaluation of {∇u} and {∇T}	p. 258
SPAM Evaluation of the Constitutive Relations	p. 260
Applications of SPAM to Rayleigh-Bénard Flows	p. 262
SPAM with and without a Core Potential	p. 266
SPAM and Kinetic-Energy Fluctuations	p. 268
Summary	p. 271
Notes and References	p. 271
Chaos, Lyapunov Instability, Fractals	p. 273
Introduction	p. 273
Continuum Mathematics	p. 277
Chaos	p. 278
The Spectrum of Lyapunov Exponents	p. 279
Fractal Dimensions	p. 284
A Simple Ergodic Fractal	p. 288
Fractal Attractor-Repeller Pairs	p. 290
A Global Second Law from Reversible Chaos	p. 292
Coarse-Grained and Fine-Grained Entropy	p. 297
Oscillators, Lyapunov Algorithms, Fractal Dimensions	p. 298
A Thought-Provoking Oscillator Exercise	p. 298
Doubly-Thermostated Oscillator; Lyapunov Spectra	p. 300
Lyapunov Spectra from a Chaotic Double Pendulum	p. 310
Coarse-Grained Galton Board Entropy	p. 312
Color Conductivity	p. 313
Summary	p. 316
Notes and References	p. 317
Resolving the Reversibility Paradox	p. 319
Introduction	p. 319
Irreversibility from Boltzmann's Kinetic Theory	p. 320
Boltzmann's Equation Today	p. 325
Gibbs' Statistical Mechanics	p. 327
Jaynes' Information theory	p. 330
Green and Kubo's Linear Response Theory	p. 332
Thermomechanics	p. 334
The Delay Times Separating Causes from their Effects	p. 336
A Fluctuation Theorem	p. 337
Are Initial Conditions Relevant?	p. 340
Constrained Hamiltonian Ensembles	p. 343
Anosov Systems and Sinai-Ruelle-Bowen Measures	p. 344
Trajectories versus Distribution Functions	p. 347
Are Maps Relevant?	p. 348
Irreversibility ← Time-Reversible Motion Equations	p. 351
Boltzmann-Equation Shockwave-Structure Algorithm	p. 353
Summary	p. 359
Notes and References	p. 361
Afterword-a Research Perspective	p. 363
Introduction	p. 363
What do we Know?	p. 364
Why Reversibility is Still a Problem	p. 366
Change and Innovation	p. 369
Role of Examples	p. 372
Role of Chaos and Fractals	p. 374
Role of Mathematics	p. 374
Remaining Puzzles	p. 376
Summary	p. 379
Acknowledgments	p. 383
Bibliography	p. 387
Index	p. 397
Table of Contents provided by Ingram. All Rights Reserved.

Time Reversibility, Computer Simulation, Algorithms, Chaos (2nd Edition)

COMPUTER SIMULATION

At a Glance

Hardcover

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