Time reversibility, computer simulation, algorithms, chaos
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| Hauptverfasser: | , |
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Singapore [u.a.]
World Scientific
2012
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| Ausgabe: | 2. ed. |
| Schriftenreihe: | Advanced series in nonlinear dynamics
13 |
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| 007 | t| | ||
| 008 | 120419s2012 xx ad|| |||| 00||| eng d | ||
| 020 | |a 9789814383165 |9 978-981-4383-16-5 | ||
| 020 | |a 9814383163 |9 981-4383-16-3 | ||
| 035 | |a (OCoLC)796207808 | ||
| 035 | |a (DE-599)BVBBV040108723 | ||
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| 084 | |a UG 3900 |0 (DE-625)145629: |2 rvk | ||
| 100 | 1 | |a Hoover, William G. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Time reversibility, computer simulation, algorithms, chaos |c William Graham Hoover ; Carol Griswold Hoover |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a Singapore [u.a.] |b World Scientific |c 2012 | |
| 300 | |a XXIV, 401 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Advanced series in nonlinear dynamics |v 13 | |
| 650 | 0 | 7 | |a Computersimulation |0 (DE-588)4148259-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Nichtlineare Optimierung |0 (DE-588)4128192-5 |2 gnd |9 rswk-swf |
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| 689 | 0 | 1 | |a Computersimulation |0 (DE-588)4148259-1 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Hoover, Carol G. |e Verfasser |4 aut | |
| 830 | 0 | |a Advanced series in nonlinear dynamics |v 13 |w (DE-604)BV004464593 |9 13 | |
| 856 | 4 | 2 | |m Digitalisierung UB Regensburg |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024965122&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-024965122 | |
Datensatz im Suchindex
| DE-19_call_number | 1705/UG 3900 H789(2) |
|---|---|
| DE-19_location | 95 |
| DE-BY-UBM_katkey | 4691925 |
| DE-BY-UBM_media_number | 41620563550014 |
| _version_ | 1823055112445100032 |
| adam_text | Contents
Preface vii
Preface
to the
First
Edition
xi
Glossary of Technical Terms
xxi
1.
Time Reversibility, Computer Simulation, Algorithms, Chaos
1
1.1
Microscopic Reversibility; Macroscopic
Irreversibili
ty
... 1
1.2
Time Reversibility of Irreversible Processes
........ 6
1.3
Classical Microscopic and Macroscopic Simulation
.... 8
1.4
Continuity, Information, and Bit Reversibility
....... 10
1.5
Instability and Chaos
.................... 11
1.6
Simple Explanations of Complex Phenomena
....... 13
1.7
The Paradox: Irreversibility from Reversible Dynamics
. . 15
1.8
Algorithm: Fourth-Order Runge-Kutta Integrator
.... 16
1.9
Example Problems
...................... 20
1.9.1
Equilibrium Baker Map
............... 21
1.9.2
Equilibrium Galton Board
............. 25
1.9.3
Equilibrium Hookean Pendulum
.......... 29
1.9.4
Nose-Hoover Oscillator with a Temperature
Gradient
....................... 32
1.10
Summary and Notes
..................... 36
1.10.1
Notes and References
................ 37
2.
Time-Reversibility in Physics and Computation
39
2.1
Introduction
.......................... 39
2.2
Time Reversibility
...................... 41
xvi
Time Reversibility, Computer Simulation, Algorithms, Chaos
2.3
Levesque and Verlet s Bit-Reversible Algorithm
...... 44
2.4
Lagrangian and Hamiltonian Mechanics
.......... 46
2.5
Liouville s Incompressible Theorem
............. 49
2.6
What Is Macroscopic Thermodynamics?
.......... 50
2.7
First and Second Laws of Thermodynamics
........ 52
2.8
Temperature, Zeroth Law, Reservoirs, Thermostats
.... 54
2.9
Irreversibility from Stochastic Irreversible Equations
... 58
2.10
Irreversibility from Time-Reversible Equations?
...... 60
2.11
An Algorithm Implementing Bit-Reversible Dynamics
. . 61
2.12
Example Problems
...................... 67
2.12.1
Time-Reversible Dissipative Map
......... 68
2.12.2
A Smooth-Potential Galton Board
......... 73
2.13
Summary
........................... 77
2.13.1
Notes and References
................ 78
3.
Gibbs Statistical Mechanics
81
3.1
Scope and History
...................... 81
3.2
Formal Structure of Gibbs Statistical Mechanics
..... 83
3.3
Initial Conditions, Boundary Conditions, Ergodicity
... 86
3.4
From Hamiltonian Dynamics to Gibbs Probability
.... 89
3.5
From Gibbs Probability to Thermodynamics
....... 90
3.6
Pressure and Energy from Gibbs Canonical Ensemble
. . 92
3.7
Gibbs Entropy versus Boltzmann s Entropy
........ 93
3.8
Number-Dependence and Thermodynamic Fluctuations
. 96
3.9
Green and Kubo s Linear-Response Theory
........ 97
3.10
An Algorithm for Local Smooth-Particle Averages
.... 99
3.11
Example Problems
...................... 103
3.11.1
Quasiharmonic Thermodynamics
......... 104
3.11.2
Hard-Disk and Hard-Sphere Thermodynamics
. . 106
3.11.3
Time-Reversible Confined Free Expansion
.... 108
3.12
Summary
...........................
Ill
3.12.1
Notes and References
................ 112
4.
Irreversibility in Real Life
113
4.1
Introduction
.......................... 113
4.2
Phenomenology
—
the Linear Dissipative Laws
...... 116
4.3
Microscopic Basis of the Irreversible Linear Laws
..... 117
4.4
Solving the Linear Macroscopic Equations
......... 119
Contents xvii
4.5 Nonequilibrium
Entropy Changes
.............. 120
4.6
Fluctuations and Nonequilibrium States
.......... 123
4.7
Deviations from the Phenomenological Linear Laws
.... 124
4.8
Causes of Irreversibility
à
la Boltzmann and Lyapunov
. . 126
4.9
Rayleigh-Bénard
Algorithm with Atomistic Flow
..... 128
4.10
Rayleigh-Bénard
Algorithm for a Continuum
....... 135
4.11
Three
Rayleigh-Bénard
Example Problems
........ 140
4.11.1
Rayleigh-Bénard
Flow via
Lorenz
Attractor
. . . 142
4.11.2
Rayleigh-Bénard
Flow with Continuum Mechanics
144
4.11.3
Rayleigh-Bénard
Flow with Molecular Dynamics
. 154
4.12
Summary
........................... 159
4.12.1
Notes and References
................ 160
5.
Microscopic Computer Simulation
163
5.1
Introduction
.......................... 163
5.2
Integrating the Motion Equations
.............. 164
5.3
Interpretation of Results
................... 165
5.4
Control of a Falling Particle
................. 168
5.5
Second Law of Thermodynamics
.............. 176
5.6
Simulating Shear Flow and Heat Flow
........... 177
5.7
Shockwaves
.......................... 181
5.8
Algorithm for Periodic Shear Flow with Doll s Tensor
. . 184
5.9
Example Problems
...................... 188
5.9.1
Isokinetic Nonequilibrium Galton Board
..... 189
5.9.2
Heat-Conducting One-Dimensional Oscillator
. . . 192
5.9.3
Many-Body Heat Flow
............... 195
5.10
Summary
........................... 196
5.10.1
Notes and References
................ 197
6.
Shockwaves Revisited
199
6.1
Introduction
.......................... 199
6.2
Equation of State Information from Shockwaves
...... 201
6.3
Shockwave Conditions for Molecular Dynamics
...... 203
6.4
Shockwave Stability
..................... 206
6.5
Thermodynamic Variables
.................. 214
6.6
Shockwave Profiles from Continuum Mechanics
...... 215
6.6.1
Shockwave Profile with Shear Viscosity
...... 217
xviii
Time Reversibility, Computer Simulation, Algorithms, Chaos
6.6.2
Shockwave Profile with Viscosity and
Conductivity
..................... 220
6.6.3
Shockwave Profiles with Tensor Temperatures
. . 222
6.6.4
Flow Algorithm with Maxwell-Cattaneo
Time Delays
..................... 223
6.7
Comparing Model Profiles with Molecular Dynamics
. . . 229
6.8
Lyapunov Instability in Strong Shockwaves
........ 232
6.9
Summary
........................... 238
6.9.1
Notes and References
................ 238
7.
Macroscopic Computer Simulation
241
7.1
Introduction
.......................... 241
7.2
Continuity and Coordinate Systems
............ 243
7.3
Macroscopic Flow Variables
................. 245
7.4
Finite-Difference Methods
.................. 246
7.5
Finite-Element Methods
................... 248
7.6
Smooth Particle Applied Mechanics [SPAM]
........ 251
7.7
A SPAM Algorithm for
Rayleigh-Bénard
Convection
. . . 255
7.7.1
Initial Conditions
.................. 255
7.7.2
SPAM Evaluation of the Particle Densities
.... 257
7.7.3
SPAM Evaluation of
{Vu}
and {VT}
...... 258
7.7.4
SPAM Evaluation of the Constitutive Relations
. 260
7.8
Applications of SPAM to
Rayleigh-Bénard
Flows
..... 262
7.8.1
SPAM with and without a Core Potential
..... 266
7.8.2
SPAM and Kinetic-Energy Fluctuations
...... 268
7.9
Summary
........................... 271
7.9.1
Notes and References
................ 271
8.
Chaos, Lyapunov Instability, Fractals
273
8.1
Introduction
.......................... 273
8.2
Continuum Mathematics
................... 277
8.3
Chaos
............................. 278
8.4
The Spectrum of Lyapunov Exponents
........... 279
8.5
Fractal Dimensions
...................... 284
8.6
A Simple Ergodic Fractal
.................. 288
8.7
Fractal Attractor-Repeller Pairs
.............. . 290
8.8
A Global Second Law from Reversible Chaos
....... 292
8.9
Coarse-Grained and Fine-Grained Entropy
......... 297
Contents xix
8.10
Oscillators, Lyapunov Algorithms, Fractal Dimensions
. . 298
8.10.1
A Thought-Provoking Oscillator Exercise
..... 298
8.10.2
Doubly-Thermostated Oscillator; Lyapunov
Spectra
........................ 300
8.10.3
Lyapunov Spectra for a Chaotic Double
Pendulum
...................... 310
8.10.4
Coarse-Grained Galton Board Entropy
...... 312
8.10.5
Color Conductivity
................. 313
8.11
Summary
........................... 316
8.11.1
Notes and References
................ 317
9.
Resolving the Reversibility Paradox
319
9.1
Introduction
.......................... 319
9.2
Irreversibility from Boltzmann s Kinetic Theory
...... 320
9.3
Boltzmann s Equation Today
................ 325
9.4
Gibbs Statistical Mechanics
................. 327
9.5
Jaynes Information Theory
................. 330
9.6
Green and Kubo s Linear Response Theory
........ 332
9.7
Thermomechanics
...................... 334
9.8
The Delay Times Separating Causes from their Effects
. . 336
9.9
A Fluctuation Theorem
................... 337
9.10
Are Initial Conditions Relevant?
.............. 340
9.11
Constrained Hamiltonian Ensembles
............ 343
9.12
Anosov Systems and Sinai-Ruelle-Bowen Measures
.... 344
9.13
Trajectories versus Distribution Functions
......... 347
9.14
Are Maps Relevant?
..................... 348
9.15
Irreversibility
<—
Time-Reversible Motion Equations
. . 351
9.16
Boltzmann-Equation Shockwave-Structure Algorithm
. . . 353
9.17
Summary
........................... 359
9.17.1
Notes and References
................ 361
10.
Afterword
—
a Research Perspective
363
10.1
Introduction
.......................... 363
10.2
What do We Know?
..................... 364
10.3
Why Reversibility is Still a Problem
............ 366
10.4
Change and Innovation
................... 369
10.5
Role of Examples
....................... 372
10.6
Role of Chaos and Fractals
................. 374
xx
Time Reversibility, Computer Simulation, Algorithms, Chaos
10.7
Role of Mathematics
.............. ....... 374
10.8
Remaining Puzzles
...................... 376
10.9
Summary
........................... 379
10.10
Acknowledgments
....................... 383
Bibliography
387
Index
397
|
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| author_facet | Hoover, William G. Hoover, Carol G. |
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| discipline | Physik Informatik Mathematik |
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| format | Book |
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| id | DE-604.BV040108723 |
| illustrated | Illustrated |
| indexdate | 2025-02-03T17:28:01Z |
| institution | BVB |
| isbn | 9789814383165 9814383163 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-024965122 |
| oclc_num | 796207808 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR DE-19 DE-BY-UBM |
| owner_facet | DE-355 DE-BY-UBR DE-19 DE-BY-UBM |
| physical | XXIV, 401 S. Ill., graph. Darst. |
| publishDate | 2012 |
| publishDateSearch | 2012 |
| publishDateSort | 2012 |
| publisher | World Scientific |
| record_format | marc |
| series | Advanced series in nonlinear dynamics |
| series2 | Advanced series in nonlinear dynamics |
| spellingShingle | Hoover, William G. Hoover, Carol G. Time reversibility, computer simulation, algorithms, chaos Advanced series in nonlinear dynamics Computersimulation (DE-588)4148259-1 gnd Nichtlineare Optimierung (DE-588)4128192-5 gnd |
| subject_GND | (DE-588)4148259-1 (DE-588)4128192-5 |
| title | Time reversibility, computer simulation, algorithms, chaos |
| title_auth | Time reversibility, computer simulation, algorithms, chaos |
| title_exact_search | Time reversibility, computer simulation, algorithms, chaos |
| title_full | Time reversibility, computer simulation, algorithms, chaos William Graham Hoover ; Carol Griswold Hoover |
| title_fullStr | Time reversibility, computer simulation, algorithms, chaos William Graham Hoover ; Carol Griswold Hoover |
| title_full_unstemmed | Time reversibility, computer simulation, algorithms, chaos William Graham Hoover ; Carol Griswold Hoover |
| title_short | Time reversibility, computer simulation, algorithms, chaos |
| title_sort | time reversibility computer simulation algorithms chaos |
| topic | Computersimulation (DE-588)4148259-1 gnd Nichtlineare Optimierung (DE-588)4128192-5 gnd |
| topic_facet | Computersimulation Nichtlineare Optimierung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024965122&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV004464593 |
| work_keys_str_mv | AT hooverwilliamg timereversibilitycomputersimulationalgorithmschaos AT hoovercarolg timereversibilitycomputersimulationalgorithmschaos |