Table of contents for An introduction to computer simulation methods : applications to physical systems / Harvey Gould, Jan Tobochnik, Wolfgang Christian.

Bibliographic record and links to related information available from the Library of Congress catalog.

Note: Contents data are machine generated based on pre-publication provided by the publisher. Contents may have variations from the printed book or be incomplete or contain other coding.


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1 Introduction 1
1.1 Importance of Computers in Physics 1 
1.2 The Importance of Computer Simulation 3
1.3 Programming Languages 4
1.4 Object-Oriented Techniques 5
1.5 How to Use this Book 6
2 Tools for Doing Simulations 12
2.1 Introduction 12
2.2 Simulating Free Fall 14
2.3 Getting Started with Object-Oriented Programming 19
2.4 Inheritance 26
2.5 The Open Source Physics Library 29
2.6 Animation and Simulation 35
2.7 Model-View-Controller 41
3 Simulating Particle Motion 45
3.1 Modified Euler Algorithms 45
3.2 Interfaces 47
3.3 Drawing 48
3.4 Specifying the State of a System Using Arrays 51
3.5 The ODE Interface 54
3.6 The ODE-Solver Interface 55
3.7 Effects of Drag Resistance 57
3.8 Two-Dimensional Trajectories 64
3.9 Decay Processes 66
*3.10 Visualizing Three-Dimensional Motion 69
3.11 Levels of Simulation 74
4 Oscillations 86
4.1 Simple Harmonic Motion 86
4.2 The Motion of a Pendulum 89
4.3 Damped Harmonic Oscillator 93
4.4 Response to External Forces 94
4.5 Electrical Circuit Oscillations 98
4.6 Accuracy and Stability 102
4.7 Projects 104
5 Few-Body Problems: The Motion of the Planets 108
5.1 Planetary Motion 108
5.2 The Equations of Motion 108
5.3 Circular and Elliptical Orbits 110
5.4 Astronomical Units 112
5.5 Log-Log and Semilog Plots 112
5.6 Simulation of the Orbit 115
5.7 Impulsive Forces 119
5.8 Velocity Space 122
5.9 A Mini-Solar System 123
5.10 Two-Body Scattering 126
5.11 Three-Body Problems 133
5.12 Projects 137
6 The Chaotic Motion of Dynamical Systems 141
6.1 Introduction 141
6.2 A Simple One-Dimensional Map 141
6.3 Period Doubling 147
6.4 Universal Properties and Self-Similarity 153
6.5 Measuring Chaos 157
*6.6 Controlling Chaos 162
6.7 Higher-Dimensional Models 166
6.8 Forced Damped Pendulum 169
*6.9 Hamiltonian Chaos 173
6.10 Perspective 181
6.11 Projects 181
7 Random Processes 197
7.1 Order to Disorder 197
7.2 Random Walks 203
7.3 Modified Random Walks 210
7.4 The Poisson Distribution and Nuclear Decay 217
7.5 Problems in Probability 219
7.6 Method of Least Squares 221
7.7 Applications to Polymers 225
7.8 Diffusion-Controlled Chemical Reactions 233
7.9 Random Number Sequences 236
7.10 Variational Methods 240
7.11 Projects 245
Appendix 7A: Random Walks and the Diffusion Equation 249
8 The Dynamics of Many-Particle Systems 255
8.1 Introduction 255
8.2 The Intermolecular Potential 255
8.3 Units 256
8.4 The Numerical Algorithm 258
8.5 Periodic Boundary Conditions 258
8.6 A Molecular Dynamics Program 261
8.7 Thermodynamic Quantities 273
8.8 Radial Distribution Function 280
8.9 Hard Disks 282
8.10 Dynamical Properties 293
8.11 Extensions 297
8.12 Projects 300
9 Normal Modes and Waves 313
9.1 Coupled Oscillators and Normal Modes 313
9.2 Numerical Solutions 319
9.3 Fourier Series 322
9.4 Two-Dimensional Fourier Series 333
9.5 Fourier Integrals 335
9.6 Power Spectrum 336
9.7 Wave Motion 340
9.8 Interference 345
9.9 Fraunhofer Diffraction 352
9.10 Fresnel Diffraction 355
Appendix 9A: Complex Fourier Series 358
Appendix 9B: Fast Fourier Transform 359
Appendix 9C: Plotting Scalar Fields 362
10 Electrodynamics 366
10.1 Static Charges 366
10.2 Electric Fields 366
10.3 Electric Field Lines 370
10.4 Electric Potential 376
10.5 Numerical Solutions of Boundary Value Problems 378
10.6 Random Walk Solution of Laplace's Equation 387
*10.7 Fields Due to Moving Charges 390
*10.8 Maxwell's Equations 398
10.9 Projects 407
Appendix A: Plotting Vector Fields 408
11 Numerical and Monte Carlo Methods 412
11.1 Numerical Integration Methods in One Dimension 412
11.2 Simple Monte Carlo Evaluation of Integrals 421
11.3 Multidimensional Integrals 424
11.4 Monte Carlo Error Analysis 426
11.5 Nonuniform Probability Distributions 429
11.6 Importance Sampling 433
11.7 Metropolis Algorithm 435
*11.8 Neutron Transport 438
12 Percolation 452
12.1 Introduction 452
12.2 The Percolation Threshold 454
12.3 Finding Clusters 463
12.4 Critical Exponents and Finite Size Scaling 471
12.5 The Renormalization Group 475
12.6 Projects 482
13 Fractals and Kinetic Growth Models 491
13.1 The Fractal Dimension 491
13.2 Regular Fractals 499
13.3 Kinetic Growth Processes 502
13.4 Fractals and Chaos 520
13.5 Many Dimensions 522
13.6 Projects 523
14 Complex Systems 530
14.1 Cellular Automata 530
14.2 Self-Organized Critical Phenomena 543
14.3 The Hopfield Model and Neural Networks 551
14.4 Growing Networks 555
14.5 Genetic Algorithms 561
14.6 Lattice Gas Models of Fluid Flow 568
14.7 Overview and Projects 579
15 Monte Carlo Simulations of Thermal Systems 591
15.1 Introduction 591
15.2 The Microcanonical Ensemble 591
15.3 The Demon Algorithm 593
15.4 The Demon as a Thermometer 597
15.5 The Ising Model 599
15.6 The Metropolis Algorithm 604
15.7 Simulation of the Ising Model 610
15.8 The Ising Phase Transition 619
15.9 Other Applications of the Ising Model 624
15.10 Simulation of Classical Fluids 628
15.11 Optimized Monte Carlo Data Analysis 634
*15.12 Other Ensembles 639
15.13 More Applications 644
15.14 Projects 646
16 Quantum Systems 674
16.1 Introduction 674
16.2 Review of Quantum Theory 675
16.3 Bound State Solutions 680
16.4 Time Development of Eigenstate Superpositions 685
16.5 The Time-Dependent Schr\"odinger Equation 690
16.6 Fourier Transformations and Momentum Space 696
16.7 Variational Methods 700
16.8 Random Walk Solutions of the Schr\"odinger Equation 702
16.9 Diffusion Quantum Monte Carlo 709
16.10 Path Integral Quantum Monte Carlo 712
16.11 Projects 716
Appendix A: Visualizing Complex Functions 718
17 Visualization and Rigid Body Dynamics 723
17.1 Two-Dimensional Transformations 723
17.2 Three-Dimensional Transformations 727
17.3 The Three-Dimensional Open Source Physics Library 733
17.4 Dynamics of a Rigid Body 736
17.5 Quaternion Arithmetic 741
17.6 Quaternion Equations of Motion 743
17.7 Rigid Body Model 749
17.8 Motion of a Spinning Top 754
17.9 Projects 757
18 Seeing in Special and General Relativity 764
18.1 Special Relativity 764
18.2 General Relativity 768
18.3 Dynamics in Polar Coordinates 769
18.4 Black Holes and Schwarzschild Coordinates 771
18.5 Particle and Light Trajectories 773
18.6 Seeing 775
18.7 General Relativistic Dynamics 776
*18.8 The Kerr Metric 777
18.9 Projects 779
19 Epilogue: The Unity of Physics 781
19.1 The Unity of Physics 781
19.2 Spiral Galaxies 782
19.3 Numbers, Pretty Pictures, and Insight 783
19.4 Constrained Dynamics 785
19.5 What are Computers Doing to Physics? 789

Library of Congress Subject Headings for this publication:

Physics -- Data processing.
Physics -- Simulation methods.
Physics -- Computer simulation.