Introduction to Computer Simulation Methods

second edition

Table of Contents

Preface
Chapter 1 Introduction
1.1 Importance of Computers in Physics
1.2 The Nature of Computer Simulation
1.3 Importance of Graphics
1.4 Programming Languages
1.5 Learning to Program
1.6 How to Use This Book
1A Laboratory Report
Chapter 2 The Coffee Cooling Problem
2.1 Background
2.2 The Euler Algorithm
2.3 Simple Example
2.4 Some True BASIC Programs
2.5 Computer Program for the Euler Method
2.6 The Coffee Cooling Problem
2.7 Accuracy and Stability
2.8 Simple Plots
2.9 Visualization
2.10 Nuclear Decay
2.11 Overview
2A Integer and Real Variables
Chapter 3 The Motion of Falling Objects
3.1 Background
3.2 The Force on a Falling Object
3.3 The Euler Method for Newton's Laws of Motion
3.4 A Program for One-Dimensional Motion
3.5 Two-Dimensional Trajectories
3.6 Levels of Simulation
3.7 Further Applications
3A Subroutine for Drawing Axes
3B Data Files
3C Strong Typing and Debugging
3D The Euler-Richardson Method
Chapter 4 The Two-Body Problem
4.1 Introduction
4.2 The Equations of Motion
4.3 Circular and Elliptical Orbits
4.4 Astronomical Units
4.5 Array Variables and Aspect Ratio
4.6 Log-log and Semilog Plots
4.7 Simulation of the Orbit
4.8 Perturbations
4.9 Velocity Space
4.10 A Mini-Solar System
4.11 Two-Body Scattering
4.12 Projects
Chapter 5 Simple Linear and Nonlinear Systems
5.1 Simple Harmonic Motion
5.2 Numerical Simulation of the Harmonic Oscillator
5.3 The Simple Pendulum
5.4 Output and Animation
5.5 Dissipative Systems
5.6 Response to External Forces
5.7 Electrical Circuit Oscillations
5.8 Projects
5A Numerical Integration of Newton's Equation of Motion
Chapter 6 The Chaotic Motion of Dynamical Systems
6.1 Introduction
6.2 A Simple One-Dimensional Map
6.3 Period-Doubling
6.4 Universal Properties and Self-Similarity
6.5 Measuring Chaos
6.6 Controlling Chaos
6.7 Higher-Dimensional Models
6.8 Forced Damped Pendulum
6.9 Hamiltonian Chaos
6.10 Perspective
6.11 Projects
Chapter 7 Random Processes
7.1 Order to Disorder
7.2 The Poisson Distribution and Nuclear Decay
7.3 Introduction to Random Walks
7.4 Problems in Probability
7.5 Method of Least Squares
7.6 Introduction to Variational Monte Carlo
7A Random Walks and the Diffusion Equation
Chapter 8 The Dynamics of Many Particle Systems
8.1 Introduction
8.2 The Intermolecular Potential
8.3 The Numerical Algorithm
8.4 Boundary Conditions
8.5 Units
8.6 A Molecular Dynamics Program
8.7 Thermodynamic Quantities
8.8 Radial Distribution Function
8.9 Hard disks
8.10 Dynamical Properties
8.11 Extensions
8.12 Projects
Chapter 9 Normal Modes and Waves
9.1 Coupled Oscillators and Normal Modes
9.2 Fourier Transforms
9.3 Wave Motion
9.4 Interference and Diffraction
Chapter 10 Electrodynamics
10.1 Static Charges
10.2 Numerical Solutions of Laplace's Equation
10.3 Random Walk Solution of Laplace's Equation
10.4 Fields Due to Moving Charges
10.5 Maxwell's Equations
Chapter 11 Numerical Integration and Monte Carlo Methods
11.1 Numerical Integration Methods in One Dimension
11.2 Simple Monte Carlo Evaluation of Integrals
11.3 Numerical Integration of MultiDimensional Integrals
11.4 Monte Carlo Error Analysis
11.5 Nonuniform Probability Distributions
11.6 Neutron Transmission
11.7 Importance Sampling
11.8 Metropolis Monte Carlo Method
11A Error Estimates for Numerical Integration
11B The Standard Deviation of the Mean
11C The Acceptance-Rejection Method
Chapter 12 Random Walks
12.1 Introduction
12.2 Applications To Polymers
12.3 The Continuum Limit
12.4 Random Number Sequences
Chapter 13 The Percolation Problem
13.1 Introduction
13.2 The Percolation Threshold
13.3 Cluster Labeling
13.4 Critical Exponents and Finite Size Scaling
13.5 The Renormalization Group
Chapter 14 Fractals
14.1 Fractal Dimension
14.2 Regular Fractals
14.3 Fractal Growth Processes
14.4 Fractals and Chaos
14.5 Many Dimensions
14.6 Projects
Chapter 15 Complexity
15.1 Cellular Automata
15.2 Lattice Gas Models of Fluid Flow
15.3 Self-Organized Criticality
15.4 Neural Networks
15.5 Genetic Algorithms
15.6 Overview
Chapter 16 The Microcanonical Ensemble
16.1 Introduction
16.2 The Microcanonical Ensemble
16.3 The Demon Algorithm
16.4 One-Dimensional Classical Ideal Gas
16.5 The Temperature and the Canonical Ensemble
16.6 The Ising Model
16.7 Heat Flow
16.8 Comment
16A Relation of the Mean Demon Energy to the Temperature
Chapter 17 Monte Carlo Simulation of the Canonical Ensemble
17.1 The Canonical Ensemble
17.2 The Metropolis Algorithm
17.3 Verification of the Boltzmann Distribution
17.4 The Ising Model
17.5 The Ising Phase Transition
17.6 Other Applications of the Ising Model
17.7 Simulation of Classical Fluids
17.8 Optimized Monte Carlo Data Analysis
17.9 Other Ensembles
17.10 Other Applications
17.11 Projects
17A The Canonical Ensemble
17B Exact Enumeration of the 2 x 2 Ising Model
Chapter 18 Quantum Systems
18.1 Introduction
18.2 Review of Quantum Theory
18.3 Bound State Solutions
18.4 The Time-Dependent Schrodinger Equation
18.5 Variational Methods
18.6 Random Walk Quantum Monte Carlo
18.7 Diffusion Quantum Monte Carlo
18.8 Path Integral Quantum Monte Carlo
Chapter 19 Epilogue: The Same Programs Have the Same Solutions
19.1 The Unity of Physics
19.2 Percolation and Galaxies
19.3 Insight Versus Numbers and Pretty Pictures
19.4 What are Computers Doing to Physics?
Appendix A From BASIC to Fortran
Appendix B From BASIC to C