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