Introduction to Computer Simulation Methods: Applications to Physical Systems
third edition
Harvey Gould,
Jan Tobochnik, and
Wolfgang Christian
Addison-Wesley (2006)
Preface
- Introduction
- Importance of computers in physics
- The importance of computer simulation
- Programming languages
- Object-oriented techniques
- How to use this book
- Appendix 1A: Laboratory Reports
- Tools for Doing Simulations
- Introduction
- Simulating free fall
- Getting started with object oriented programming
- Inheritance
- The Open Source Physics library
- Animation and Simulation
- Model-View-Controller
- Appendix 2A: Complex Numbers
- Simulating Particle Motion
- Modified Euler algorithms
- Interfaces
- Drawing
- Specifying the state of a system using arrays
- The ODE interface
- The ODESolver interface
- Effects of Drag Resistance
- Two-Dimensional Trajectories
- Decay processes
- Visualizing Three-Dimensional Motion
- Levels of Simulation
- Oscillatory Systems
- Simple Harmonic Motion
- The Motion of a Pendulum
- Damped Harmonic Oscillator
- Response to External Forces
- Electrical Circuit Oscillations
- Accuracy and Stability
- Projects
- Few-Body Problems: The Motion of the Planets
- Planetary Motion
- The Equations of Motion
- Circular and Elliptical Orbits
- Astronomical Units
- Log-log and Semilog Plots
- Simulation of the Orbit
- Impulsive Forces
- Velocity Space
- A Mini-Solar System
- Two-Body Scattering
- Three-body problems
- Projects
- The Chaotic Motion of Dynamical Systems
- Introduction
- A Simple One-Dimensional Map
- Period Doubling
- Universal Properties and Self-Similarity
- Measuring Chaos
- *Controlling Chaos
- Higher-Dimensional Models
- Forced Damped Pendulum
- *Hamiltonian Chaos
- Perspective
- Projects
- Random Processes
- Order to Disorder
- Random Walks
- Modified Random Walks
- The Poisson Distribution and Nuclear Decay
- Problems in Probability
- Method of Least Squares
- Applications to Polymers
- Diffusion Controlled Chemical Reactions
- Random Number Sequences
- Variational Methods
- Projects
- Appendix 7A: Random Walks and the Diffusion Equation
- The Dynamics of Many Particle Systems
- Introduction
- The Intermolecular Potential
- Units
- The Numerical Algorithm
- Periodic Boundary Conditions
- A Molecular Dynamics Program
- Thermodynamic Quantities
- Radial Distribution Function
- Hard disks
- Dynamical Properties
- Extensions
- Projects
- Normal Modes and Waves
- Coupled Oscillators and Normal Modes
- Numerical Solutions
- Fourier Series
- Two-Dimensional Fourier Series
- Fourier Integrals
- Power Spectrum
- Wave Motion
- Interference
- Fraunhofer Diffraction
- Fresnel Diffraction
- Appendix 9A: Complex Fourier Series
- Appendix 9B: Fast Fourier Transform
- Appendix 9C: Plotting Scalar Fields
- Electrodynamics
- Static Charges
- Electric Fields
- Electric Field Lines
- Electric Potential
- Numerical Solutions of Boundary Value Problems
- Random Walk Solution of Laplace's Equation
- Fields Due to Moving Charges
- Maxwell's Equations
- Projects
- Appendix 10A: Vector Fields
- Numerical and Monte Carlo Methods
- Numerical Integration Methods in One Dimension
- Integrals as Differential Equations
- Simple Monte Carlo Evaluation of Integrals
- Multidimensional Integrals
- Monte Carlo Error Analysis
- Nonuniform Probability Distributions
- Importance Sampling
- *Neutron Transport
- Metropolis Algorithm
- Appendix 11A: Error Estimates for Numerical Integration
- Appendix 11B: The Standard Deviation of the Mean
- Appendix 11C: The Acceptance-Rejection Method
- Appendix 11D: Polynomials and Interpolation
- Percolation
- Introduction
- The Percolation Threshold
- Finding Clusters
- Critical Exponents and Finite Size Scaling
- The Renormalization Group
- Projects
- Fractals and Kinetic Growth Models
- The Fractal Dimension
- Regular Fractals
- Kinetic Growth Processes
- Fractals and Chaos
- Many Dimensions
- Projects
- Complex Systems
- Cellular Automata
- Self-Organized Critical Phenomenon
- The Hopfield Model and Neural Networks
- Growing Networks
- Genetic Algorithms
- Lattice Gas Models of Fluid Flow
- Overview and Projects
- Monte Carlo Simulations of Thermal Systems
- Introduction
- The Microcanonical Ensemble
- The Demon Algorithm
- The Demon as a Thermometer
- The Ising Model
- The Metropolis Algorithm
- Simulation of the Ising Model
- The Ising Phase Transition
- Other Applications of the Ising Model
- Simulation of Classical Fluids
- Optimized Monte Carlo Data Analysis
- Other Ensembles
- More Applications
- Projects
- Appendix 16A: Relation of the Mean Demon Energy to the Temperature
- Appendix 16B: Fluctuations in the Canonical Ensemble
- Appendix 16C: Exact Enumeration of the 2 × 2 Ising Model
- Quantum Systems
- Introduction
- Review of Quantum Theory
- Bound State Solutions
- Time Development of Eigenstate Superpositions
- The Time-Dependent Schr\"odinger Equation
- Fourier Transformations and Momentum
- Variational Methods
- Random Walk Solutions of the Schr\"odinger Equation
- Diffusion Quantum Monte Carlo
- Path Integral Quantum Monte Carlo
- Projects
- Appendix 17A: Visualizing Complex Functions
- Visualization and Rigid Body Dynamics
- Seeing in Special and General Relativity
- Epilogue: The Unity of Physics