计算机模拟方法在物理学中的应用

作者简介

主页：http://sip.clarku.edu/

本书是在美国大学使用很广泛的一本经典的，讲解如何使用计算机进行物理学数字模拟的教材，该书为刚刚出版的第三版。该书不是简单的物理学研究中的数学方法的介绍，而更注重在使用计算机模拟物理学问题中帮助学生更深刻的理解物理学，帮助学生在学习中了解和掌握使用计算机做物理学研究的一些基本手段，并学会如何根据具体的物理问题选择相应的研究方法。此外，还通过对具体的例子的讲解也为学习物理学的学生介绍了物理学广阔的应用天地。    本书可作为高等学校物理类专业或其它理工类专业计算物理课程的教材或参考书，对于相关学科的研究人员也是一本有用的参考书。

书籍目录

~~~ Introduction

1.1 Importance of Computers in Physics

1.2 The Importance of Computer Simulation

1.3 Programming Languages

1.4 Object-Oriented Techniques

1.5 How to Use this Book

Appendix 1A: Laboratory Reports

2 ~~ Tools for Doing Simulations

2. l Introduction

2.2 Simulating Free Fall

2.3 Getting Started with Object-Oriented Programming

2.4 Inheritance

2.5 The Open Source Physics Library

2.6 Animation and Simulation

2.7 Model-View-Controller

Appendix 2A: Complex Numbers

3 ~~ Simulating Particle Motion

3.1 Modified Euler Algorithms

3.2 Interfaces

. 3.3 Drawing

3.4 Specifying the State of a System Using Arrays

3.5 The ODE Interface

3.6 The ODESolver Interface

3.7 Effects of Drag Resistance

3.8 Two-Dimensional Trajectories

3.9 Decay Processes

*3.10 Visualizing Three-Dimensional Motion

3.11 Levels of Simulation

Appendix 3A: Numerical Integration of Newton's Equation of Motion

4 ~~ Oscillatory Systems

4.1 Simple Harmonic Motion

4.2 The Motion of a Pendulum

4.3 Damped Harmonic Oscillator

4.4 Response to External Forces

4.5 Electrical Circuit Oscillations

4.6 Accuracy and Stability

4.7 Projects

5 ~~ Few-Body Problems: The Motion of the Planets

5. l Planetary Motion

5.2 The Equations of Motion

5.3 Circular and Elliptical Orbits

5.4 Astronomical Units

5.5 Log-Log and Semilog Plots

5.6 Simulation of the Orbit

5.7 Impulsive Forces

5.8 Velocity Space

5.9 AMini-Solar System

5.10 Two-Body Scattering

5.11 Three-Body Problems

5.12 Projects

6 ~~ The Chaotic Motion of Dynamical Systems

6.1 Introduction

6.2 ASimple 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

Appendix 6A: Stability of the Fixed Points of the Logistic Map

Appendix 6B: Finding the Roots of a Function

7 ~~ Random Processes

7.1 Order to Disorder

7.2 Random Walks

7.3 Modified Random Walks

7.4 The Poisson Distribution and Nuclear Decay

7.5 Problems in Probability

7.6 Method of Least Squares

7.7 Applications to Polymers

7.8 Diffusion-Controlled Chemical Reactions

7.9 Random Number Sequences

7.10 Variational Methods

7.11 Projects

Appendix 7A: Random Walks and the Diffusion Equation

8 ~~ The Dynamics of Many-Particle Systems

8.1 Introduction

8.2 The Interrnolecular Potential

8.3 Units

8.4 The Numerical Algorithm

8.5 Periodic Boundary Conditions

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

Appendix 8A: Reading and Saving Configurations

9 ~~ Normal Modes and Waves

9.1 Coupled Oscillators and Normal Modes

9.2 Numerical Solutions

9.3 Fourier Series

9.4 Two-Dimensional Fourier Series

9.5 Fourier Integrals

9.6 Power Spectrum

9.7 Wave Motion

9.8 Interference

9.9 Fraunhofer Diffraction

9.10 Fresnel Diffraction

Appendix 9A: Complex Fourier Series

Appendix 9B: Fast Fourier Transform

Appendix 9C: Plotting Scalar Fields

10 ~~ Electrodynamics

10.1 Static Charges

10.2 Electric Fields

10.3 Electric Field Lines

10.4 Electric Potential

10.5 Numerical Solutions of Boundary Value Problems

10.6 Random Walk Solution of Laplace's Equation

"10.7 Fields Due to Moving Charges

"10.8 Maxwell's Equations

10.9 Projects 407

Appendix 10A: Plotting Vector Fields

11 ~~ Numerical and Monte Carlo Methods

11.1 Numerical Integration Methods in One Dimension

11.2 Simple Monte Carlo Evaluation of Integrals

11.3 Multidimensional Integrals

11.4 Monte Carlo Error Analysis

11.5 Nonuniform Probability Distributions

11.6 Importance Sampling

11.7 Metropolis Algorithm

* 11.8 Neutron Transport

Appendix 11A: Error Estimates for Numerical Integration

Appendix 11B: The Standard Deviation of the Mean

Appendix 11C: The Acceptance-Rejection Method

Appendix llD: Polynomials and Interpolation

12 ~~ Percolation

12.1 Introduction

12.2 The Percolation Threshold

12.3 Finding Clusters

12.4 Critical Exponents and Finite Size Scaling

12.5 The Renormalization Group

12.6 Projects

13 ~~ Fractals and Kinetic Growth Models

13.1 The Fractal Dimension

13.2 Regular Fractals

13.3 Kinetic Growth Processes

13.4 Fractals and Chaos

13.5 Many Dimensions

13.6 Projects

14 ~~ Complex Systems

14.1 Cellular Automata

14.2 Self-Organized Critical Phenomena

14.3 The Hopfield Model and Neural Networks

14.4 Growing Networks

14.5 Genetic Algorithms

14.6 Lattice Gas Models of Fluid Flow

14.7 Overview and Projects

15 ~~ Monte Carlo Simulations of Thermal Systems

15.1 Introduction

15.2 The Microcanonical Ensemble

15.3 The Demon Algorithm

15.4 The Demon as a Thermometer

15.5 The Ising Model

15.6 The Metropolis Algorithm

15.7 Simulation of the Ising Model

15.8 The Ising Phase Transition

15.9 Other Applications of the Ising Model

15.10 Simulation of Classical Fluids

15.11 Optimized Monte Carlo Data Analysis

* 15.12 Other Ensembles

15.13 More Applications

15.14 Projects

Appendix 15A: Relation of the Mean Demon Energy to the Temperature

Appendix 15B: Fluctuations in the Canonical Ensemble

Appendix 15C: Exact Enumeration of the 2 x 2 Ising Model

16 ~~ Quantum Systems

16.1 Introduction

16.2 Review of Quantum Theory

16.3 Bound State Solutions

16.4 Time Development of Eigenstate Superpositions

16.5 The Time-Dependent Schrrdinger Equation

16.6 Fourier Transformations and Momentum Space

16.7 Variational Methods

16.8 Random Walk Solutions of the Schrrdinger Equation

16.9 Diffusion Quantum Monte Carlo

16.10 Path Integral Quantum Monte Carlo

16.11 Projects

Appendix 16A: Visualizing Complex Functions

17 ~~ Visualization and Rigid Body Dynamics

17.1 Two-Dimensional Transformations

17.2 Three-Dimensional Transformations

17.3 The Three-Dimensional Open Source Physics Library

17.4 Dynamics of a Rigid Body

17.5 Quaternion Arithmetic

17.6 Quaternion Equations of Motion

17.7 Rigid Body Model

17.8 Motion of a Spinning Top

17.9 Projects

Appendix 17A: Matrix Transformations

Appendix 17B: Conversions

18 ~~ Seeing in Special and General Relativity

t8.1 Special Relativity

18.2 General Relativity

18.3 Dynamics in Polar Coordinates

18.4 Black Holes and Schwarzschild Coordinates

18.5 Particle and Light Trajectories

18.6 Seeing

18.7 General Relativistic Dynamics

* 18.8 The Kerr Metric

18.9 Projects

19 ~~ Epilogue: The Unity of Physics

19.1 The Unity of Physics

19.2 Spiral Galaxies

19.3 Numbers, Pretty Pictures, and Insight

19.4 Constrained Dynamics

19.5 What are Computers Doing to Physics?

Index~

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《计算机模拟方法在物理学中的应用》(第3版影印版)可作为高等学校物理类专业或其它理工类专业计算物理课程的教材或参考书，对于相关学科的研究人员也是一本有用的参考书。

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作者：(美)古德

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