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A Survey of Computational Physics

Author Cristian C. Bordeianu , José Páez , Rubin H. Landau
Release Date: 2011/10/01
ISBN: 9781400841189
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Book Description

Computational physics is a rapidly growing subfield of computational science, in large part because computers can solve previously intractable problems or simulate natural processes that do not have analytic solutions. The next step beyond Landau's First Course in Scientific Computing and a follow-up to Landau and Páez's Computational Physics, this text presents a broad survey of key topics in computational physics for advanced undergraduates and beginning graduate students, including new discussions of visualization tools, wavelet analysis, molecular dynamics, and computational fluid dynamics. By treating science, applied mathematics, and computer science together, the book reveals how this knowledge base can be applied to a wider range of real-world problems than computational physics texts normally address.


Designed for a one- or two-semester course, A Survey of Computational Physics will also interest anyone who wants a reference on or practical experience in the basics of computational physics.


  • Accessible to advanced undergraduates

  • Real-world problem-solving approach

  • Java codes and applets integrated with text

  • Companion Web site includes videos of lectures

Table of Contents

  1. Cover
  2. Title
  3. Copyright
  4. Contents
  5. Preface
  6. 1 Computational Science Basics
    1. 1.1 Computational Physics and Science
    2. 1.2 How to Read and Use This Book
    3. 1.3 Making Computers Obey; Languages (Theory)
    4. 1.4 Programming Warmup
      1. 1.4.1 Structured Program Design
      2. 1.4.2 Shells, Editors, and Execution
      3. 1.4.3 Java I/O, Scanner Class with printf
      4. 1.4.4 I/O Redirection
      5. 1.4.5 Command-Line Input
      6. 1.4.6 I/O Exceptions: FileCatchThrow.java
      7. 1.4.7 Automatic Code Documentation Θ
    5. 1.5 Computer Number Representations (Theory)
      1. 1.5.1 IEEE Floating-Point Numbers
      2. 1.5.2 Over/Underflows Exercises
      3. 1.5.3 Machine Precision (Model)
      4. 1.5.4 Determine Your Machine Precision
    6. 1.6 Problem: Summing Series
      1. 1.6.1 Numerical Summation (Method)
      2. 1.6.2 Implementation and Assessment
  7. 2 Errors & Uncertainties in Computations
    1. 2.1 Types of Errors (Theory)
      1. 2.1.1 Model for Disaster: Subtractive Cancellation
      2. 2.1.2 Subtractive Cancellation Exercises
      3. 2.1.3 Round-off Error in a Single Step
      4. 2.1.4 Round-off Error Accumulation After Many Steps
    2. 2.2 Errors in Spherical Bessel Functions (Problem)
      1. 2.2.1 Numerical Recursion Relations (Method)
      2. 2.2.2 Implementation and Assessment: Recursion Relations
    3. 2.3 Experimental Error Investigation (Problem)
      1. 2.3.1 Error Assessment
  8. 3 Visualization Tools
    1. 3.1 Data Visualization
    2. 3.2 PtPlot: 2-D Graphs Within Java
    3. 3.3 Grace/ACE: Superb 2-D Graphs for Unix/Linux
      1. 3.3.1 Grace Basics
      2. 3.4 Gnuplot: Reliable 2-D and 3-D Plots
      3. 3.4.1 Gnuplot Input Data Format Θ
      4. 3.4.2 Printing Plots
      5. 3.4.3 Gnuplot Surface (3-D) Plots
      6. 3.4.4 Gnuplot Vector Fields
      7. 3.4.5 Animations from a Plotting Program (Gnuplot) Θ
    4. 3.5 OpenDX for Dicing and Slicing
    5. 3.6 Texturing and 3-D Imaging
  9. 4 Object-Oriented Programs: Impedance & Batons
    1. 4.1 Unit I. Basic Objects: Complex Impedance
    2. 4.2 Complex Numbers (Math)
    3. 4.3 Resistance Becomes Impedance (Theory)
    4. 4.4 Abstract Data Structures, Objects (CS)
      1. 4.4.1 Object Declaration and Construction
      2. 4.4.2 Implementation in Java
      3. 4.4.3 Static and Nonstatic Methods
      4. 4.4.4 Nonstatic Methods
    5. 4.5 Complex Currents (Solution)
    6. 4.6 OOP Worked Examples
      1. 4.6.1 OOP Beats
      2. 4.6.2 OOP Planet
    7. 4.7 Unit II. Advanced Objects: Baton Projectiles Θ
    8. 4.8 Trajectory of a Thrown Baton (Problem)
      1. 4.8.1 Combined Translation and Rotation (Theory)
    9. 4.9 OOP Design Concepts (CS)
      1. 4.9.1 Including Multiple Classes
      2. 4.9.2 Ball and Path Class Implementation
      3. 4.9.3 Composition, Objects Within Objects
      4. 4.9.4 Baton Class Implementation
      5. 4.9.5 Composition Exercise
      6. 4.9.6 Calculating the Baton’s Energy (Extension)
      7. 4.9.7 Examples of Inheritance and Object Hierarchies
      8. 4.9.8 Baton with a Lead Weight (Application)
      9. 4.9.9 Encapsulation to Protect Classes
      10. 4.9.10 Encapsulation Exercise
      11. 4.9.11 Complex Object Interface (Extension)
      12. 4.9.12 Polymorphism, Variable Multityping
    10. 4.10 Supplementary Exercises
    11. 4.11 OOP Example: Superposition of Motions
    12. 4.12 Newton’s Laws of Motion (Theory)
    13. 4.13 OOP Class Structure (Method)
    14. 4.14 Java Implementation
  10. 5 Monte Carlo Simulations (Nonthermal)
    1. 5.1 Unit I. Deterministic Randomness
    2. 5.2 Random Sequences (Theory)
      1. 5.2.1 Random-Number Generation (Algorithm)
      2. 5.2.2 Implementation: Random Sequence
      3. 5.2.3 Assessing Randomness and Uniformity
    3. 5.3 Unit II. Monte Carlo Applications
    4. 5.4 A Random Walk (Problem)
      1. 5.4.1 Random-Walk Simulation
      2. 5.4.2 Implementation: Random Walk
    5. 5.5 Radioactive Decay (Problem)
      1. 5.5.1 Discrete Decay (Model)
      2. 5.5.2 Continuous Decay (Model)
      3. 5.5.3 Decay Simulation
    6. 5.6 Decay Implementation and Visualization
  11. 6 Integration
    1. 6.1 Integrating a Spectrum (Problem)
    2. 6.2 Quadrature as Box Counting (Math)
      1. 6.2.1 Algorithm: Trapezoid Rule
      2. 6.2.2 Algorithm: Simpson’s Rule
      3. 6.2.3 Integration Error (Analytic Assessment)
      4. 6.2.4 Algorithm: Gaussian Quadrature
      5. 6.2.5 Integration Implementation and Error Assessment
    3. 6.3 Experimentation
    4. 6.4 Higher-Order Rules (Algorithm)
    5. 6.5 Monte Carlo Integration by Stone Throwing
      1. 6.5.1 Stone Throwing Implementation
      2. 6.5.2 Integration by Mean Value (Math)
    6. 6.6 High-Dimensional Integration (Problem)
      1. 6.6.1 Multidimensional Monte Carlo
      2. 6.6.2 Error in Multidimensional Integration (Assessment)
      3. 6.6.3 Implementation: 10-D Monte Carlo Integration
      4. 6.7 Integrating Rapidly Varying Functions (Problem)
      5. 6.7.1 Variance Reduction (Method)
      6. 6.7.2 Importance Sampling (Method)
      7. 6.7.3 Von Neumann Rejection (Method)
      8. 6.7.4 Simple Gaussian Distribution
    7. 6.8 Nonuniform Assessment ©
      1. 6.8.1 Implementation: Nonuniform Randomness ©
  12. 7 Differentiation & Searching
    1. 7.1 Unit I. Numerical Differentiation
    2. 7.2 Forward Difference (Algorithm)
    3. 7.3 Central Difference (Algorithm)
    4. 7.4 Extrapolated Difference (Method)
    5. 7.5 Error Analysis (Assessment)
    6. 7.6 Second Derivatives (Problem)
      1. 7.6.1 Second-Derivative Assessment
    7. 7.7 Unit II. Trial-and-Error Searching
    8. 7.8 Quantum States in a Square Well (Problem)
    9. 7.9 Trial-and-Error Roots via the Bisection Algorithm
      1. 7.9.1 Bisection Algorithm Implementation
    10. 7.10 Newton-Raphson Searching (A Faster Algorithm)
      1. 7.10.1 Newton-Raphson Algorithm with Backtracking
      2. 7.10.2 Newton-Raphson Algorithm Implementation
  13. 8 Solving Systems of Equations with Matrices; Data Fitting
    1. 8.1 Unit I. Systems of Equations and Matrix Computing
    2. 8.2 Two Masses on a String
      1. 8.2.1 Statics (Theory)
      2. 8.2.2 Multidimensional Newton-Raphson Searching
    3. 8.3 Classes of Matrix Problems (Math)
      1. 8.3.1 Practical Aspects of Matrix Computing
      2. 8.3.2 Implementation: Scientific Libraries, World Wide Web
      3. 8.3.3 JAMA: Java Matrix Library
      4. 8.3.4 Exercises for Testing Matrix Calls
      5. 8.3.5 Matrix Solution of the String Problem
      6. 8.3.6 Explorations
    4. 8.4 Unit II. Data Fitting
    5. 8.5 Fitting an Experimental Spectrum (Problem)
      1. 8.5.1 Lagrange Interpolation (Method)
      2. 8.5.2 Lagrange Implementation and Assessment
      3. 8.5.3 Explore Extrapolation
      4. 8.5.4 Cubic Splines (Method)
      5. 8.5.5 Spline Fit of Cross Section (Implementation)
    6. 8.6 Fitting Exponential Decay (Problem)
      1. 8.6.1 Theory to Fit
    7. 8.7 Least-Squares Fitting (Method)
      1. 8.7.1 Least-Squares Fitting: Theory and Implementation
      2. 8.7.2 Exponential Decay Fit Assessment
      3. 8.7.3 Exercise: Fitting Heat Flow
      4. 8.7.4 Linear Quadratic Fit (Extension)
      5. 8.7.5 Linear Quadratic Fit Assessment
      6. 8.7.6 Nonlinear Fit of the Breit–Wigner Formula to a Cross Section
  14. 9 Differential Equation Applications
    1. 9.1 Unit I. Free Nonlinear Oscillations
    2. 9.2 Nonlinear Oscillators (Models)
    3. 9.3 Types of Differential Equations (Math)
    4. 9.4 Dynamic Form for ODEs (Theory)
    5. 9.5 ODE Algorithms
      1. 9.5.1 Euler’s Rule
      2. 9.5.2 Runge–Kutta Algorithm
      3. 9.5.3 Adams–Bashforth–Moulton Predictor-Corrector
      4. 9.5.4 Assessment: rk2 versus rk4 versus rk45
    6. 9.6 Solution for Nonlinear Oscillations (Assessment)
      1. 9.6.1 Precision Assessment: Energy Conservation
    7. 9.7 Extensions: Nonlinear Resonances, Beats, and Friction
      1. 9.7.1 Friction: Model and Implementation
      2. 9.7.2 Resonances and Beats: Model and Implementation
    8. 9.8 Implementation: Inclusion of Time-Dependent Force
    9. 9.9 Unit II. Binding A Quantum Particle
    10. 9.10 The Quantum Eigenvalue Problem (Theory)
      1. 9.10.1 Nucleon in a Box (Model)
    11. 9.11 Combined Algorithms: Eigenvalues via ODE Solver Plus Search
      1. 9.11.1 Numerov Algorithm for the Schrödinger ODE ©
      2. 9.11.2 Implementation: Eigenvalues via an ODE Solver Plus Bisection Algorithm
    12. 9.12 Explorations
    13. 9.13 Unit III. Scattering, Projectiles, and Planetary Orbits
    14. 9.14 Problem 1: Classical Chaotic Scattering
      1. 9.14.1 Model and Theory
      2. 9.14.2 Implementation
      3. 9.14.3 Assessment
    15. 9.15 Problem 2: Balls Falling Out of the Sky
    16. 9.16 Theory: Projectile Motion with Drag
      1. 9.16.1 Simultaneous Second-Order ODEs
      2. 9.16.2 Assessment
    17. 9.17 Problem 3: Planetary Motion
      1. 9.17.1 Implementation: Planetary Motion
  15. 10 Fourier Analysis: Signals and Filters
    1. 10.1 Unit I. Fourier Analysis of Nonlinear Oscillations
    2. 10.2 Fourier Series (Math)
      1. 10.2.1 Example 1: Sawtooth Function
      2. 10.2.2 Example 2: Half-wave Function
    3. 10.3 Summation of Fourier Series (Exercise)
      1. 10.4 Fourier Transforms (Theory)
      2. 10.4.1 Discrete Fourier Transform Algorithm
      3. 10.4.2 Aliasing and Anti-aliasing Θ
      4. 10.4.3 DFT for Fourier Series (Algorithm)
      5. 10.4.4 Assessments
      6. 10.4.5 DFT of Nonperiodic Functions (Exploration)
    4. 10.5 Unit II. Filtering Noisy Signals
    5. 10.6 Noise Reduction via Autocorrelation (Theory)
      1. 10.6.1 Autocorrelation Function Exercises
    6. 10.7 Filtering with Transforms (Theory)
      1. 10.7.1 Digital Filters: Windowed Sinc Filters ©
    7. 10.8 Unit III. Fast Fourier Transform Algorithm ©
      1. 10.8.1 Bit Reversal
    8. 10.9 FFT Implementation
    9. 10.10 FFT Assessment
  16. 11 Wavelet Analysis & Data Compression
    1. 11.1 Unit I. Wavelet Basics
    2. 11.2 Wave Packets and Uncertainty Principle (Theory)
      1. 11.2.1 Wave Packet Assessment
    3. 11.3 Short-Time Fourier Transforms (Math)
    4. 11.4 The Wavelet Transform
      1. 11.4.1 Generating Wavelet Basis Functions
      2. 11.4.2 Continuous Wavelet Transform Implementation
    5. 11.5 Unit II. Discrete Wavelet Transform and Multiresolution Analysis Θ
      1. 11.5.1 Pyramid Scheme Implementation Θ
      2. 11.5.2 Daubechies Wavelets via Filtering
      3. 11.5.3 DWT Implementation and Exercise
  17. 12 Discrete & Continuous Nonlinear Dynamics
    1. 12.1 Unit I. Bug Population Dynamics (Discrete)
    2. 12.2 The Logistic Map (Model)
    3. 12.3 Properties of Nonlinear Maps (Theory)
      1. 12.3.1 Fixed Points
      2. 12.3.2 Period Doubling, Attractors
    4. 12.4 Mapping Implementation
    5. 12.5 Bifurcation Diagram (Assessment)
      1. 12.5.1 Bifurcation Diagram Implementation
      2. 12.5.2 Visualization Algorithm: Binning
      3. 12.5.3 Feigenbaum Constants (Exploration)
    6. 12.6 Random Numbers via Logistic Map (Exploration) ©
    7. 12.7 Other Maps (Exploration)
    8. 12.8 Signals of Chaos: Lyapunov Coefficients Θ
      1. 12.8.1 Shannon Entropy ©
    9. 12.9 UnitI Quiz
    10. 12.10 Unit II. Pendulums Become Chaotic (Continuous)
    11. 12.11 Chaotic Pendulum ODE
      1. 12.11.1 Free Pendulum Oscillations
      2. 12.11.2 Solution as Elliptic Integrals
      3. 12.11.3 Implementation and Test: Free Pendulum
    12. 12.12 Visualization: Phase Space Orbits
    13. 12.12.1 Chaos in Phase Space
      1. 12.12.2 Assessment in Phase Space
    14. 12.13 Exploration: Bifurcations of Chaotic Pendulums
    15. 12.14 Alternative Problem: The Double Pendulum
    16. 12.15 Assessment: Fourier/Wavelet Analysis of Chaos
    17. 12.16 Exploration: Another Type of Phase Space Plot
    18. 12.17 Further Explorations
    19. 12.18 Unit III. Coupled Predator-Prey Models Θ
    20. 12.19 Lotka-Volterra Model
      1. 12.19.1 LVM with Prey Limit
      2. 12.19.2 LVM with Predation Efficiency
      3. 12.19.3 LVM Implementation and Assessment
      4. 12.19.4 Two Predators, One Prey (Exploration)
  18. 13 Fractals & Statistical Growth
    1. 13.1 Fractional Dimension (Math)
    2. 13.2 The Sierpinski Gasket (Problem 1)
      1. 13.2.1 Sierpinski Implementation
      2. 13.2.2 Assessing Fractal Dimension
    3. 13.3 Beautiful Plants (Problem 2)
      1. 13.3.1 Self-affine Connection (Theory)
      2. 13.3.2 Barnsley’s Fern Implementation
      3. 13.3.3 Self-affinity in Trees Implementation
    4. 13.4 Ballistic Deposition (Problem 3)
      1. 13.4.1 Random Deposition Algorithm
    5. 13.5 Length of the British Coastline (Problem 4)
      1. 13.5.1 Coastlines as Fractals (Model)
      2. 13.5.2 Box Counting Algorithm
      3. 13.5.3 Coastline Implementation and Exercise
    6. 13.6 Correlated Growth, Forests, and Films (Problem 5)
      1. 13.6.1 Correlated Ballistic Deposition Algorithm
    7. 13.7 Globular Cluster (Problem 6)
      1. 13.7.1 Diffusion-Limited Aggregation Algorithm
      2. 13.7.2 Fractal Analysis of a DLA (or Pollock) Graph (Assessment)
    8. 13.8 Fractal Structures in a Bifurcation Graph (Problem 7)
    9. 13.9 Fractals from Cellular Automata
    10. 13.10 Perlin Noise Adds Realism Θ
      1. 13.10.1 Including Ray Tracing
    11. 13.11 Quiz
  19. 14 High-Performance Computing Hardware, Tuning, and Parallel Computing
    1. 14.1 Unit I. High-Performance Computers (CS)
    2. 14.2 Memory Hierarchy
    3. 14.3 The Central Processing Unit
    4. 14.4 CPU Design: Reduced Instruction Set Computer
    5. 14.5 CPU Design: Multiple-Core Processors
    6. 14.6 CPU Design: Vector Processor
    7. 14.7 Unit II. Parallel Computing
    8. 14.8 Parallel Semantics (Theory)
    9. 14.9 Distributed Memory Programming
    10. 14.10 Parallel Performance
      1. 14.10.1 Communication Overhead
    11. 14.11 Parallelization Strategy
    12. 14.12 Practical Aspects of Message Passing for MIMD
      1. 14.12.1 High-Level View of Message Passing
    13. 14.13 Example of a Supercomputer: IBM Blue Gene/L
    14. 14.14 Unit III. HPC Program Optimization
      1. 14.14.1 Programming for Virtual Memory (Method)
      2. 14.14.2 Optimizing Programs; Java versus Fortran/C
      3. 14.14.3 Experimental Effects of Hardware on Performance
      4. 14.14.4 Java versus Fortran/C
    15. 14.15 Programming for the Data Cache (Method)
      1. 14.15.1 Exercise 1: Cache Misses
      2. 14.15.2 Exercise 2: Cache Flow
      3. 14.15.3 Exercise 3: Large-Matrix Multiplication
  20. 15 Thermodynamic Simulations & Feynman Quantum Path Integration
    1. 15.1 Unit I. Magnets via the Metropolis Algorithm
    2. 15.2 An Ising Chain (Model)
    3. 15.3 Statistical Mechanics (Theory)
      1. 15.3.1 Analytic Solutions
    4. 15.4 Metropolis Algorithm
      1. 15.4.1 Metropolis Algorithm Implementation
      2. 15.4.2 Equilibration, Thermodynamic Properties (Assessment)
      3. 15.4.3 Beyond Nearest Neighbors and 1-D (Exploration)
    5. 15.5 Unit II. Magnets via Wang-Landau Sampling Θ
    6. 15.6 Wang-Landau Sampling
      1. 15.6.1 WLS Ising Model Implementation
      2. 15.6.2 WLS Ising Model Assessment
    7. 15.7 UnitIII. Feynman Path Integrals Θ
    8. 15.8 Feynman’s Space-Time Propagation (Theory)
      1. 15.8.1 Bound-State Wave Function (Theory)
      2. 15.8.2 Lattice Path Integration (Algorithm)
      3. 15.8.3 Lattice Implementation
      4. 15.8.4 Assessment and Exploration
    9. 15.9 Exploration: Quantum Bouncer’s Paths Θ
  21. 16 Simulating Matter with Molecular Dynamics
    1. 16.1 Molecular Dynamics (Theory)
      1. 16.1.1 Connection to Thermodynamic Variables
      2. 16.1.2 Setting Initial Velocity Distribution
      3. 16.1.3 Periodic Boundary Conditions and Potential Cutoff
    2. 16.2 Verlet and Velocity-Verlet Algorithms
    3. 16.3 1-D Implementation and Exercise
    4. 16.4 Trajectory Analysis
    5. 16.5 Quiz
  22. 17 PDEs for Electrostatics & Heat Flow
    1. 17.1 PDE Generalities
    2. 17.2 Unit I. Electrostatic Potentials
      1. 17.2.1 Laplace’s Elliptic PDE (Theory)
    3. 17.3 Fourier Series Solution of a PDE
      1. 17.3.1 Polynomial Expansion As an Algorithm
    4. 17.4 Solution: Finite-Difference Method
      1. 17.4.1 Relaxation and Overrelaxation
      2. 17.4.2 Lattice PDE Implementation
    5. 17.5 Assessment via Surface Plot
    6. 17.6 Alternate Capacitor Problems
    7. 17.7 Implementation and Assessment
    8. 17.8 Electric Field Visualization (Exploration)
    9. 17.9 Laplace Quiz
    10. 17.10 Unit II. Finite-Element Method Θ
    11. 17.11 Electric Field from Charge Density (Problem)
    12. 17.12 Analytic Solution
    13. 17.13 Finite-Element (Not Difference) Methods
      1. 17.13.1 Weak Form of PDE
      2. 17.13.2 Galerkin Spectral Decomposition
    14. 17.14 FEM Implementation and Exercises
    15. 17.15 Exploration
    16. 17.16 Unit III. Heat Flow via Time-Stepping (Leapfrogging)
    17. 17.17 The Parabolic Heat Equation (Theory)
      1. 17.17.1 Solution: Analytic Expansion
      2. 17.17.2 Solution: Time-Stepping
      3. 17.17.3 Von Neumann Stability Assessment
      4. 17.17.4 Heat Equation Implementation
    18. 17.18 Assessment and Visualization
    19. 17.19 Improved Heat Flow: Crank-Nicolson Method
      1. 17.19.1 Solution of Tridiagonal Matrix Equations ©
      2. 17.19.2 Crank-Nicolson Method Implementation and Assessment
  23. 18 PDE Waves: String, Quantum Packet, and E&M
    1. 18.1 Unit I. Vibrating String
    2. 18.2 The Hyperbolic Wave Equation (Theory)
      1. 18.2.1 Solution via Normal-Mode Expansion
      2. 18.2.2 Algorithm: Time-Stepping
      3. 18.2.3 Wave Equation Implementation
      4. 18.2.4 Assessment and Exploration
    3. 18.3 Waves with Friction (Extension)
    4. 18.4 Waves for Variable Tension and Density (Extension)
      1. 18.4.1 Waves on a Catenary
      2. 18.4.2 Derivation of a Catenary Shape
      3. 18.4.3 Catenary and Frictional Wave Exercises
    5. 18.5 Unit II. Quantum Wave Packets
    6. 18.6 Time-Dependent Schrödinger Equation (Theory)
      1. 18.6.1 Finite-Difference Algorithm
      2. 18.6.2 Wave Packet Implementation and Animation
    7. 18.7 Wave Packets in Other Wells (Exploration)
    8. 18.8 Algorithm for the 2-D Schrödinger Equation
    9. 18.9 Unit III. E&M Waves via Finite-Difference Time Domain ©
    10. 18.10 Maxwell’s Equations
    11. 18.11 FDTD Algorithm
      1. 18.11.1 Implementation
      2. 18.11.2 Assessment
      3. 18.11.3 Extension: Circularly Polarized EM Waves
  24. 19 Solitons & Computational Fluid Dynamics
    1. 19.1 Unit I. Advection, Shocks, and Russell’s Soliton
    2. 19.2 Theory: Continuity and Advection Equations
      1. 19.2.1 Advection Implementation
    3. 19.3 Theory: Shock Waves via Burgers’ Equation
      1. 19.3.1 Algorithm: The Lax-Wendroff Method for Burgers’ Equation
      2. 19.3.2 Implementation and Assessment of Burgers’ Shock Equation
    4. 19.4 Including Dispersion
    5. 19.5 Shallow-Water Solitons, the KdeV Equation
      1. 19.5.1 Analytic Soliton Solution
      2. 19.5.2 Algorithm for KdeV Solitons
      3. 19.5.3 Implementation: KdeV Solitons
      4. 19.5.4 Exploration: Solitons in Phase Space and Crossing
    6. 19.6 Unit II. River Hydrodynamics
    7. 19.7 Hydrodynamics, the Navier-Stokes Equation (Theory)
      1. 19.7.1 Boundary Conditions for Parallel Plates
      2. 19.7.2 Analytic Solution for Parallel Plates
      3. 19.7.3 Finite-Difference Algorithm and Overrelaxation
      4. 19.7.4 Successive Overrelaxation Implementation
    8. 19.8 2-D Flow over a Beam
    9. 19.9 Theory: Vorticity Form of the Navier-Stokes Equation
      1. 19.9.1 Finite Differences and the SOR Algorithm
      2. 19.9.2 Boundary Conditions for a Beam
      3. 19.9.3 SOR on a Grid Implementation
      4. 19.9.4 Assessment
      5. 19.9.5 Exploration
  25. 20 Integral Equations in Quantum Mechanics
    1. 20.1 Unit I. Bound States of Nonlocal Potentials
    2. 20.2 Momentum-Space Schrödinger Equation (Theory)
      1. 20.2.1 Integral to Linear Equations (Method)
      2. 20.2.2 Delta-Shell Potential (Model)
      3. 20.2.3 Binding Energies Implementation
      4. 20.2.4 Wave Function (Exploration)
    3. 20.3 Unit II. Nonlocal Potential Scattering Θ
    4. 20.4 Lippmann-Schwinger Equation (Theory)
      1. 20.4.1 Singular Integrals (Math)
      2. 20.4.2 Numerical Principal Values
      3. 20.4.3 Reducing Integral Equations to Matrix-Equations (Algorithm)
      4. 20.4.4 Solution via Inversion or Elimination
      5. 20.4.5 Scattering Implementation
      6. 20.4.6 Scattering Wave Function (Exploration)
  26. Appendix A: Glossary
  27. Appendix B: Installing Packages
    1. B.1 Installing Java Developer’s Kit
    2. B.2 Using Classes and Packages
      1. B.2.1 Including Packages
  28. Appendix C: OpenDX: Industrial-Strength Data Visualization
    1. C.1 Getting DX and Unix Running (for Windows)
    2. C.2 Test Drive of DX Visual Programming
    3. C.3 DX Tools Summary
    4. C.4 DX Data Structure and Storage
    5. C.5 Sample Visual Programs
      1. C.5.1 Sample 1: Linear Plot
      2. C.5.2 Sample 2: Fourier Transform
      3. C.5.3 Sample 3: Potential of a 2-D Capacitor
      4. C.5.4 Sample 4: Vector Field Plots
      5. C.5.5 Sample 5: 3-D Scalar Potentials
      6. C.5.6 Sample 6: 3-D Functions, the Hydrogen Atom
    6. C.6 Animations with OpenDX
      1. C.6.1 Scripted Animation with OpenDX
      2. C.6.2 Wave Packet and Slit Animation
  29. Appendix D: An MPI Tutorial
    1. D.1 Running on a Beowulf
    2. D.2 Running MPI
      1. D.2.1 MPI under the SGE Queueing System
      2. D.2.2 MPI Under the Torque/PBS Queueing System
      3. D.2.3 Running Parallel Jobs with Torque
    3. D.3 Your First MPI Program: MPIhello.c
      1. D.3.1 MPIhello.c Explained
      2. D.3.2 Send/Receive Messages: MPImessage2.c
      3. D.3.3 Receive More Messages: MPImessage3.c
      4. D.3.4 Broadcast Messages
      5. D.3.5 Exercise
    4. D.4 Parallel Tuning
    5. D.5 A String Vibrating in Parallel
      1. D.5.1 MPIstring.c Exercise
    6. D.6 Deadlock
      1. D.6.1 Nonblocking Communication
      2. D.6.2 Collective Communication
    7. D.7 Bootable Cluster CD ©
    8. D.8 Parallel Computing Exercises
    9. D.9 List of MPI Commands
  30. Appendix E: Calling LAPAC K from C
    1. E.1 Calling LAPACK Fortran from C
    2. E.2 Compiling C Programs with Fortran Calls
  31. Appendix F: Software on the CD
    1. Appendix G: Compression via DWT with Thresholding
    2. G.1 More on Thresholding
    3. G.2 Wavelet Implementation and Assessment
  32. Bibliography
  33. Index
18.118.12.222