A Survey of Computational Physics
by Cristian C. Bordeianu, José Páez, Rubin H. Landau
A Survey of Computational Physics
- Cover
- Title
- Copyright
- Contents
- Preface
- 1 Computational Science Basics
- 2 Errors & Uncertainties in Computations
- 3 Visualization Tools
- 4 Object-Oriented Programs: Impedance & Batons
- 4.1 Unit I. Basic Objects: Complex Impedance
- 4.2 Complex Numbers (Math)
- 4.3 Resistance Becomes Impedance (Theory)
- 4.4 Abstract Data Structures, Objects (CS)
- 4.5 Complex Currents (Solution)
- 4.6 OOP Worked Examples
- 4.7 Unit II. Advanced Objects: Baton Projectiles Θ
- 4.8 Trajectory of a Thrown Baton (Problem)
- 4.9 OOP Design Concepts (CS)
- 4.9.1 Including Multiple Classes
- 4.9.2 Ball and Path Class Implementation
- 4.9.3 Composition, Objects Within Objects
- 4.9.4 Baton Class Implementation
- 4.9.5 Composition Exercise
- 4.9.6 Calculating the Baton’s Energy (Extension)
- 4.9.7 Examples of Inheritance and Object Hierarchies
- 4.9.8 Baton with a Lead Weight (Application)
- 4.9.9 Encapsulation to Protect Classes
- 4.9.10 Encapsulation Exercise
- 4.9.11 Complex Object Interface (Extension)
- 4.9.12 Polymorphism, Variable Multityping
- 4.10 Supplementary Exercises
- 4.11 OOP Example: Superposition of Motions
- 4.12 Newton’s Laws of Motion (Theory)
- 4.13 OOP Class Structure (Method)
- 4.14 Java Implementation
- 5 Monte Carlo Simulations (Nonthermal)
- 6 Integration
- 6.1 Integrating a Spectrum (Problem)
- 6.2 Quadrature as Box Counting (Math)
- 6.3 Experimentation
- 6.4 Higher-Order Rules (Algorithm)
- 6.5 Monte Carlo Integration by Stone Throwing
- 6.6 High-Dimensional Integration (Problem)
- 6.6.1 Multidimensional Monte Carlo
- 6.6.2 Error in Multidimensional Integration (Assessment)
- 6.6.3 Implementation: 10-D Monte Carlo Integration
- 6.7 Integrating Rapidly Varying Functions (Problem)
- 6.7.1 Variance Reduction (Method)
- 6.7.2 Importance Sampling (Method)
- 6.7.3 Von Neumann Rejection (Method)
- 6.7.4 Simple Gaussian Distribution
- 6.8 Nonuniform Assessment ©
- 7 Differentiation & Searching
- 7.1 Unit I. Numerical Differentiation
- 7.2 Forward Difference (Algorithm)
- 7.3 Central Difference (Algorithm)
- 7.4 Extrapolated Difference (Method)
- 7.5 Error Analysis (Assessment)
- 7.6 Second Derivatives (Problem)
- 7.7 Unit II. Trial-and-Error Searching
- 7.8 Quantum States in a Square Well (Problem)
- 7.9 Trial-and-Error Roots via the Bisection Algorithm
- 7.10 Newton-Raphson Searching (A Faster Algorithm)
- 8 Solving Systems of Equations with Matrices; Data Fitting
- 9 Differential Equation Applications
- 9.1 Unit I. Free Nonlinear Oscillations
- 9.2 Nonlinear Oscillators (Models)
- 9.3 Types of Differential Equations (Math)
- 9.4 Dynamic Form for ODEs (Theory)
- 9.5 ODE Algorithms
- 9.6 Solution for Nonlinear Oscillations (Assessment)
- 9.7 Extensions: Nonlinear Resonances, Beats, and Friction
- 9.8 Implementation: Inclusion of Time-Dependent Force
- 9.9 Unit II. Binding A Quantum Particle
- 9.10 The Quantum Eigenvalue Problem (Theory)
- 9.11 Combined Algorithms: Eigenvalues via ODE Solver Plus Search
- 9.12 Explorations
- 9.13 Unit III. Scattering, Projectiles, and Planetary Orbits
- 9.14 Problem 1: Classical Chaotic Scattering
- 9.15 Problem 2: Balls Falling Out of the Sky
- 9.16 Theory: Projectile Motion with Drag
- 9.17 Problem 3: Planetary Motion
- 10 Fourier Analysis: Signals and Filters
- 10.1 Unit I. Fourier Analysis of Nonlinear Oscillations
- 10.2 Fourier Series (Math)
- 10.3 Summation of Fourier Series (Exercise)
- 10.5 Unit II. Filtering Noisy Signals
- 10.6 Noise Reduction via Autocorrelation (Theory)
- 10.7 Filtering with Transforms (Theory)
- 10.8 Unit III. Fast Fourier Transform Algorithm ©
- 10.9 FFT Implementation
- 10.10 FFT Assessment
- 11 Wavelet Analysis & Data Compression
- 12 Discrete & Continuous Nonlinear Dynamics
- 12.1 Unit I. Bug Population Dynamics (Discrete)
- 12.2 The Logistic Map (Model)
- 12.3 Properties of Nonlinear Maps (Theory)
- 12.4 Mapping Implementation
- 12.5 Bifurcation Diagram (Assessment)
- 12.6 Random Numbers via Logistic Map (Exploration) ©
- 12.7 Other Maps (Exploration)
- 12.8 Signals of Chaos: Lyapunov Coefficients Θ
- 12.9 UnitI Quiz
- 12.10 Unit II. Pendulums Become Chaotic (Continuous)
- 12.11 Chaotic Pendulum ODE
- 12.12 Visualization: Phase Space Orbits
- 12.12.1 Chaos in Phase Space
- 12.13 Exploration: Bifurcations of Chaotic Pendulums
- 12.14 Alternative Problem: The Double Pendulum
- 12.15 Assessment: Fourier/Wavelet Analysis of Chaos
- 12.16 Exploration: Another Type of Phase Space Plot
- 12.17 Further Explorations
- 12.18 Unit III. Coupled Predator-Prey Models Θ
- 12.19 Lotka-Volterra Model
- 13 Fractals & Statistical Growth
- 13.1 Fractional Dimension (Math)
- 13.2 The Sierpinski Gasket (Problem 1)
- 13.3 Beautiful Plants (Problem 2)
- 13.4 Ballistic Deposition (Problem 3)
- 13.5 Length of the British Coastline (Problem 4)
- 13.6 Correlated Growth, Forests, and Films (Problem 5)
- 13.7 Globular Cluster (Problem 6)
- 13.8 Fractal Structures in a Bifurcation Graph (Problem 7)
- 13.9 Fractals from Cellular Automata
- 13.10 Perlin Noise Adds Realism Θ
- 13.11 Quiz
- 14 High-Performance Computing Hardware, Tuning, and Parallel Computing
- 14.1 Unit I. High-Performance Computers (CS)
- 14.2 Memory Hierarchy
- 14.3 The Central Processing Unit
- 14.4 CPU Design: Reduced Instruction Set Computer
- 14.5 CPU Design: Multiple-Core Processors
- 14.6 CPU Design: Vector Processor
- 14.7 Unit II. Parallel Computing
- 14.8 Parallel Semantics (Theory)
- 14.9 Distributed Memory Programming
- 14.10 Parallel Performance
- 14.11 Parallelization Strategy
- 14.12 Practical Aspects of Message Passing for MIMD
- 14.13 Example of a Supercomputer: IBM Blue Gene/L
- 14.14 Unit III. HPC Program Optimization
- 14.15 Programming for the Data Cache (Method)
- 15 Thermodynamic Simulations & Feynman Quantum Path Integration
- 15.1 Unit I. Magnets via the Metropolis Algorithm
- 15.2 An Ising Chain (Model)
- 15.3 Statistical Mechanics (Theory)
- 15.4 Metropolis Algorithm
- 15.5 Unit II. Magnets via Wang-Landau Sampling Θ
- 15.6 Wang-Landau Sampling
- 15.7 UnitIII. Feynman Path Integrals Θ
- 15.8 Feynman’s Space-Time Propagation (Theory)
- 15.9 Exploration: Quantum Bouncer’s Paths Θ
- 16 Simulating Matter with Molecular Dynamics
- 17 PDEs for Electrostatics & Heat Flow
- 17.1 PDE Generalities
- 17.2 Unit I. Electrostatic Potentials
- 17.3 Fourier Series Solution of a PDE
- 17.4 Solution: Finite-Difference Method
- 17.5 Assessment via Surface Plot
- 17.6 Alternate Capacitor Problems
- 17.7 Implementation and Assessment
- 17.8 Electric Field Visualization (Exploration)
- 17.9 Laplace Quiz
- 17.10 Unit II. Finite-Element Method Θ
- 17.11 Electric Field from Charge Density (Problem)
- 17.12 Analytic Solution
- 17.13 Finite-Element (Not Difference) Methods
- 17.14 FEM Implementation and Exercises
- 17.15 Exploration
- 17.16 Unit III. Heat Flow via Time-Stepping (Leapfrogging)
- 17.17 The Parabolic Heat Equation (Theory)
- 17.18 Assessment and Visualization
- 17.19 Improved Heat Flow: Crank-Nicolson Method
- 18 PDE Waves: String, Quantum Packet, and E&M
- 18.1 Unit I. Vibrating String
- 18.2 The Hyperbolic Wave Equation (Theory)
- 18.3 Waves with Friction (Extension)
- 18.4 Waves for Variable Tension and Density (Extension)
- 18.5 Unit II. Quantum Wave Packets
- 18.6 Time-Dependent Schrödinger Equation (Theory)
- 18.7 Wave Packets in Other Wells (Exploration)
- 18.8 Algorithm for the 2-D Schrödinger Equation
- 18.9 Unit III. E&M Waves via Finite-Difference Time Domain ©
- 18.10 Maxwell’s Equations
- 18.11 FDTD Algorithm
- 19 Solitons & Computational Fluid Dynamics
- 19.1 Unit I. Advection, Shocks, and Russell’s Soliton
- 19.2 Theory: Continuity and Advection Equations
- 19.3 Theory: Shock Waves via Burgers’ Equation
- 19.4 Including Dispersion
- 19.5 Shallow-Water Solitons, the KdeV Equation
- 19.6 Unit II. River Hydrodynamics
- 19.7 Hydrodynamics, the Navier-Stokes Equation (Theory)
- 19.8 2-D Flow over a Beam
- 19.9 Theory: Vorticity Form of the Navier-Stokes Equation
- 20 Integral Equations in Quantum Mechanics
- Appendix A: Glossary
- Appendix B: Installing Packages
- Appendix C: OpenDX: Industrial-Strength Data Visualization
- Appendix D: An MPI Tutorial
- Appendix E: Calling LAPAC K from C
- Appendix F: Software on the CD
- Bibliography
- Index
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