Computational Physics, 3rd Ed

Transcription

1 Surveys All of CP, Separate Digital & ebook Versions Computational Physics, 3rd Ed Problem Solving with Python Rubin H Landau, Manuel J Paez & Cristian Bordeianu Wiley-VCH Verlag GmbH & Co., 2015 (buy here) Multifaceted Video Lecture Package Expanded version of Computational Physics, 2nd Edition (Java Based), WILEY-VCH GmbH, 2007.

2 2014/6/16 14:54 page i i Contents 1 Introduction Computational Physics & Computational Science This Book s Subjects This Book s Problems This Book s Language: The Python Ecosystem Python Packages (Libraries) This Book s Packages The Easy Way: Python Distributions Python s Visualization Tools Visual (VPython) s 2-D Plots Vpython s Animations Matplotlib s 2-D Plots Matplotlib s 3-D Surface Plots Matplotlib s Animations Mayavi s Visualizations Beyond Plotting* Plotting Exercises Python s Algebraic Tools 30 2 Computing Software Basics Making Computers Obey Programming Warmup Structured & Reproducible Program Design Shells, Editors and Execution Python I/O Computer Number Representations (Theory) IEEE Floating-Point Numbers Python and the IEEE 754 Standard Over & Underflow Exercises Machine Precision (Model) Experiment: Your Machine s Precision Problem: Summing Series Numerical Summation (Method) Implementation and Assessment 52

3 2014/6/16 14:54 page ii ii 3 Errors & Uncertainties in Computations Types of Errors (Theory) Model for Disaster: Subtractive Cancellation Subtractive Cancellation Exercises Round-off Errors Round-off Error Accumulation Error in Bessel Functions (Problem) Numerical Recursion (Method) Recursion Relations Assessment Experimental Error Investigation Error Assessment 65 4 Monte Carlo: Randomness, Walks & Decays Deterministic Randomness Random Sequences (Theory) Random-Number Generation (Algorithm) Implementation: Random Sequences Assessing Randomness and Uniformity Random Walks (Problem) Random-Walk Simulation Implementation: Random Walk Extension: Protein Folding & Self-Avoiding Random Walks Spontaneous Decay (Problem) Discrete Decay (Model) Continuous Decay (Model) Decay Simulation Decay Implementation and Visualization 84 5 Differentiation & Integration Differentiation Forward Difference (Algorithm) Central Difference (Algorithm) Extrapolated Difference (Algorithm) Error Assessment Second Derivatives (Problem) Second-Derivative Assessment Integration Quadrature as Box Counting (Math) Algorithm: Trapezoid Rule Algorithm: Simpson s Rule Integration Error (Assessment) Algorithm: Gaussian Quadrature Mapping Integration Points Gaussian Points Derivation Integration Error Assessment 100

4 2014/6/16 14:54 page iii iii 5.13 Higher-Order Rules (Algorithm) Monte Carlo Integration by Stone Throwing Stone Throwing Implementation Mean Value Integration (Theory & Math) Integration Exercises Multidimensional Monte Carlo Integration (Problem) Multi Dimension Integration Error Assessment Implementation: 10-D Monte Carlo Integration Integrating Rapidly Varying Functions (Problem) Variance Reduction (Method) Importance Sampling (Method) Von Neumann Rejection (Method) Simple Random Gaussian Distribution Nonuniform Assessment Implementation Matrix Computing Problem 3: N-D Newton-Raphson; Two Masses on a String Theory: Statics Algorithm: Multidimensional Searching Why Matrix Computing? Classes of Matrix Problems (Maths) Practical Matrix Computing Python Lists as Arrays Numerical Python (NumPy) Arrays NumPy s linalg Package Exercise: Testing Matrix Programs Matrix Solution of the String Problem Explorations Trial-and-Error Searching & Data Fitting Problem 1: A Search for Quantum States in a Box Algorithm: Trial-and-Error Roots via Bisection Implementation: Bisection Algorithm Improved Algorithm: Newton-Raphson Searching Newton-Raphson with Backtracking Implementation: Newton-Raphson Algorithm Problem 2: Temperature Dependence of Magnetization Searching Exercise Problem 3: Fitting An Experimental Spectrum Lagrange Implementation, Assessment Cubic Spline Interpolation Problem 4:Fitting Exponential Decay Least-Squares Fitting (Theory) Theory and Implementation 160

5 2014/6/16 14:54 page iv iv 7.8 Exercises: Fitting Exponential Decay, Heat Flow & Hubble s Law Linear Quadratic Fit Problem 5: Nonlinear Fit to a Breit-Wigner Solving Differential Equations; Nonlinear Oscillations Free Nonlinear Oscillations Nonlinear Oscillators (Models) Types of Differential Equations (Math) Dynamic Form for ODE s (Theory) ODE Algorithms Euler s Rule Runge-Kutta Rule ABM Predictor-Corrector Rule Assessment: rk2 versus rk4 versus rk Solution for Nonlinear Oscillations (Assessment) Precision Assessment: Energy Conservation Extensions: Nonlinear Resonances, Beats, Friction Friction (Model) Resonances & Beats: Model, Implementation Extension: Time-Dependent Forces ODE Applications Problem: Quantum Eigenvalues in Arbitrary Potential Model: Nucleon in a Box Algorithm: Eigenvalues via ODE Solver + Search Numerov Algorithm for Schrödinger ODE Implementation Explorations Problem: Classical Chaotic Scattering Model and Theory Implementation Assessment Problem: Balls Falling Out of the Sky Theory: Projectile Motion with Drag Simultaneous Second-Order ODE s Assessment Exercises: 2- & 3-Body Planet Orbits & Chaotic Weather High-Performance Hardware & Parallel Computers High-Performance Computers Memory Hierarchy The Central Processing Unit CPU Design: Reduced Instruction Set Processors CPU Design: Multiple-Core Processors CPU Design: Vector Processors 222

6 2014/6/16 14:54 page v v 10.7 Introduction to Parallel Computing Parallel Semantics (Theory) Distributed Memory Programming Parallel Performance Communication Overhead Parallelization Strategies Practical Aspects of MIMD Message Passing High-Level View of Message Passing Message Passing Example & Exercise Scalability Scalability Exercises Data Parallelism and Domain Decomposition Domain Decomposition Exercises The IBM Blue Gene Supercomputers Exascale Computing via Multinode-Multicore-GPU s Applied HPC: Optimization, Tuning & GPU Programming General Program Optimization Programming for Virtual Memory Optimization Exercises Optimized Matrix Programming with NumPy NumPy Optimization Exercises Empirical Performance of Hardware Racing Python versus Fortran/C Programming for the Data Cache (Method) Exercise 1: Cache Misses Exercise 2: Cache Flow Exercise 3: Large-Matrix Multiplication Graphical Processing Units for High Performance Computing The GPU Card Practical Tips for Multicore & GPU Programming CUDA Memory Usage CUDA Programming Fourier Analysis: Signals & Filters Fourier Analysis of Nonlinear Oscillations Fourier Series (Math) Examples: Sawtooth & Half-Wave Functions Exercise: Summation of Fourier Series Fourier Transforms (Theory) The Discrete Fourier Transform Aliasing (Assessment) Fourier Series DFT (Example) Assessments Nonperiodic Function DFT (Exploration) 290

7 2014/6/16 14:54 page vi vi 12.6 Filtering Noisy Signals Noise Reduction via Autocorrelation (Theory) Exercises Filtering with Transforms (Theory) Digital Filters: Windowed Sinc Filters The Fast Fourier Transform Algorithm (FFT) Bit Reversal FFT Implementation FFT Assessment Wavelet & Principal Components Analyses: Nonstationary Signals & Data Compression Problem: Spectral Analysis of Nonstationary Signals Wavelet Basics Wave Packets and Uncertainty Principle (Theory) Wave Packet Assessment Short-Time Fourier Transforms (Math) The Wavelet Transform Wavelet Basis Functions Continuous Wavelet Transform Discrete Wavelet Transforms, Multi Resolution Analysis Pyramid Scheme Implementation Daubechies Wavelets via Filtering DWT Implementation and Exercise Principal Components Analysis Demonstration of Principal Component Analysis PCA Exercises Nonlinear Population Dynamics Bug Population Dynamics The Logistic Map (Model) Properties of Nonlinear Maps (Theory & Exercise) Fixed Points Period Doubling, Attractors Mapping Implementation Bifurcation Diagram Implementation Visualization Algorithm: Binning Feigenbaum Constants (Exploration) Logistic Map Random Numbers (Exploration) Other Maps (Exploration) Signals of Chaos: Lyapunov Coefficients & Shannon Entropy Coupled Predator-Prey Models Lotka-Volterra Model Lotka-Volterra Assessment 357

8 2014/6/16 14:54 page vii vii Predator-Prey Chaos Exercises LVM with Prey Limit LVM with Predation Efficiency LVM Implementation and Assessment Two Predators, One Prey (Exploration) Continuous Nonlinear Dynamics Chaotic Pendulum Free Pendulum Oscillations Solution as Elliptic Integrals Implementation and Test: Free Pendulum Visualization: Phase Space Orbits Chaos in Phase Space Assessment in Phase Space Exploration: Bifurcations of Chaotic Pendulums Alternate Problem: The Double Pendulum Assessment: Fourier/Wavelet Analysis of Chaos Exploration: Alternate Phase Space Plots Further Explorations Fractals & Statistical Growth Models Fractional Dimension (Math) The Sierpiński Gasket (Problem 1) Sierpiński Implementation Assessing Fractal Dimension Growing Plants (Problem 2) Self-Affine Connection (Theory) Barnsley s Fern Implementation Self-Affinity in Trees Implementation Ballistic Deposition (Problem 3) Random Deposition Algorithm Length of British Coastline (Problem 4) Coastlines as Fractals (Model) Box Counting Algorithm Coastline Implementation and Exercise Correlated Growth, Forests, Films (Problem 5) Correlated Ballistic Deposition Algorithm Globular Cluster (Problem 6) Diffusion-Limited Aggregation Algorithm Fractal Assessment of DLA or a Pollock Fractals in Bifurcation Plot (Problem 7) Fractals from Cellular Automata Perlin Noise Adds Realism Ray Tracing Algorithms 404

9 2014/6/16 14:54 page vii vii Predator-Prey Chaos Exercises LVM with Prey Limit LVM with Predation Efficiency LVM Implementation and Assessment Two Predators, One Prey (Exploration) Continuous Nonlinear Dynamics Chaotic Pendulum Free Pendulum Oscillations Solution as Elliptic Integrals Implementation and Test: Free Pendulum Visualization: Phase Space Orbits Chaos in Phase Space Assessment in Phase Space Exploration: Bifurcations of Chaotic Pendulums Alternate Problem: The Double Pendulum Assessment: Fourier/Wavelet Analysis of Chaos Exploration: Alternate Phase Space Plots Further Explorations Fractals & Statistical Growth Models Fractional Dimension (Math) The Sierpiński Gasket (Problem 1) Sierpiński Implementation Assessing Fractal Dimension Growing Plants (Problem 2) Self-Affine Connection (Theory) Barnsley s Fern Implementation Self-Affinity in Trees Implementation Ballistic Deposition (Problem 3) Random Deposition Algorithm Length of British Coastline (Problem 4) Coastlines as Fractals (Model) Box Counting Algorithm Coastline Implementation and Exercise Correlated Growth, Forests, Films (Problem 5) Correlated Ballistic Deposition Algorithm Globular Cluster (Problem 6) Diffusion-Limited Aggregation Algorithm Fractal Assessment of DLA or a Pollock Fractals in Bifurcation Plot (Problem 7) Fractals from Cellular Automata Perlin Noise Adds Realism Ray Tracing Algorithms 404

10 2014/6/16 14:54 page viii viii Exercises Thermodynamic Simulations & Feynman Path Integrals Magnets via Metropolis Algorithm An Ising Chain (Model) Statistical Mechanics (Theory) Analytic Solution Metropolis Algorithm Metropolis Algorithm Implementation Equilibration, Thermodynamic Properties Beyond Nearest Neighbors, 1-D (Exploration) Magnets via Wang-Landau Sampling Wang-Landau Algorithm Ising Model Implementation Assessment Feynman Path Integral Quantum Mechanics Feynman s Space-Time Propagation (Theory) Bound-State Wave Function (Theory) Lattice Path Integration (Algorithm) Lattice Implementation Assessment and Exploration Exploration: Quantum Bouncer s Paths Molecular Dynamics Simulations Molecular Dynamics (Theory) Connection to Thermodynamic Variables Setting Initial Velocities Periodic Boundary Conditions & V (r) Cutoff Verlet and Velocity-Verlet Algorithms D Implementation and Exercise Analysis PDE Review PDE Generalities Electrostatic Potentials Laplace s Elliptic PDE (Theory) Fourier Series Solution of a PDE Polynomial Expansion As an Algorithm Finite-Difference Algorithm Relaxation and Overrelaxation Lattice PDE Implementation Assessment via Surface Plot Alternate Capacitor Problems Implementation and Assessment Electric Field Visualization (Exploration) 475

11 2014/6/16 14:54 page ix ix 19.9 Review Exercise Heat Flow via Time Stepping Heat Flow via Time-Stepping (Leapfrog) The Parabolic Heat Equation (Theory) Solution: Analytic Expansion Solution: Time-Stepping Von Neumann Stability Assessment Heat Equation Implementation Assessment and Visualization Improved Heat Flow: Crank-Nicolson Method Solution of Tridiagonal Matrix Equations Implementation, Assessment Wave Equations I: Strings & Membranes A Vibrating String The Hyperbolic Wave Equation (Theory) Solution via Normal-Mode Expansion Algorithm: Time-Stepping Wave Equation Implementation Assessment, Exploration Strings with Friction (Extension) Strings with Variable Tension & Density Waves on Catenary Derivation of Catenary Shape Catenary & Frictional Wave Exercises Vibrating Membrane (2-D Waves) Analytical Solution Numerical Solution for 2-D Waves Wave Equations II: Quantum Packets & E-M Quantum Wave Packets Time-Dependent Schrödinger Equation (Theory) Finite-Difference Algorithm Wave Packet Implementation, Animation Wave Packets in Other Wells (Exploration) Algorithm for the 2-D Schrödinger Equation Exploration: Bound & Diffracted 2-D Packet E&M Waves via Finite-Difference Time Domain Maxwell s Equations FDTD Algorithm Implementation Assessment Extension: Circularly Polarized Waves Application: Wave Plates 527

12 2014/6/16 14:54 page x x 22.8 Algorithm FDTD Exercise & Assessment Electrostatics via Finite Elements Finite-Element Method Electric Field from Charge Density (Problem) Analytic Solution Finite-Element (Not Difference) Methods, 1-D Weak Form of PDE Galerkin Spectral Decomposition D FEM Implementation and Exercises D Exploration Extension to 2-D Finite Elements Weak Form of PDE Galerkin s Spectral Decomposition Triangular Elements Solution as Linear Equations Imposing Boundary Conditions FEM 2D Implementation & Exercise FEM 2D Exercises Shock Waves and Solitons Shocks & Solitons in Shallow Water Theory: Continuity and Advection Equations Advection Implementation Theory: Shock Waves via Burgers Equation Lax-Wendroff Algorithm for Burgers Equation Implementation and Assessment Including Dispersion Shallow-Water Solitons; the KdeV Equation Analytic Soliton Solution Algorithm for KdeV Solitons Implementation: KdeV Solitons Exploration: Solitons in Phase Space, Crossing Solitons on Pendulum Chain Including Dispersion Continuum Limit, the SGE Analytic SGE Solution Numeric Solution: 2-D SGE Solitons D Soliton Implementation Visualization Fluid Dynamics River Hydrodynamics Navier-Stokes Equation (Theory) 570

13 33) : Computational Physics A Survey of Applications with Python 2014/6/16 14:54 page xi xi Boundary Conditions for Parallel Plates Analytic Solution for Parallel Plates Finite-Difference Algorithm and Overrelaxation Successive Overrelaxation Implementation D Flow over a Beam Theory: Vorticity Form of Navier-Stokes Equation Finite Differences and the SOR Algorithm Boundary Conditions for a Beam SOR on a Grid Flow Assessment Exploration Integral Equations of Quantum Mechanics Bound States of Nonlocal Potentials Momentum-Space Schrödinger Equation (Theory) Integral to Matrix Equations Delta-Shell Potential (Model) Binding Energies Solution Wave Function (Exploration) Scattering States of Nonlocal Potentials Lippmann-Schwinger Equation (Theory) Singular Integrals (Math) Numerical Principal Values Reducing Integral to Matrix Equations Solution via Inversion, Elimination Scattering Implementation Scattering Wave Function (Exploration) 600 A Codes, Applets & Animations 601 B Video Lecture Modules 605 Index 615