Computational Physics : Problem Solving with Python.

Format:

Book

Author/Creator:

Landau, Rubin H.

Contributor:

Páez, Manuel J.

Bordeianu, Cristian C.

Language:

English

Subjects (All):

Physics--Problems, exercises, etc. -- Data processing.

Physics -- Problems, exercises, etc. -- Data processing.

Physics--Computer simulation.

Physics -- Computer simulation.

Physical Description:

1 online resource (647 pages)

Edition:

3rd ed.

Place of Publication:

Berlin : John Wiley & Sons, Incorporated, 2015.

Contents:

Cover

Copyright page

Dedication

Contents

Preface

1 Introduction

1.1 Computational Physics and Computational Science

1.2 This Book's Subjects

1.3 This Book's Problems

1.4 This Book's Language: The Python Ecosystem

1.4.1 Python Packages (Libraries)

1.4.2 This Book's Packages

1.4.3 The Easy Way: Python Distributions (Package Collections)

1.5 Python's Visualization Tools

1.5.1 Visual (VPython)'s 2D Plots

1.5.2 VPython's Animations

1.5.3 Matplotlib's 2D Plots

1.5.4 Matplotlib's 3D Surface Plots

1.5.5 Matplotlib's Animations

1.5.6 Mayavi's Visualizations Beyond Plotting

1.6 Plotting Exercises

1.7 Python's Algebraic Tools

2 Computing Software Basics

2.1 Making Computers Obey

2.2 Programming Warmup

2.2.1 Structured and Reproducible Program Design

2.2.2 Shells, Editors, and Execution

2.3 Python I/O

2.4 Computer Number Representations (Theory)

2.4.1 IEEE Floating-Point Numbers

2.4.2 Python and the IEEE 754 Standard

2.4.3 Over and Underflow Exercises

2.4.4 Machine Precision (Model)

2.4.5 Experiment: Your Machine's Precision

2.5 Problem: Summing Series

2.5.1 Numerical Summation (Method)

2.5.2 Implementation and Assessment

3 Errors and Uncertainties in Computations

3.1 Types of Errors (Theory)

3.1.1 Model for Disaster: Subtractive Cancelation

3.1.2 Subtractive Cancelation Exercises

3.1.3 Round-off Errors

3.1.4 Round-off Error Accumulation

3.2 Error in Bessel Functions (Problem)

3.2.1 Numerical Recursion (Method)

3.2.2 Implementation and Assessment: Recursion Relations

3.3 Experimental Error Investigation

3.3.1 Error Assessment

4 Monte Carlo: Randomness, Walks, and Decays

4.1 Deterministic Randomness

4.2 Random Sequences (Theory)

4.2.1 Random-Number Generation (Algorithm).

4.2.2 Implementation: Random Sequences

4.2.3 Assessing Randomness and Uniformity

4.3 Random Walks (Problem)

4.3.1 Random-Walk Simulation

4.3.2 Implementation: Random Walk

4.4 Extension: Protein Folding and Self-Avoiding Random Walks

4.5 Spontaneous Decay (Problem)

4.5.1 Discrete Decay (Model)

4.5.2 Continuous Decay (Model)

4.5.3 Decay Simulation with Geiger Counter Sound

4.6 Decay Implementation and Visualization

5 Differentiation and Integration

5.1 Differentiation

5.2 Forward Difference (Algorithm)

5.3 Central Difference (Algorithm)

5.4 Extrapolated Difference (Algorithm)

5.5 Error Assessment

5.6 Second Derivatives (Problem)

5.6.1 Second-Derivative Assessment

5.7 Integration

5.8 Quadrature as Box Counting (Math)

5.9 Algorithm: Trapezoid Rule

5.10 Algorithm: Simpson's Rule

5.11 Integration Error (Assessment)

5.12 Algorithm: Gaussian Quadrature

5.12.1 Mapping Integration Points

5.12.2 Gaussian Points Derivation

5.12.3 Integration Error Assessment

5.13 Higher Order Rules (Algorithm)

5.14 Monte Carlo Integration by Stone Throwing (Problem)

5.14.1 Stone Throwing Implementation

5.15 Mean Value Integration (Theory and Math)

5.16 Integration Exercises

5.17 Multidimensional Monte Carlo Integration (Problem)

5.17.1 Multi Dimension Integration Error Assessment

5.17.2 Implementation: 10D Monte Carlo Integration

5.18 Integrating Rapidly Varying Functions (Problem)

5.19 Variance Reduction (Method)

5.20 Importance Sampling (Method)

5.21 von Neumann Rejection (Method)

5.21.1 Simple Random Gaussian Distribution

5.22 Nonuniform Assessment

5.22.1 Implementation

6 Matrix Computing

6.1 Problem 3: N-D Newton-Raphson

Two Masses on a String

6.1.1 Theory: Statics

6.1.2 Algorithm: Multidimensional Searching

6.2 Why Matrix Computing?.

6.3 Classes of Matrix Problems (Math)

6.3.1 Practical Matrix Computing

6.4 Python Lists as Arrays

6.5 Numerical Python (NumPy) Arrays

6.5.1 NumPy's linalg Package

6.6 Exercise: Testing Matrix Programs

6.6.1 Matrix Solution of the String Problem

6.6.2 Explorations

7 Trial-and-Error Searching and Data Fitting

7.1 Problem 1: A Search for Quantum States in a Box

7.2 Algorithm: Trial-and-Error Roots via Bisection

7.2.1 Implementation: Bisection Algorithm

7.3 Improved Algorithm: Newton-Raphson Searching

7.3.1 Newton-Raphson with Backtracking

7.3.2 Implementation: Newton-Raphson Algorithm

7.4 Problem 2: Temperature Dependence of Magnetization

7.4.1 Searching Exercise

7.5 Problem 3: Fitting An Experimental Spectrum

7.5.1 Lagrange Implementation, Assessment

7.5.2 Cubic Spline Interpolation (Method)

7.6 Problem 4: Fitting Exponential Decay

7.7 Least-Squares Fitting (Theory)

7.7.1 Least-Squares Fitting: Theory and Implementation

7.8 Exercises: Fitting Exponential Decay, Heat Flow and Hubble's Law

7.8.1 Linear Quadratic Fit

7.8.2 Problem 5: Nonlinear Fit to a Breit-Wigner

8 Solving Differential Equations: Nonlinear Oscillations

8.1 Free Nonlinear Oscillations

8.2 Nonlinear Oscillators (Models)

8.3 Types of Differential Equations (Math)

8.4 Dynamic Form for ODEs (Theory)

8.5 ODE Algorithms

8.5.1 Euler's Rule

8.6 Runge-Kutta Rule

8.7 Adams-Bashforth-Moulton Predictor-Corrector Rule

8.7.1 Assessment: rk2 vs. rk4 vs. rk45

8.8 Solution for Nonlinear Oscillations (Assessment)

8.8.1 Precision Assessment: Energy Conservation

8.9 Extensions: Nonlinear Resonances, Beats, Friction

8.9.1 Friction (Model)

8.9.2 Resonances and Beats: Model, Implementation

8.10 Extension: Time-Dependent Forces

9 ODE Applications: Eigenvalues, Scattering, and Projectiles.

9.1 Problem: Quantum Eigenvalues in Arbitrary Potential

9.1.1 Model: Nucleon in a Box

9.2 Algorithms: Eigenvalues via ODE Solver + Search

9.2.1 Numerov Algorithm for Schrödinger ODE

9.2.2 Implementation: Eigenvalues via ODE Solver + Bisection Algorithm

9.3 Explorations

9.4 Problem: Classical Chaotic Scattering

9.4.1 Model and Theory

9.4.2 Implementation

9.4.3 Assessment

9.5 Problem: Balls Falling Out of the Sky

9.6 Theory: Projectile Motion with Drag

9.6.1 Simultaneous Second-Order ODEs

9.6.2 Assessment

9.7 Exercises: 2- and 3-Body Planet Orbits and Chaotic Weather

10 High-Performance Hardware and Parallel Computers

10.1 High-Performance Computers

10.2 Memory Hierarchy

10.3 The Central Processing Unit

10.4 CPU Design: Reduced Instruction Set Processors

10.5 CPU Design: Multiple-Core Processors

10.6 CPU Design: Vector Processors

10.7 Introduction to Parallel Computing

10.8 Parallel Semantics (Theory)

10.9 Distributed Memory Programming

10.10 Parallel Performance

10.10.1 Communication Overhead

10.11 Parallelization Strategies

10.12 Practical Aspects of MIMD Message Passing

10.12.1 High-Level View of Message Passing

10.12.2 Message Passing Example and Exercise

10.13 Scalability

10.13.1 Scalability Exercises

10.14 Data Parallelism and Domain Decomposition

10.14.1 Domain Decomposition Exercises

10.15 Example: The IBM Blue Gene Supercomputers

10.16 Exascale Computing via Multinode-Multicore GPUs

11 Applied HPC: Optimization, Tuning, and GPU Programming

11.1 General Program Optimization

11.1.1 Programming for Virtual Memory (Method)

11.1.2 Optimization Exercises

11.2 Optimized Matrix Programming with NumPy

11.2.1 NumPy Optimization Exercises

11.3 Empirical Performance of Hardware

11.3.1 Racing Python vs. Fortran/C.

11.4 Programming for the Data Cache (Method)

11.4.1 Exercise 1: Cache Misses

11.4.2 Exercise 2: Cache Flow

11.4.3 Exercise 3: Large-Matrix Multiplication

11.5 Graphical Processing Units for High Performance Computing

11.5.1 The GPU Card

11.6 Practical Tips for Multicore and GPU Programming

11.6.1 CUDA Memory Usage

11.6.2 CUDA Programming

12 Fourier Analysis: Signals and Filters

12.1 Fourier Analysis of Nonlinear Oscillations

12.2 Fourier Series (Math)

12.2.1 Examples: Sawtooth and Half-Wave Functions

12.3 Exercise: Summation of Fourier Series

12.4 Fourier Transforms (Theory)

12.5 The Discrete Fourier Transform

12.5.1 Aliasing (Assessment)

12.5.2 Fourier Series DFT (Example)

12.5.3 Assessments

12.5.4 Nonperiodic Function DFT (Exploration)

12.6 Filtering Noisy Signals

12.7 Noise Reduction via Autocorrelation (Theory)

12.7.1 Autocorrelation Function Exercises

12.8 Filtering with Transforms (Theory)

12.8.1 Digital Filters: Windowed Sinc Filters (Exploration)

12.9 The Fast Fourier Transform Algorithm

12.9.1 Bit Reversal

12.10 FFT Implementation

12.11 FFT Assessment

13 Wavelet and Principal Components Analyses: Nonstationary Signals and Data Compression

13.1 Problem: Spectral Analysis of Nonstationary Signals

13.2 Wavelet Basics

13.3 Wave Packets and Uncertainty Principle (Theory)

13.3.1 Wave Packet Assessment

13.4 Short-Time Fourier Transforms (Math)

13.5 The Wavelet Transform

13.5.1 Generating Wavelet Basis Functions

13.5.2 Continuous Wavelet Transform Implementation

13.6 Discrete Wavelet Transforms, Multiresolution Analysis

13.6.1 Pyramid Scheme Implementation

13.6.2 Daubechies Wavelets via Filtering

13.6.3 DWT Implementation and Exercise

13.7 Principal Components Analysis

13.7.1 Demonstration of Principal Component Analysis.

13.7.2 PCA Exercises.

Notes:

Description based on publisher supplied metadata and other sources.

Other Format:

Print version: Landau, Rubin H. Computational Physics

ISBN:

9783527684694

OCLC:

927509579