Details

Computational Physics

Problem Solving with Python
4. Aufl.

von: Rubin H. Landau, Manuel J. Páez, Cristian C. Bordeianu
97,99 €
Verlag:	Wiley-VCH
Format:	EPUB
Veröffentl.:	20.03.2024
ISBN/EAN:	9783527843312
Sprache:	englisch
Anzahl Seiten:	592

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Beschreibungen

Titelbeschreibung

Computational Physics The classic in the field for more than 25 years, now with increased emphasis on data science and new chapters on quantum computing, machine learning (AI), and general relativity Computational physics combines physics, applied mathematics, and computer science in a cutting-edge multidisciplinary approach to solving realistic physical problems. It has become integral to modern physics research because of its capacity to bridge the gap between mathematical theory and real-world system behavior. Computational Physics provides the reader with the essential knowledge to understand computational tools and mathematical methods well enough to be successful. Its philosophy is rooted in “learning by doing”, assisted by many sample programs in the popular Python programming language. The first third of the book lays the fundamentals of scientific computing, including programming basics, stable algorithms for differentiation and integration, and matrix computing. The latter two-thirds of the textbook cover more advanced topics such linear and nonlinear differential equations, chaos and fractals, Fourier analysis, nonlinear dynamics, and finite difference and finite elements methods. A particular focus in on the applications of these methods for solving realistic physical problems. Readers of the fourth edition of Computational Physics will also find: <ul><li>An exceptionally broad range of topics, from simple matrix manipulations to intricate computations in nonlinear dynamics</li><li>A whole suite of supplementary material: Python programs, Jupyter notebooks and videos</li></ul> Computational Physics is ideal for students in physics, engineering, materials science, and any subjects drawing on applied physics.

Inhaltsverzeichnis

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 of Packages 1.5. NEW: Installing Python and Its Packages 2. Python Programming Basics and Visualizations 2.1. Making Computers Obey 2.2. Program, Shells, Editors, and All that 2.3. Variables 2.4. Operations 2.5. Functions, Packages, and Modules 2.6. I/O 2.7. Control Statements 2.8. Arrays, Matrices, Lists 2.9. Floating-Point Numbers-Limits 2.10. Problem: Summing Series 2.11. Visualizations with Matplotlib 2.12. Plotting Exercises 2.13. Algebraic Tools 3. Errors and Uncertainties in Computations 3.1. Types of Errors 3.2. Error in Bessel Function Computations 3.3. Experimental Error Investigation 4. Monte Carlo: Randomness, Walks, and Decays 4.1. Deterministic Randomness 4.2. Random Sequences 4.3. Random Walks 4.4. Protein Folding & Self-Avoiding Walks 4.5. Problem: Spontaneous Decay Physics 4.6. Decay Implementation and Visualization 5. Differentiation 5.1. Differentiation 5.2. Forward Difference 5.3. Central Difference 5.4. Extrapolated Difference 5.5. Errors 5.6. Second Derivatives 6. Integration 6.1. Quadrature as Box Counting 6.2. Trapezoid Rule 6.3. Simpson's Rule 6.4. Errors 6.5. Gaussian Quadrature 6.6. Higher Order Rules 6.7. Monte Carlo Integration (Stone Throwing) 6.8. Mean Value Integration 6.9. Exercises 6.10. N-D Monte Carlo 6.11. Integrating Rapidly Varying Functions 6.12. Variance Reduction 6.13. Importance Sampling 6.14. von Neumann Rejection 7. Matrix Computing 7.1. Problem: Masses on String - Newton-Raphson 7.2. Why Matrix Computing? 7.3. Classes of Matrix Problems 7.4. Gaussian vs Inverse Methods for Solving Linear Equations 7.5. Lists, Arrays, Matrices (Again) 7.6. Numerical Python (NumPy) Arrays 7.7. Testing Matrix Programs 8. Trial-and-Error Searching and Data Fitting 8.1. Problem:Quantum States in a Box 8.2. Trial-and-Error Roots via Bisection 8.3. Newton'Raphson Searching 8.4. Problem: T Dependence of Magnetization 8.5. Problem: Fitting An Experimental Spectrum 8.6. Interpolation Methods 8.7. Problem: Fitting Exponential Decay 8.8. Least-Squares Fitting 8.9. Exercises: Decay, Heat Flow, Hubble's Law 8.10. Linear Quadratic Fits 8.11. Nonlinear Fit to Breit-Wigner 9. Differential Equations & Nonlinear Oscillations 9.1. Free Nonlinear Oscillations 9.2. Nonlinear Models 9.3. Types of Differential Equations 9.4. Dynamic Form for ODEs 9.5. ODE Algorithms and Euler's Method 9.6. Runge-Kutta Method 9.7. Predictor-Corrector Method 9.8. Nonlinear Oscillation Solutions 9.9. Nonlinear Resonances, Beats, Friction 9.10. Extension: Time-Dependent Forces 10. ODE Applications: Eigenvalues, Scattering, Projectiles 10.1. Quantum States for Arbitrary Potentials 10.2. Eigenvalues via ODE plus Search 10.3. Explorations 10.4. Classical Chaotic Scattering 10.5. Objects Falling from the Sky 10.6. Projectile Motion with Drag 10.7. Two- and Three-Body Orbits, Chaotic Weather 11. Program Optimization, Tuning, and GPU Programming 11.1. General Program Optimization Exascale Computing via Multinode- Multicore GPUs 11.2. Optimized Matrix Programming with NumPy 11.3. Empirical Performance of Hardware 11.4. Programming for the Data Cache 11.5. Graphical Processing Units for High Performance Computing 11.6. Practical Tips for Multicore and GPU Programming 12. Data Science I: Fourier Analysis 12.1. Problem: Fourier Analysis of Nonlinear Oscillations 12.2. Fourier Series 12.3. Exercise: Summation of Series 12.4. Fourier Transforms 12.5. Discrete Fourier Transforms 12.6. Filtering Noisy Signals 12.7. Autocorrelation Noise Reduction 12.8. Filtering via Transforms 12.9. Fast Fourier Transforms (FFT) 12.10. FFT Implementation & Assessment 13. Data Science II: Wavelet and Principal Components Analyses for Nonstationary Signals & Data Compression 13.1. Spectral Analysis of Nonstationary Signals 13.2. Wavelet Basics 13.3. Wave Packets and Uncertainty Principle 13.4. Short-Time Fourier Transforms 13.5. The Wavelet Transform 13.6. Discrete Wavelet Transforms, Multiresolution Analysis 13.7. Principal Components Analysis 14. Neural Nets and Machine Learning 15. Nonlinear Population Dynamics 15.1. Bug Population Dynamics 15.2. The Logistic Map (Model) 15.3. Properties of Nonlinear Maps 15.4. Mapping Implementation 15.5. Bifurcation Diagram Analysis 15.6. Logistic Map Randomness 15.7. Exploring Other Maps 15.8. Chaotic Signal: Lyapunov Coeffient 15.9. Coupled Predator-Prey Models 15.10. The Lotka-Volterra Model 15.11. Predator-Prey Chaos 16. Continuous Nonlinear Dynamics 16.1. Chaotic Pendulum 16.2. Phase-Space Orbits 16.3. Bifurcations of Chaotic Pendulums 16.4. Alternate Problem: The Double Pendulum 16.5. Fourier/Wavelet Analysis of Chaos 16.6. Alternate Phase-Space Plots 16.7. Further Explorations 17. Fractals and Statistical Growth Models 17.1. Fractional Dimension 17.2. The Sierpinski Gasket 17.3. Growing Plants 17.4. Ballistic Deposition 17.5. Length of Coastline (Problem 17.6. Correlated Growth, Forests, Films 17.7. Globular Cluster, Diffusion-Limited Aggregation 17.8. Fractals in Bifurcation Plot 17.9. Fractals from Cellular Automata 17.10. Perlin Noise Adds Realism 17.11. Exercises 18. Thermodynamic Simulations 18.1. Magnets via Metropolis Algorithm 18.2. An Ising Chain 18.3. Statistical Mechanics 18.4. Metropolis Algorithm 18.5. Magnets via Wang-Landau Sampling 21. Molecular Dynamics Simulations 21.1. Molecular Dynamics Theory 21.2. Connection to Thermodynamic Variables 21.3. Periodic Boundary Conditions and Potential Cutoff 21.4. Verlet and Velocity-Verlet Algorithms 21.5. 1D Implementation and Exercise 21.6. Analysis 22. Soft Matter and Jamming 23. Electrostatics via Finite Differences 23.1. PDE Review 23.2. Electrostatic Potentials 23.3. Fourier Series Solutions 23.4. Finite-Difference Algorithm 23.5. Assessment via Surface Plot 23.6. Capacitor Problems 23.7. Electric Field Visualization 23.8. Review Exercise 24. Electrostatics via Finite Elements 24.1. Finite-Element Method 24.2. Field due to Charge Density 24.3. Analytic Solution 24.4. Finite-Element Solution 24.5. Implementation and Exercises 24.6. 2D Finite Elements 25. Heat Flow via Time Stepping 25.1. Leapfrog Algorithm 25.2. The Parabolic Heat Equation 25.3. Analytic Solution 25.4. Time Stepping Solution 25.5. von Neumann Stability Assessment 25.6. Implementation 25.7. Assessment and Visualization 25.8. Crank-Nicolson Improvement 26. Waves on Strings and Membranes 26.1. Hyperbolic Equation of Vibrating String 26.2. Normal-Mode Solution 26.3. Time Stepping Algorithm 26.4. Implementation 26.5. Assessment and Exploration 26.6. With Friction 26.7. With Variable Tension, Density 26.8. Catenary and Frictional Wave Exercises 26.9. Vibrating 2D Membrane 26.10. Analytical Solution 26.11. Numerical Solution 27. Quantum Wave Packets 27.1. Time-Dependent Schrodinger Equation 27.2. Finite-Difference Algorithm 27.3. 2D Finite-Difference 27.4. Bound and Diffracted Packets 27.5. Packet-Packet Scattering 27.6. Implementation and Visualization 28. Electromagnetic Waves 28.1. Finite-Difference Time Domain 28.2. Maxwell's Equations 28.3. FDTD Algorithm 28.4. Circularly Polarized Waves 28.5. Wave Plates 28.6. FDTD Exercises and Assessment 29. Shocks Waves and Solitons 29.1. Shallow Water Shocks and Solitons 29.2. Continuity and Advection Equations 29.3. Shock Waves via Burgers? Equation 29.4. Lax-Wendroff Algorithm 29.5. Including Dispersion 29.6. KdeV Equation 29.7. Analytic KdeV Solitons 29.8. Numeric KdeV Solitons 29.9. Phase Space and Crossing Solitons 29.10. Pendulum Chain Solitons 29.11. Including Dispersion 29.12. Continuum Limit, the Sine-Gordon Equation 29.13. Analytic SGE Solution 29.14. Numeric Solution: 2D SGE Solitons 30. General Relativity 30.1. Visualizing Wormholes 30.2. Gravitational Lensing 30.3. Particle Orbits in GR 30.4. Riemann and Ricci Tensors 30.5. GR Code Listings 31. Appendices 31.1. Installing Packages 31.2. Chapter-Linked Video Lectures & Slides 31.3. Jupyter Notebooks 31.4. Web Materials

Autorenportrait

Rubin H. Landau, PhD, is Professor Emeritus in the Department of Physics at Oregon State University, Corvallis, Oregon, USA. In his long and distinguished research career he has been instrumental in the development of computational physics as a defined subject, and founded both the Computational Physics Degree Program and the Northwest Alliance for Computational Science and Engineering. Manuel J. Páez, PhD, is a Professor in the Department of Physics at the University of Antioquia in Medellin, Colombia. He teaches courses in both physics and programming, and he and Professor Landau have collaborated on pathbreaking computational physics investigations. Cristian C. Bordeianu, PhD, taught Physics and Computer Science at the Military College “Stefan cel Mare,” Campulung Moldovenesc, Romania.

Back cover copy

The classic in the field for more than 25 years, now with increased emphasis on data science and new chapters on quantum computing, machine learning (AI), and general relativity Computational physics combines physics, applied mathematics, and computer science in a cutting-edge multidisciplinary approach to solving realistic physical problems. It has become integral to modern physics research because of its capacity to bridge the gap between mathematical theory and real-world system behavior. Computational Physics provides the reader with the essential knowledge to understand computational tools and mathematical methods well enough to be successful. Its philosophy is rooted in “learning by doing”, assisted by many sample programs in the popular Python programming language. The first third of the book lays the fundamentals of scientific computing, including programming basics, stable algorithms for differentiation and integration, and matrix computing. The latter two-thirds of the textbook cover more advanced topics such linear and nonlinear differential equations, chaos and fractals, Fourier analysis, nonlinear dynamics, and finite difference and finite elements methods. A particular focus in on the applications of these methods for solving realistic physical problems. Readers of the fourth edition of Computational Physics will also find: <ul><li>An exceptionally broad range of topics, from simple matrix manipulations to intricate computations in nonlinear dynamics</li><li>A whole suite of supplementary material: Python programs, Jupyter notebooks and videos</li></ul> Computational Physics is ideal for students in physics, engineering, materials science, and any subjects drawing on applied physics.