Computational Physics

Problem Solving with Python

Häftad, Engelska, 2024

AvRubin H. Landau,Manuel J. Páez,Cristian C. Bordeianu,Corvallis) Landau, Rubin H. (Oregon State University,Colombia) Paez, Manuel J. (University of Antioquia, Medellin,Romania) Bordeianu, Cristian C. (Bucharest University

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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 relativityComputational 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: An exceptionally broad range of topics, from simple matrix manipulations to intricate computations in nonlinear dynamicsA whole suite of supplementary material: Python programs, Jupyter notebooks and videosComputational Physics is ideal for students in physics, engineering, materials science, and any subjects drawing on applied physics.

Produktinformation

Utgivningsdatum2024-04-17
Mått170 x 244 x 30 mm
Vikt1 106 g
FormatHäftad
SpråkEngelska
Antal sidor592
Upplaga4
FörlagWiley-VCH Verlag GmbH
ISBN9783527414253

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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.

Preface xviiAcknowledgments xixPart I Basics 11 Introduction 31.1 Computational Physics and Science 31.2 This Book’s Subjects 41.3 Video Lecture Supplements 41.4 This Book’s Codes and Problems 51.5 Our Language: The Python Ecosystem 61.6 The Easy Way: Python Distributions 62 Software Basics 92.1 Making Computers Obey 92.2 Computer Number Representations 112.3 Python Mini Tutorial 182.4 Programming Warmup 252.5 Python’s Visualization Tools 302.6 Plotting Exercises 362.7 Code Listings 383 Errors and Uncertainties 443.1 Types of Errors 443.2 Experimental Error Investigation 493.3 Errors with Power Series 523.4 Errors in Bessel Functions 553.5 Code Listing 584 Monte Carlo Simulations 594.1 Random Numbers 594.2 Simulating a Random Walk 634.3 Spontaneous Decay 684.4 Testing and Generating Random Distributions 714.5 Code Listings 735 Differentiation and Integration 785.1 Differentiation Algorithms 785.2 Extrapolated Difference 805.3 Integration Algorithms 835.4 Gaussian Quadrature 895.5 Monte Carlo Integrations 915.6 Mean Value and N–D Integration 945.7 mc Variance Reduction 965.8 Importance Sampling and von Neumann Rejection 965.9 Code Listings 976 Trial-and-Error Searching and Data Fitting 1006.1 Quantum Bound States I 1006.2 Bisection Search 1016.3 Newton–Raphson Search 1026.4 Magnetization Search 1056.5 Data Fitting 1076.6 Fitting Exponential Decay 1126.7 Least-Squares Fitting 1136.8 Nonlinear Fit to a Resonance 1186.9 Code Listings 1207 Matrix Computing and N–D Searching 1237.1 Masses on a String and N–D Searching 1237.2 Matrix Generalities 1267.3 Matrices in Python 1297.4 Exercise: Tests Before Use 1367.5 Solution to String Problem 1397.6 Spin States and Hyperfine Structure 1397.7 Speeding Up Matrix Computing ⊙ 1417.8 Code Listing 1448 Differential Equations and Nonlinear Oscillations 1478.1 Nonlinear Oscillators 1478.2 ODE Review 1498.3 Dynamic Form of ODEs 1508.4 ODE Algorithms 1528.5 Solution for Nonlinear Oscillations 1578.6 Extensions: Nonlinear Resonances, Beats, Friction 1598.7 Code Listings 161Part II Data Science 1659 Fourier Analyses 1679.1 Fourier Series 1679.2 Fourier Transforms 1709.3 Discrete Fourier Transforms 1729.4 Noise Filtering 1789.5 Fast Fourier Transform ⊙ 1859.6 FFT Implementation 1899.7 FFT Assessment 1909.8 Code Listings 19010 Wavelet and Principal Components Analysis 19310.1 Part I: Wavelet Analysis 19310.2 Wave Packets and Uncertainty Principle 19510.3 Short-Time Fourier Transforms 19710.4 Wavelet Transforms 19810.5 Discrete Wavelet Transforms ⊙ 20310.6 Part II: Principal Components Analysis 21310.7 Code Listings 22011 Neural Networks and Machine Learning 22411.1 Part I: Biological and Artificial Neural Networks 22511.2 A Simple Neural Network 22611.3 A Graphical Deep Net 23211.4 Part II: Machine Learning Software 23411.5 TensorFlow and SkLearn Examples 23511.6 ml Clustering 24011.7 Keras: Python’s Deep Learning API 24411.8 Image Processing with OpenCV 24411.9 Explore ML Data Repositories 24711.10 Code Listings 24712 Quantum Computing (G. He, Coauthor) 25412.1 Dirac Notation in Quantum Mechanics 25412.2 From Bits to Qubits 25512.3 Entangled and Separable States 25712.4 Logic Gates 26012.5 An Intro to QC Programming 26412.6 Accessing the IBM Quantum Computer 27012.7 Qiskit Plus IBM Quantum 27212.8 The Quantum Fourier Transform 27512.9 Oracle + Diffuser = Grover’s Search Algorithm 27812.10 Shor’s Factoring ⊙ 28112.11 Code Listings 284Part III Applications 28913 ODE Applications; Eigenvalues, Scattering, Trajectories 29113.1 Quantum Eigenvalues for Arbitrary Potentials 29113.2 Algorithm: ODE Solver + Search 29313.3 Classical Chaotic Scattering 29613.4 Projectile Motion with Drag 29913.5 2- and 3-Body Planetary Orbits 30113.6 Code Listings 30314 Fractals and Statistical Growth Models 30714.1 The Sierpiński Gasket 30814.2 Growing Plants 31014.3 Ballistic Deposition 31214.4 Length of British Coastline 31314.5 Correlated Growth 31714.6 Diffusion-Limited Aggregation 31814.7 Fractals in Bifurcations 32014.8 Cellular Automata Fractals 32014.9 Perlin Noise Adds Realism ⊙ 32114.10 Code Listings 32415 Nonlinear Population Dynamics 32915.1 The Logistic Map, A Bug Population Model 32915.2 Chaos 33315.3 Bifurcation Diagrams 33315.4 Measures of Chaos 33615.5 Coupled Predator–Prey Models ⨀ 33815.6 Code Listings 34416 Nonlinear Dynamics of Continuous Systems 34816.1 The Chaotic Pendulum 34816.2 Phase Space 35116.3 Chaotic Explorations 35416.4 Other Chaotic Systems 35816.5 Code Listings 36417 Thermodynamics Simulations and Feynman Path Integrals 36517.1 An Ising Magnetic Chain 36517.2 Metropolis Algorithm 36817.3 Fast Equilibration via Wang–Landau Sampling ⊙ 37217.4 Path Integral Quantum Mechanics ⊙ 37417.5 Lattice Path Integration 37717.6 Implementation 38117.7 Code Listings 38518 Molecular Dynamics Simulations 39118.1 MD Versus Thermodynamics 39418.2 Initial, Boundary, and Large r Conditions 39418.3 Verlet Algorithms 39618.4 MD for 16 Particles 40018.5 Code Listing 40219 General Relativity 40819.1 Einstein’s Field Equations 40819.2 Gravitational Deflection of Light 41219.3 Planetary Orbits in GR Gravity 41419.4 Visualizing Wormholes 41819.5 Problems 42019.6 Code Listings 42020 Integral Equations 42520.1 Nonlocal Potential Binding 42520.2 Momentum-Space Schrödinger Equation 42520.3 Scattering in Momentum Space ⊙ 42920.4 Code Listings 434Part IV PDE Applications 43721 PDE Review, Electrostatics and Relaxation 43921.1 Review 43921.2 Laplace’s Equation 44121.3 Finite-Difference Algorithm 44421.4 Alternate Capacitor Problems 44721.5 Electric Field Visualization 44921.6 Code Listings 45022 Heat Flow and Leapfrogging 45222.1 The Parabolic Heat Equation 45222.2 Time Stepping (Leapfrog) Algorithm 45422.3 Newton’s Radiative Cooling 45722.4 The Crank–Nicolson Algorithm 45822.5 Code Listings 46223 String and Membrane Waves 46423.1 A Vibrating String’s Hyperbolic Wave Equation 46423.2 Time-Stepping Algorithm 46623.3 von Neumann Stability Analysis 46823.4 Beyond The Simple Wave Equation 46923.5 Vibrating Membrane (2D Waves) 47423.6 Analytical Solution 47523.7 Numerical Solution 47623.8 Code Listings 47824 Quantum Wave Packets and EM Waves 48024.1 Time-Dependent Schrödinger Equation 48024.2 Split-Time Algorithm 48224.3 Special Schrödinger Algorithm 48424.4 Quantum Chaos 48524.5 E&M Waves: Finite Difference Time Domain 48824.6 Maxwell’s Equations 48824.7 Split-Time FDTD 48924.8 More E&M Problems 49224.9 Code Listings 49625 Shock and Soliton Waves 50125.1 The Continuity and Advection Equations 50225.2 Shock Waves via Burgers’ Equation 50325.3 Including Dispersion 50525.4 KdeV Solitons 50625.5 Pendulum Chain Solitons 51025.6 Continuum Limit, the Sine-Gordon Equation 51225.7 Code Listings 51626 Fluid Hydrodynamics 51826.1 Navier–Stokes Equation 51826.2 Flow Through Parallel Plates 52026.3 Navier–Stokes Difference Equation 52226.4 Vorticity Form of Navier–Stokes Equation 52326.5 Assessment and Exploration 52726.6 Code Lisitings 52927 Finite Element Electrostatics ⊙ 53127.1 The Potential of Two Metal Plates 53127.2 Finite Element Method 53227.3 1D FEM Problems 53627.4 2D FEM Exercises 53727.5 Code Listings 539Appendix Codes and Animations 543References 546Index 555