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Computational Modeling and Visualization of Physical Systems with Python

Book Description

Computational Modeling, by Jay Wang introduces computational modeling and visualization of physical systems that are commonly found in physics and related areas. The authors begin with a framework that integrates model building, algorithm development, and data visualization for problem solving via scientific computing. Through carefully selected problems, methods, and projects, the reader is guided to learning and discovery by actively doing rather than just knowing physics.

Table of Contents

  1. Cover Page
  2. Title Page
  3. Dedication
  4. Preface
  5. Contents
  6. Chapter 1: Introduction
    1. 1.1 Computational modeling and visualization
    2. 1.2 The science and art of numerics
    3. 1.3 Fundamentals of programming and visualization
    4. 1.4 Exercises and Projects
    5. 1.A Floating point representation
    6. 1.B Python installation
    7. 1.C The Matplotlib plot function
    8. 1.D Basic NumPy array operations
  7. Chapter 2: Free fall and ordinary differential equations
    1. 2.1 Free fall with Euler’s method
    2. 2.2 The Runge-Kutta (RK) methods
    3. 2.3 System of first order ODEs
    4. 2.4 The leapfrog method
    5. 2.5 Exercises and Projects
    6. 2.A Area preservation of the leapfrog method
    7. 2.B Program listings and descriptions
  8. Chapter 3: Realistic projectile motion with air resistance
    1. 3.1 Visualization of ideal projectile motion
    2. 3.2 Modeling air resistance
    3. 3.3 Linear air resistance
    4. 3.4 The Lambert W function
    5. 3.5 Quadratic air resistance and spin
    6. 3.6 Physics of ball sports
    7. 3.7 Shooting methods
    8. 3.8 Exercises and Projects
    9. 3.A Bisection and Newton's root finders
    10. 3.B Program listings and descriptions
  9. Chapter 4: Planetary motion and few-body problems
    1. 4.1 Motion of a planet
    2. 4.2 Properties of planetary motion
    3. 4.3 Precession of Mercury
    4. 4.4 Star wobbles and exoplanets
    5. 4.5 Planar three-body problems
    6. 4.6 The restricted three-body problem
    7. 4.7 Exercises and Projects
    8. 4.A Rotating frames and rate of change of vectors
    9. 4.B Rotation matrices
    10. 4.C Radial velocity transformation
    11. 4.D Program listings and descriptions
  10. Chapter 5: Nonlinear dynamics and chaos
    1. 5.1 A first model: the logistic map
    2. 5.2 Chaos
    3. 5.3 A nonlinear driven oscillator
    4. 5.4 The Lorenz flow
    5. 5.5 Power spectrum and Fourier transform
    6. 5.6 Fractals
    7. 5.7 Exercises and Projects
    8. 5.A Program listings and descriptions
  11. Chapter 6: Oscillations and waves
    1. 6.1 A damped harmonic oscillator
    2. 6.2 Vibrations of triatomic molecules
    3. 6.3 Displacement of a string under a load
    4. 6.4 Point source and finite element method
    5. 6.5 Waves on a string
    6. 6.6 Standing waves
    7. 6.7 Waves on a membrane
    8. 6.8 A falling tablecloth toward equilibrium
    9. 6.9 Exercises and Projects
    10. 6.A Program listings and descriptions
  12. Chapter 7: Electromagnetic fields
    1. 7.1 The game of electric field hockey
    2. 7.2 Electric potentials and fields
    3. 7.3 Laplace equation and finite element method
    4. 7.4 Boundary value problems with FEM
    5. 7.5 Meshfree methods for potentials and fields
    6. 7.6 Visualization of electromagnetic fields
    7. 7.7 Exercises and Projects
    8. 7.A Program listings and descriptions
  13. Chapter 8: Time-dependent quantum mechanics
    1. 8.1 Time-dependent Schrödinger equation
    2. 8.2 Direct simulation
    3. 8.3 Free fall, the quantum way
    4. 8.4 Two-state systems and Rabi flopping
    5. 8.5 Quantum waves in 2D
    6. 8.6 Exercises and Projects
    7. 8.A Numerical integration
    8. 8.B Program listings and descriptions
  14. Chapter 9: Time-independent quantum mechanics
    1. 9.1 Bound states by shooting methods
    2. 9.2 Periodic potentials and energy bands
    3. 9.3 Eigenenergies by FDM and FEM methods
    4. 9.4 Basis expansion method
    5. 9.5 Central field potentials
    6. 9.6 Quantum dot
    7. 9.7 Exercises and Projects
    8. 9.A Numerov's method
    9. 9.B The linear potential and Airy function
    10. 9.C Program listings and descriptions
  15. Chapter 10: Simple random problems
    1. 10.1 Random numbers and radioactive decay
    2. 10.2 Random walk
    3. 10.3 Brownian motion
    4. 10.4 Potential energy by Monte Carlo integration
    5. 10.5 Exercises and Projects
    6. 10.A Statistical theory of Brownian motion
    7. 10.B Nonuniform distributions
    8. 10.C Program listings and descriptions
  16. Chapter 11: Thermal systems
    1. 11.1 Thermodynamics of equilibrium
    2. 11.2 The Ising model
    3. 11.3 Thermal relaxation by simulated annealing
    4. 11.4 Molecular dynamics
    5. 11.5 Exercises and Projects
    6. 11.A Boltzmann factor and entropy
    7. 11.B Exact solutions of the 2D Ising model
    8. 11.C Program listings and descriptions
  17. Chapter 12: Classical and quantum scattering
    1. 12.1 Scattering and cross sections
    2. 12.2 Rainbow and glory scattering
    3. 12.3 Quantum scattering amplitude
    4. 12.4 Partial waves
    5. 12.5 Exercises and Projects
    6. 12.A Derivation of the deflection function
    7. 12.B Partial wave analysis
    8. 12.C Program listings and descriptions
  18. List of programs
  19. Bibliography
  20. Index