book

Computational Modeling and Visualization of Physical Systems with Python

by Jay Wang

January 2016

Intermediate to advanced

492 pages

17h 34m

English

Wiley

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1.1 Computational modeling and visualization1.2 The science and art of numerics1.3 Fundamentals of programming and visualization1.4 Exercises and Projects1.A Floating point representation1.B Python installation1.C The Matplotlib plot function1.D Basic NumPy array operations
2.1 Free fall with Euler’s method2.2 The Runge-Kutta (RK) methods2.3 System of first order ODEs2.4 The leapfrog method2.5 Exercises and Projects2.A Area preservation of the leapfrog method2.B Program listings and descriptions
3.1 Visualization of ideal projectile motion3.2 Modeling air resistance3.3 Linear air resistance3.4 The Lambert W function3.5 Quadratic air resistance and spin3.6 Physics of ball sports3.7 Shooting methods3.8 Exercises and Projects3.A Bisection and Newton's root finders3.B Program listings and descriptions
4.1 Motion of a planet4.2 Properties of planetary motion4.3 Precession of Mercury4.4 Star wobbles and exoplanets4.5 Planar three-body problems4.6 The restricted three-body problem4.7 Exercises and Projects4.A Rotating frames and rate of change of vectors4.B Rotation matrices4.C Radial velocity transformation4.D Program listings and descriptions
5.1 A first model: the logistic map5.2 Chaos5.3 A nonlinear driven oscillator5.4 The Lorenz flow5.5 Power spectrum and Fourier transform5.6 Fractals5.7 Exercises and Projects5.A Program listings and descriptions

6.1 A damped harmonic oscillator6.2 Vibrations of triatomic molecules6.3 Displacement of a string under a load6.4 Point source and finite element method6.5 Waves on a string6.6 Standing waves6.7 Waves on a membrane6.8 A falling tablecloth toward equilibrium6.9 Exercises and Projects6.A Program listings and descriptions
7.1 The game of electric field hockey7.2 Electric potentials and fields7.3 Laplace equation and finite element method7.4 Boundary value problems with FEM7.5 Meshfree methods for potentials and fields7.6 Visualization of electromagnetic fields7.7 Exercises and Projects7.A Program listings and descriptions
8.1 Time-dependent Schrödinger equation8.2 Direct simulation8.3 Free fall, the quantum way8.4 Two-state systems and Rabi flopping8.5 Quantum waves in 2D8.6 Exercises and Projects8.A Numerical integration8.B Program listings and descriptions
9.1 Bound states by shooting methods9.2 Periodic potentials and energy bands9.3 Eigenenergies by FDM and FEM methods9.4 Basis expansion method9.5 Central field potentials9.6 Quantum dot9.7 Exercises and Projects9.A Numerov's method9.B The linear potential and Airy function9.C Program listings and descriptions
10.1 Random numbers and radioactive decay10.2 Random walk10.3 Brownian motion10.4 Potential energy by Monte Carlo integration10.5 Exercises and Projects10.A Statistical theory of Brownian motion10.B Nonuniform distributions10.C Program listings and descriptions
11.1 Thermodynamics of equilibrium11.2 The Ising model11.3 Thermal relaxation by simulated annealing11.4 Molecular dynamics11.5 Exercises and Projects11.A Boltzmann factor and entropy11.B Exact solutions of the 2D Ising model11.C Program listings and descriptions
12.1 Scattering and cross sections12.2 Rainbow and glory scattering12.3 Quantum scattering amplitude12.4 Partial waves12.5 Exercises and Projects12.A Derivation of the deflection function12.B Partial wave analysis12.C Program listings and descriptions

Content preview from Computational Modeling and Visualization of Physical Systems with Python

List of programs

We have built many programs in this book. The table below summarizes these programs and dependencies. Standard libraries such as Matplotlib (2D), NumPy, and SciPy are omitted. Library abbreviations are: fft – fast Fourier transform (fft.py, Chapter 5); fem – finite element method (fem.py, Chapter 9); fileio – file input/output (fileio.py, Chapter 9); itg – numerical integration (integral.py, Chapter 8); ode – ordinary differential equation (ode.py, Chapter 2); rtf – root finders (rootfinder.py, Chapter 3); and vpm – VPython Modules (vpm.py, Chapter 6). In addition, we also note the use of 3D and animation libraries: Axes3D – Matplotlib 3D plotting; am – Matplotlib animation; and vp – VPython.

Page numbers with the “S:” prefix are entries from the Digital Online Companion.

Program	Description	Dependence
3body, 206	Three-body motion	ode, rtf, vp
balltoss, 84	Ideal projectile motion	vp
baseball, 132	Flight of baseball	ode, vp
bdipole, 391	Magnetic dipole field	vp
bem, 522	Basis expansion method	itg
bisect, 130	Bisection root finder
boltzmann, 627	Boltzmann distribution
bouncing_ball, 40	Bouncing ball	vp
brownian, 559	Brownian motion	am
coupled, S:112	Quantum transitions	ode, vp, vpm
ctmc, S:263	Classical ion-atom collisions	ode, rtf. vp, vpm
deflect, 679	Deflection function	itg, rtf
dipole, 394	Dipole distribution	Axes3D
earth, 136	Planetary motion	ode, vp
edipole, 393	Electric dipole radiation	vp
eigh, 285	Eigenvalue problem ...