PHY 256 Computational Physics

Semester: Spring
Credit Hours: 4
Prerequisite: PHY 141, 142, 143 or PHY 121, 122, 123

Introduction of numerical and computational methods, with special emphasis on their utilities and applications in contemporary physics topics.

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syllabus

I. Introduction to programming language
High level computer languages and execution; Editing, commands, debug, input, and output; Language codex; Program styles; Flow chart; Constant and variables; Input and output statements; Built-in functions; String handling; Decision structures; Loop structures; Arrays and matrices; Function and subroutines.

II. Numerical considerations
Choice of algorithm; Sources of numerical errors; Error, accuracy, and stability.

III. Ordinary differential equations (I)
Euler method; Comparison to exact solution; Effect of step size; Radiation decay; Realistic projectile motion; Effects of air drag, atmosphere density, velocity dependent of drag coefficient, wind, and spin.

IV. Ordinary differential equations (II)
Euler-Cromer method; Runge-Kutta method; Verlet method; Simple harmonic motion; Driven nonlinear pendulum; Chaotic behavior; Poincare plot; Feigenbaum parameter; Frequency plot with FFT.

V. Partial differential equations (I)
Jacobi method; Gauss-Seidel method; Aitken's method; Discussion of convergence; Simpson's rule; Difference equation for Laplace's equation; Electric field of capacitor in non-infinite-plate boundaries; Poisson's Equation; Electric field of a line charge in noncylindrical boundaries; Magnetic field of a current line or loop.

VI. Partial differential equations (II)
Waves and wave equation; Boundary conditions; Stability and step size; Frequency spectrum with FFT; Realistic string with damping and stiffness. Shooting method; Time independent Schrodinger equation; 1-D Schrödinger equation; 1-D potential well.

VII. Analysis of data
Relaxation method for f(x)=0; Newton's method for f(x)=0; Curve fitting; Spectral analysis; Normal modes.

VIII. Random numbers and evaluation
Generation of random numbers; Non-uniform distribution; Fluctuation and/or randomness; Random walks and diffusion; Diffusion equation; Comparison to analytical solution; Random walk and displacement.

IX. Growth and fractal
Cluster growth; Eden growth; Variation in growth conditions; Diffusion limited aggregation growth; Scaling of growth; Growth equation; Fractal and percolation; Koch curves; Fractal dimensionality; Percolation of 2-D lattice.

X. Monte Carlo method
Monte Carlo method; Ising model; Ferromagnetism; Phase transition of 2-D Ising model of a square lattice.

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