Project Options

The project subject will be based on one of the chapters from the book:

Nicholas J. Giordano. Computational Physics. Prentice Hall, 1997.

The chapters of this book are as follows:

1. A first numerical problem
2.  Realistic projectile motion
   • Bicycle racing: the effect of air resistance
   • Projectile motion: the trajectory
   • Baseball: motion of a batted ball
   • Throwing a baseball: the effects of spin
   • Golf
3. Oscillatory motion and chaos
   • Simple harmonic motion
   • Chaos in the driven nonlinear pendulum
   • Routes to chaos: period doubling
   • The Lorenz model
   • the billiard problem
   • Bouncing balls: a chaotic mechanical system
   • Behavior in the frequency domain
4. The solar system
   • Kepler’s laws
   • The inverse-square law and the stability of planetary orbits
   • Precision of the perihelion of mercury
   • The three-body problem and the effect of Jupiter on Earth
   • Resonances in the solar system: kirkwood gaps and planetary rings
   • Chaotic tumbling of hyperlion
5. potentials and fields
   • Electric potentials and fields: Laplace’s equation
   • Potentials and fields near electric charges
   • Magnetic field produced by a current
   • Magnetic field of a solenoid: inside and out
6. Waves
   • Waves: the ideal case
   • Frequency spectrum of waves
   • Motion of a (somewhat) realistic string
   • Waves on a string (again): spectral methods
7. Random systems
   • Why perform simulations of random processes?
   • Generation of random numbers
   • introduction to Monte Carlo methods: integration
   • Random walks
   • self-avoiding walks
   • random walks and diffusion
   • Diffusion, Entropy and the arrow of time
   • Cluster growth modles
   • Fractal dimensions of curves
   • Percolation
8. Statistical mechanics, phase transitions, and the Ising model
   • The Ising model and statistical methods
   • Mean-Field Theory
   • The Monte Carlo method
   • The Ising model and the second-order phase transitions
   • First-order phase transitions
9. Molecular dynamics
   • Introduction to the method: properties of a dilute gas
   • The melting transition
10. Quantum Mechanics
    • Time-independent Schrodinger equation: some preliminaries
    • One dimension: shooting and matching methods
    • A variational approach
    • Time-Dependent Schrodinger equation: Direct solutions
    • Spectral methods
11. Interdisciplinary topics
    • Protein Folding
    • Earthquakes and self organised Critically
    • Neural networks and the brain