Physics 410: Computational Physics: Suggested Term Projects
Note that all term projects must be approved by the instructor.
Term project outlines are due Oct 15 and the projects
themselves are due Nov 28 (last class day). Contact the
instructor for more details concerning any of the topics listed
below.
Some on-line resources which may be useful sources for
term project ideas are listed HERE.
Charges on a Sphere
Simulate the dynamics of n identically charged particles confined
to move on the surface of the sphere. Incorporate dissipation
so that the charges eventually come to rest in an equilibrium
configuration. Determine and describe the equilibrium configuration(s)
for interesting values of n.
Students undertaking this project should find the following visualization software useful:
The Game of Life
Write a simulation of the Game of Life, a two-dimensional cellular
automaton.
Students undertaking this project should find the following visualization software useful:
Solitons
Solve a non-linear wave-equation which admits solitonic solutions
using finite-difference techniques. Study the propagation
of single solitons as well as the interaction of two or more
solitons. Reference: Solitons and Nonlinear Wave Equations:
Dodd, Eilbeck, Gibbon and Morris.
Students undertaking this project may find the following handouts useful:
- Solution of Nonlinear Systems using Newton's Method: Summary Notes: (PS)
- Problem handout (PS) from
PHY/CAM 381C (1997, UT Austin). The second problem
involves the solution of the KdV equation.
- Problem set 6 (PS) and key (PS)
from PHYS410 (2000).
This homework involves solution of non-linear systems of equations, question 2 is particularly
relevant.
- Problem set 5 (PS) and key (PS)
from PHYS410 (2000).
This homework involves treament of equations via finite difference techniques, question 3
on the solution of the wave equation is particularly relevant.
Students undertaking this project should find the following visualization software useful:
Schrodinger Equation
Write a program to solve the time-dependent Schrodinger equation
in one-space dimension for an arbitrary potential V(x). Some hints
for this project are available:
(PS)
or
(PDF).
Students undertaking this project should find the following visualization software useful:
Chaos
Simulate and study the behaviour of one or more low-dimensional systems
which exhibit chaos: examples include the Lorenz model or the billiard
problem.
The Rings of Saturn
Write a program to study the dynamics of a large number of test particles
in orbit about a massive body with one or more massive satellites.
Study the impact of various satellite properties (mass, orbital radius,
orbital eccentricity etc.) on the dynamics of the test particles.
Students undertaking this project should find the following visualization software useful:
Traffic Simulation using Cellular Automata
Use a cellular automata model to simulate multi-lane traffic
flow.
Moon Landing
Design and implement a simulation of a rocket ship with a main booster
and attitude control rockets. Implement an interactive interface
to allow a user to attempt to land the rocket ship on the surface
on a planet.
2D Ising Model
Write a Monte-Carlo algorithm to simulate the two-dimensional
Ising model with external parameters T (temperature) and H
(magnetic field). Use your algorithm to study the
phase-space structure of the model.
Investigate the nature of your results as a function of lattice
size.
Students undertaking this project should find the following visualization software useful:
Dissipative Gas Simulation
Simulate the dynamics of a collection of hard spheres which
dissipate some fraction of their kinetic energy when they
collide. Work in two-dimensions and determine typical long-term
behaviour of the system for a range of dissipation parameter.
Students undertaking this project should find the following visualization software useful:
Particle Physics Simulations
Reaction-Diffusion Equations
Toda Lattices
Neural Networks
Genetic Algorithms
Simulated Annealing
Pedagogical Java Applet
Design and implement an interactive Java applet which illustrates
and/or "demos" some physical principle or set-up of your choosing.
Quantum Computation
Write an essay on the rapidly evolving field of quantum computation.