SPECIFIC SUGGESTIONS FOR TERM PROJECTS
- Non-linear dynamical systems
- Simple models for chaos using continuous equations
(ordinary differential equations (ODEs))
- Simple models for chaos using discrete equations
- Predator-prey models, and other biologically-motivated
systems
- Simulation of the motion of N
interacting particles in two dimensions using finite difference
approximations (FDAs)
- Gravitational
interactions (positive mass only)
- Electrostatic interactions (postive and negative charges)
- General potentials and types of "charge"
- Simple molecular dynamics calculations
- Simulation of the motion of N
interacting particles in three dimensions using finite difference
approximations (FDAs)
- Toomre model of galaxy collisions
- Equilibrium
configuration of N
identical charges on the surface of a sphere
- Simulation of simple
time-dependent partial differential equations (PDEs) using FDAs
- One or
two dimensional wave equations, possibly non-linear
- One or two dimensional diffusion equations, possible
non-linear
- One
dimensional time-dependent Schrodinger equation
- Solution of time-independent
partial differential equations (PDEs) using FDAs
- Two dimensional Laplace / Poisson equations
- Cellular
automata
- Neural Networks
- Simulation of simple neural network, including training
for specific task
- Genetic Algorithms
- Implementation of a basic genetic algorithm and
application to a test problem
- Particle Physics
- Simulation of basic features of a particle detector
including event generation and event reconstruction
- Optics
- Ray tracing through series of lenses, prisms, mirrors etc.
- Pedagogy
- Interactive demonstration of some physical process /
phenomena that allows user to experiment with parameters, initial
conditions etc.
- Stochastic (random)
processes
- Generalizations of diffusion limited aggregation
- Monte Carlo integration, with application to some
physical problem
- Simulated annealing, with application to some physical
problem
|