SPECIFIC
SUGGESTIONS FOR TERM PROJECTS
Italicized Blue Topics are
Preapproved
BASIC TOPICS
 Simulation of the motion of
N interacting particles in three dimensions using finite
difference approximations (FDAs); a.k.a. "Nbody
problem"
 Gravitational interactions
(positive mass only)
 General case; actual
simulations may involve motion in single plane
(2D)
 Special/restricted case:
Toomre model of galaxy collisions
 Electrostatic interactions (postive and negative
charges)
 Equilibrium configuration
of N identical charges on the surface of a
sphere
 Cellular
automata
 Forest fires
 Traffic simulations
 Models for fluid mechanics
 Stochastic (random)
processes
 Diffusion limited
aggregation (and possibly generalizations thereof)
 Simple earthquake model
 Monte Carlo integration, with application to some
physical problem
 Simulated annealing, with application to some
physical problem
 Neural Networks
 Simulation of simple neural
network, including training for specific task
 Nonlinear dynamical
systems
 Simple models for chaos using continuous equations
(ordinary differential equations (ODEs))
 Simple models for chaos using discrete equations
 Predatorprey models, and other
biologicallymotivated systems
 Optics
 Ray tracing through series of lenses, prisms,
mirrors etc.
ADVANCED TOPICS (recommended only
for those with significant programming experience)
 Simulation of simple
timedependent partial differential equations (PDEs)
using FDAs
 One or two dimensional
wave equations, possibly nonlinear
 One or two dimensional diffusion equations, possible
nonlinear
 One dimensional
timedependent Schrodinger equation
 Two dimensional
timedependent Schrodinger equation
 Reference (pages
2530 in particular) [PDF]
 Solution of
timeindependent partial differential equations (PDEs)
using FDAs
 Two dimensional Laplace / Poisson equations
 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
 Pedagogy
 Interactive demonstration of some physical process /
phenomena that allows user to experiment with
parameters, initial conditions etc.
OTHER INFORMATION
