SPECIFIC
SUGGESTIONS FOR TERM PROJECTS
Italicized Blue Topics are
Pre-approved
BASIC TOPICS
- Simulation of the motion of
N interacting particles in three dimensions using finite
difference approximations (FDAs); a.k.a. "N-body
problem"
- Gravitational interactions
(positive mass only)
- General case; actual
simulations may involve motion in single plane
(2-D)
- 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
- 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
- Optics
- Ray tracing through series of lenses, prisms,
mirrors etc.
ADVANCED TOPICS (recommended only
for those with significant programming experience)
- 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
- Two dimensional
time-dependent Schrodinger equation
- Reference (pages
25-30 in particular) [PDF]
- Solution of
time-independent 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
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