1. Term projects

2. 1. A jumping ping-pong ball

3. 2. A pendulum with vibrating pivot
Ref: Chaotic and fractal dynamics, by Francis Moon

4. 3. A rocking boat
Ref: Chaotic and fractal dynamics, by Francis Moon

5. 4. A spinning top with precession and nutation
Ref: Classical dynamics of particles and systems, by Jerry Marion
Chaotic and fractal dynamics (Sec 8.2), by Francis Moon

6. 5. Random deposition (with relaxation)
Ref: Fractal concepts in surface growth,
by Barabasi and Stanley

7. 6. Diffusion-limited aggregation
Ref: Fractal concepts in surface growth (chap 17), by Barabasi and Stanley

8. Guidelines for projects 2,3,4
1. Study the motions for different initial conditions and parameters
How do they change the solutions x(t) and phase space trajectories.
When does the chaos begin?
2. For chaotic motion, study the distribution of dots (discrete-time
sampling, ie. v(nT) v.s. x(nT)) in phase space.
3. Plot the dots in 2 for various initial conditions.
Combine the figures to make an animation.
4. Add some dissipation and see how the result changes.
Repeat the steps 2 and 3 above for the dissipative system.
5. Use POV-RAY to produce some beautiful animations for the
real physical systems.
Steps:
Literature search, theoretical analysis, run the program, produce the
figures (make sure the results are correct), make animations,
oral presentation.

9. 1. Statistical analysis of the result: for example, how do
Projects 5 and 6:
1. Statistical analysis of the result: for example, how do
the roughness (project 5) or the numbers of islands (project 6)
change with time?
2. Simulate several different growth conditions by
changing number of particles, deposition rate… etc
3. Consider changing the rules of deposition and
study its influence on the growth process.
4. Make animations of the various growth processes
Steps:
Literature search, theoretical analysis, run the program, produce the
figures (make sure the results are correct), make animations,
oral presentation.