Assignments

Homework:

Homework:

Semester Project Assignment:

The project assignment allows you to study a computational model in depth and apply the numerical algorithm and programming skills you have learned to write a non-trivial program from scratch.

Choose one of the following suggested projects:

1. The Three Body Problem: Explore order and chaos in the classical helium atom Project 4.3 and/or the restricted planar 3-body problem explored on Dr. Sethna's home page.
2. Choose one of the projects from Section 6.11. Good choices include:
   • Project 6.4: Lyapunov spectrum,
     • tobochnik.pdf: Jan Tobochnik and Harvey Gould, "Quantifying Chaos", Computers in Physics 3(6), 86 (1989)
     • Program listings from this article
   • Project 6.6: Stadium billiards,
     • Billiard Java Applets, by Dr. Victor Donnay et al., Bryn Mawr College
   • Project 6.8: Nonlinear ring laser cavity,
     • ikeda.pdf: K. Ikeda, H. Daido, and O. Akimoto, "Optical turbulence: chaotic behavior of transmitted light from a ring cavity", Phys. Rev. Lett. 45, 709 (1980)
     • hammel.pdf: S.M. Hammel, C.K.R.T. Jones, and J.V. Moloney, "Global dynamical behavior of the optical field in a ring cavity", J. Opt. Soc. Am. B2, 552 (1985)
   • Project 6.9: Chaotic scattering,
     • yalcinkaya.pdf: Tolga Yalcinkaya and Ying-Cheng Lai, "Chaotic Scattering", Computers in Physics 9, 511 (1985)
     • lau.pdf: Yun-Tung Lau, John M. Finn, and Edward Ott, "Fractal Dimension in Nonhyperbolic Chaotic Scattering", Phys. Rev. Lett. 66, 978 (1991)
   • Project 6.10: Chemical reactions.

Miscellaneous References:

• Classical and Quantum Chaos: A Cyclist Treatise , a Web Book by P. Cvitanovic et al.

To complete the project:

• read one or more of the original papers referenced in the textbook to get a deeper understanding of the theory,
• write your own program to simulate the model, and
• work most of the exercises suggested in the textbook.

The project is essentially open-ended. Depending on your interests and the time you have available you can choose to concentrate on the physics and study more original references, or to do extensive numerical analysis, or to concentrate on writing a fancy graphics program.

Deadlines:

• Project outline due Monday November 16: Your choice of project, references you will read, and exercises you would like to complete. This gives me a chance to give you some feedback and suggestions. (A brief one or two page outline is sufficient).
• Project report due Tuesday December 22, final exam day.

Maintained by: Dr. R.J. Gonsalves
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