Fractals, Power Laws, Fractional PDEs

1
Fractals, Power Laws, Fractional PDEs

• A presentation each, about 30 min. to be given at
  the end of this module (probably 5.6.) You are
  assessed according to
• Clarity of Presentation (40)
• Depth of Presentation (30)
• Mastery of Topic (30)
• Difficulty of Topic (up to an additional 10)
• Select one of the following topics.
• Each topic requires you to research information
  from the library, internet, and/or myself. It is
  essential that you come and see me often. (Once
  this week and once with almost completed
  presentation is mandatory!) Make appointments by
  e-mail bbaeumer_at_maths.otago.ac.nz or just drop in
  Sci III, 213 (479-7763).

2
Clarity of Presentation

• The material was
• presented clearly
• incomprehensible
• The presentation was
• Professional (Timed well, sources clearly
  identified, Figures were legible, etc.)
• A comedy of errors

• The presentation was
• Exciting/gripping (I would pay to see it again)
• Boring (You couldnt pay me enough)
• I learned
• A lot
• Nothing
• The speaker seems to
• Understand the material
• Have no clue

3
Topics

• 0 Difficulty
• Fractals/Fractal dimensions/Self-similarity
• Fourier transform
• The Central Limit Theorem
• Power Laws

• 5 Difficulty
• Percolation
• Continuous Time Random Walks
• Brownian motion and diffusion with advection
• Fractional derivatives
• Fast Fourier Transform
• Fishers equation/ Reaction-Diffusion equation

• 10 Difficulty
• Stable laws and Levy motion
• Fractional Advection and Dispersion
• Operator Levy motion
• Fractional Fisher equation