E6901 Handout

Handout for APMA E6901 - Fall 2005

World Wide Web: http://www.columbia.edu/~gb2030

Instructor: Guillaume Bal

  • Office: Mudd 206
  • Office Hours: by appointment
  • Office Phone: (212) 854 4731
  • e-mail: gb2030@columbia.edu
  • Class meeting: Th 12:45-2:45 Mudd 214.


    The first class will be held on Th. September 15th.

    Course Structure:

    The objective of this course is to derive macroscopic models for the energy density of high frequency waves propagating in heterogeneous media. Low frequency waves in heterogeneous (i.e. highly oscillatory) media are treated with homogenization techniques. High frequency waves in slowly varying media (low frequency media) are treated by geometrical optics. High frequency waves in high frequency media are a lot harder to model because of the multiple interactions of the waves with the underlying structure. In the so-called weak coupling regime, we'll see how to derive radiative transfer equations for the phase-space energy density of the waves. One of the main tools in such a derivation will be the Wigner transform, which will be analyzed in detail. The course will be fairly mathematical as it will involve classical tools in analysis and probability theory. However I plan to insist on the physical processes involved (and the various wave interactions with the underlying medium at different scales), which should appeal to a broader physical and engineering audience.


    Here is a (very) tentative Syllabus:


    I will try to provide a set of lecture notes. Here are useful bibliographical references, which I encourage you to read as soon as you can. All the papers I have contributed to are on my webpage http://www.columbia.edu/~gb2030/pubs.html.