Wave propagation in periodic media and dispersive effects

Add to your list(s) Download to your calendar using vCal

• Grégoire Allaire, Ecole Polytechnique
• Friday 27 March 2015, 15:00-16:00
• CMS, MR13.

If you have a question about this talk, please contact Harsha Hutridurga.

We study high frequency wave propagation in a periodic medium for times long enough so that dispersive effects are important. In other words, we consider the homogenization of the wave equation in a periodic medium for long times of the order of the inverse of the period, and for inital data that are Bloch wave packets, i.e. that are the product of a fast oscillating Bloch wave and of a smooth envelope function. We prove that the solution is approximately equal to two waves propagating in opposite directions at a large group velocity with envelope functions which obey a Schrodinger type equation. Our analysis extends the usual WKB approximation by adding a dispersive, or diffractive, effect due to the non uniformity of the group velocity which yields the dispersion tensor of the homogenized Schrodinger equation. This is a joint work with Mariapia Palombaro and Jeff Rauch.

This talk is part of the Partial Differential Equations seminar series.

This talk is included in these lists:

• All CMS events
• All Talks (aka the CURE list)
• CMS Events
• CMS, MR13
• DPMMS Lists
• DPMMS Pure Maths Seminar
• DPMMS info aggregator
• DPMMS lists
• Hanchen DaDaDash
• Interested Talks
• My seminars
• Partial Differential Equations seminar
• School of Physical Sciences
• bld31

Note that ex-directory lists are not shown.