Program
Introduction to Waves in Random Media
Student No.:20
Time:Mon & Thu, 9:50-11:25
Instructor:Jing Wenjia  
Place:Conference Room 2, Jin Chun Yuan West Bldg.
Starting Date:2018-3-5
Ending Date:2018-6-14

This course introduces the modeling and analysis of wave propagation phenomena in complex media. The precise knowledge of the media is not known and hence modeled as random. The goal is to derive large-scale behaviors of the propagated waves, in various regimes determined by the length scales involved (wave lengths, scale of media inhomogeneity and observation scale). The main emphasis will be given to the (rigorous) derivation of kinetic type equations for the “energy packets” of Schrodinger equations in random potentials. The course will be made as self-contained as possible and, hence, it includes some basic introduction to the probability modeling of complex media and some basic weak convergence theory of probability measures.

 


Prerequisite: Basic knowledge of PDEs, probability, and analysis

 

 

Reference:
[1] G. Bal, T. Komorowski and L. Ryzhik, “Kinetic limits for waves in a random media” (Review paper), Kinetic and Related Models, Vol.3 (2010), No.4, 529—644.


[2] L. Erdos and H.T. Yau, “Linear Boltzmann equation as the weak coupling limit of a random Schrodinger equation”, Comm. Pure Appl. Math. 53 (2000), 667—735.


[3] J.-P. Fouque, J. Garnier, G. Papanicolaou and K. Solna, “Wave propagations and time reversal in randomly layered media”, Springer Verlag, New York, 2007.


[4] L. Ryzhik, G. Papanicolaou and J.B. Keller, “Transport equations for elastic and other waves in random media”, Wave Motion, 24 (1996), 327-370