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Department
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Richard E. Phillips Lecture Series
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George Papanicolaou
Department of Mathematics, Stanford University
The Phillips Lecture Series will be held April 20-24, 2009, with George Papanicolaou, distinguished professor from Stanford University, giving the lectures listed below. There will be a welcoming reception for Prof. Papanicolaou on Monday, April 20th from 5 to 7 p.m. in the Mathematics Library, D101 Wells. Finger food, beer and wine will be served. Please plan on attending the reception after the first lecture. Professor
Papanicolaou is a world leader in waves and diffusion in inhomogeneous or
random media and in the mathematical analysis of multi-scale phenomena that
arise in their study. Applications come from electromagnetic wave propagation
in the atmosphere, underwater sound, waves in the lithosphere, diffusion in
porous media, etc. He has made important contributions in both linear and
nonlinear waves and diffusion, in both direct and inverse problems. He is now
working on assessing multi-pathing effects in communication systems,
especially when time reversal arrays are used. Abstract: It is somewhat surprising at first that it is possible to locate a network of sensors from cross correlations of noise signals that they record. This is assuming that the speed of propagation in the ambient environment is known and that the noise sources are sufficiently diverse. If the sensor locations are known and the propagation speed is not known then it can be estimated from cross correlation information. Although a basic understanding of these possibilities had been available for some time, it is the success of recent applications in seismology that have revealed the great potential of correlation methods, passive sensors and the constructive use of ambient noise in imaging. I will introduce these ideas in an interdisciplinary, mathematically simplified way and show that a great deal can be done with them. 2. Imaging with noise II – Tuesday, April 21, 4:10-5 p.m., A304 Wells Hall [ Lecture Slides ] Abstract: Things become more complicated, and a mathematically more interesting, when the ambient medium is also strongly scattering. I will review what is known so far in this case, and discuss what might be expected. I will also discuss in more detail passive sensor imaging and its resolution theory. 3. Imaging with noise III – Thursday, April 23, 4:10-5 p.m., A304 Wells Hall [ Lecture Slides ] Abstract: I will extend the discussion of sensor location issues when there is strong scattering, especially issues that arise in the microwave regime in which we have real data available. I will conclude with the formulation of several open problems in passive sensor location and imaging. |
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For additional information:
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