SAMSI Program on Random Media

				19 T.W. Alexander Drive P.O. Box 14006 Research Triangle Park, NC 27709-4006 Tel: 919.685.9350 Fax: 919.685.9360 [email protected]
Programs Propose a Program Visitor Info
		2007-08 Program on Random Media Research Foci Time Reversal Interface Problems Imaging Problems Scattering Theory Porous Media Description of Activities Opening Workshop, Sept. 23-26, 2007 Course on Numerical Methods for Free Boundary and Moving Interface Problems Interface Problems Workshop, Nov. 15-16, 2007 Waves and Imaging Workshop, January 31-February 1, 2008 Transition Workshop, May 1-2, 2008 Working Groups Heterogeneity in Biological Materials Stochastic PDE Interface Problems Imaging Further Information Program Poster Introduction The field of random media is a classical one which is presently receiving widespread attention as new theory, approximation techniques, and computational capabilities are applied to emerging applications. Due to the breadth of the field, the inherent deterministic, stochastic and applied components have typically been investigated in isolation. However, it is increasingly recognized that these components are inexorably coupled and that synergistic investigations are necessary to provide significant fundamental and technological advances in the field. The SAMSI Program on Random Media will provide a forum to investigate statistical and deterministic components of random media for applications including, but not limited to, time reversal, interface problems, imaging in random media, and scattering theory for discontinuous media. Program Leaders: Russel Caflisch (UCLA), Maarten De Hoop (Purdue University; Chair), Rick Durrett (Cornell University -- National Advisory Committee Liaison), Weinan E (Princeton University), Josselin Garnier (Universite Paris VII), George Papanicolaou (Stanford University), Lenya Ryzhik (University of Chicago), Ralph Smith (SAMSI, Directorate Liaison), Chrysoula Tsogka (University of Chicago), Eric Vanden-Eijnden (NYU), Jack Xin (UC Irvine), Wojbor Woyczynski (Case Western Reserve University), Hongkai Zhao (UC Irvine) Research Foci The goal of the program is to bring together researchers investigating a variety of phenomena pertaining to random media. Although specific research directions will be determined by participants in the Opening Tutorial and Kickoff Workshop, potential foci may be drawn from the following topics. Time Reversal: The component on time reversal will build upon recent analysis and experimental observations that time reversal of waves propagating in disordered media permit refocusing. This somewhat unexpected property has profound ramifications in domains such as wireless communications, medical imaging, nondestructive evaluation, and underwater acoustics. Whereas the behavior of one-dimensional acoustic waves is mathematically and statistically understood, questions regarding multidimensional media remain widely open with the exception of the baraxial wave equation. Interface Problems: Interface problems arise in a diverse range of applications including multiphase flows and phase transitions in fluid mechanics, thin film and crystal growth simulations in material science, and mathematical biology problems modeled by partial differential equations involving moving fronts. In computational fluid dynamics, electromagnetic scattering and ground water flows, efficient numerical approximation are essential for quantifying the effective property of the medium due to fluctuating inhomogeneous and random medium. The level set method has proven to be an extremely versatile tool for tracking deformations in shape geometries, moving interfaces, and free boundaries in a number of related applications, and one facet of the program will focus on extensions of this approach to include the effects of random media and stochastic processes. Other aspects of the interface component will focus on modeling and analysis of random interface growth processes including crystal growth and solidification, Monte-Carlo Wiener-Chaos expansion and homogenization methods for stochastic partial differential equations, and level set methods and Lagrangian formulations (particle approaches) for random media simulations. Imaging Problems: Imaging problems in random media arise in a number of applications including biomedical imaging and seismic analysis. In the latter category, a detailed knowledge of earth medium heterogeneities is necessary for oil and gas recovery, earthquake and volcanic predictions, and environmental analysis. One fundamental issue involves the multiscale relation between large scale structures, which are considered as deterministic, and small scale heterogeneities which are considered to be random fluctuations form the deterministic structures. A related issue concerns the analysis of coupled processes. Scattering Theory: Whereas mathematical scattering theory for one-dimensional regimes is fairly mature, little of the analysis extends to multidimensional media with the exception of the baraxial wave equation. Hence this facet will focus primarily on the development of theory, numerical methods and validation techniques pertaining to scattering theory for multidimensional media. Porous Media: It is expected that at least one working group will focus on topics pertaining to stochastic transport processes and physics associated with porous media. Aspects of this research will interface with the other focus topics. Description of Activities Workshops: The Kickoff Workshop and Tutorial will be September 23-26, 2007. The principal goal of the workshop will be to engage a broadly representative segment of the applied mathematical, statistical, physical and engineering communities to determine research directions to be pursued by working groups during the program. There will also be numerous mid-program workshops organized by the working groups, and a Transition Workshop, at the end of the program, to disseminate program results and chart a path for future research in the area. Working Groups: The working groups meet regularly throughout the program to pursue particular research topics identified in the kickoff workshop (or subsequently chosen by the working group participants). The working groups consist of SAMSI visitors, postdoctoral fellows, graduate students, and local faculty and scientists. It is not necessary to be continually resident at SAMSI to maintain connection to the working groups. Further Information Additional information about the program and opportunities to participate in it is available: For research visits, including New Researcher Fellowships and SAMSI-University Fellowships, consult Visiting and Employment Opportunities for 2007-08. For postdoctoral appointments, consult Postdoctoral Positions for 2007-08. For other questions, send E-mail to [email protected].
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