F. Cakoni, B.B. Guzina, and S. Moskow (2016). “On the homogenization of a scalar scattering problem for highly oscillating anisotropic media”, SIAM J. Math. Anal., 48, 2532-2560. Article
Archive for year: 2016
University of Minnesota, Twin Cities campus
May 15−19, 2017
The 13th International Conference on Mathematical and Numerical Aspects of Wave Propagation will be held at the University of Minnesota. This biannual conference series is one of the main venues for dissemination of the latest advances in theoretical and computational modeling of wave phenomena, catering to the emerging problems in science and technology.
Conference Themes: Forward and Inverse Scattering, Fast Computational Techniques, Numerical Analysis, Domain Decomposition, Analytical & Asymptotic Methods, Nonlinear Wave Phenomena, Water Waves, Guided Waves and Random Media, Medical and Seismic Imaging, Homogenization of Wave Problems, Modeling Aspects in Photonics and Phononics, Mathematical Problems in Optics.
Organizers: Bojan Guzina and Stefano Gonella
Paul Barbone, Professor of Theoretical Acoustics & Applied Mechanics at Boston University, is visiting CEGE as MTS Visiting Professor in Geomechanics Nov. 1-7, 2106.
This work  illustrates the pursuit of a formal two-scale homogenization approach to extract the mean wave motion in bi-periodic solids, including the effect of incipient dispersion. We show that such low-frequency expansion leads to a family of fourth-order PDEs (resembling the phenomenological models of gradient elasticity) whose coefficients derive explicitly from the microstructure.
In this collaborative study  with Ralph Sinkus and Sverre Holm, we demonstrate by experiment and theory the ability of elastic waves to sense random microstructures that are three decades smaller in size than the probing wavelength. Our analysis deploys an extension of the O’Doherty-Anstey (ODA) theory and the fact that interparticle distances in random monosized distributions may exhibit fractal character.
In this investigation , we provide theoretical justification of an experimentally-observed ability  of the Topological Sensitivity (TS) indicator to localize near the boundary of a scatterer at high frequencies. The analysis revolves around the use of catastrophe theory and highlights the importance of source aperture in solving inverse scattering problems.