F. Cakoni, B.B. Guzina, and S. Moskow (2016). “On the homogenization of a transmission problem in scattering theory for highly oscillating media”, SIAM J. Math. Anal., in press.

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

Sound of a chessboard: homogenization of wave motion in periodic solids

This work [59] 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.

Multiply scattered waves sense fractal microscopic structures via dispersion

In this collaborative study [62] 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.

Why the high-frequency inverse scattering by topological sensitivity may work

In this investigation [61], we provide theoretical justification of an experimentally-observed ability [56] 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.