Browsing by Author "Gilbert, Robert P."
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Item Acoustic wave propagation in a composite of two different poroelastic materials with a very rough periodic interface: a homogenization approach(2002-10) Gilbert, Robert P.; Ou, Miao-jungHomogenization is used to analyze the system of Biot-type partial differential equations in a domain of two different poroelastic materials with a very rough periodic interface. It is shown that by using homogenization, such a rough interface can be replaced by an equivalent flat layer within which a system of modified differential equations holds. The coefficients of this new system of equations are certain ``effective'' parameters. These coefficients are determined by solutions of the auxiliary problems which involve the detailed structure of the interface. In this paper, the auxiliary problems are derived and the homogenized system of equations is given.Item An inverse problem for harmonic acoustics in stratified oceans(1991-03) Gilbert, Robert P.; Xu, YongzhiItem A numerical transmutation approach for underwater sound propagation(1991-12) Gilbert, Robert P.; Xu, YongzhiItem A uniqueness theorem of the 3-dimensional acoustic scattering problem in a shallow ocean with a fluid-like seabed(2001-07) Gilbert, Robert P.; Ou, Miao-jungThis paper shows that under the assumption of the out-going radiation conditions at infinity, the time-harmonic acoustic scattered field off a sound-soft solid in a shallow ocean with a fluid-like seabed is unique in C2 (M1) C2 < (M2) C(Rh3 \ ). Here M1 is the water part, M2 the seabed, Rh3 the waveguide and the solid object. The associated modal problem is studied and a representation formula for the solution in terms of the Green's function is derived.