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• W810583080 abstract "We deal with the elastic scattering by a large number $M$ of rigid bodies, $D_m:=epsilon B_m+z_m$, of arbitrary shapes with $ 0<textcolor{black}{epsilon}<<1$ and with constant Lam'e coefficients $lambda$ and $mu$. We show that, when these rigid bodies are distributed arbitrarily (not necessarily periodically) in a bounded region $Omega$ of $mathbb{R}^3$ where their number is $M:=M(textcolor{black}{epsilon}):=O(textcolor{black}{epsilon}^{-1})$ and the minimum distance between them is $d:=d(textcolor{black}{epsilon})approx textcolor{black}{epsilon}^{t}$ with $t$ in some appropriate range, as $textcolor{black}{epsilon} rightarrow 0$, the generated far-field patterns approximate the far-field patterns generated by an equivalent medium given by $omega^2rho I_3-(K+1)mathbf{C}_0 $ where $rho$ is the density of the background medium (with $I_3$ as the unit matrix) and $(K+1)mathbf{C}_0$ is the shifting (and possibly variable) coefficient. This shifting coefficient is described by the two coefficients $K$ and $mathbf{C}_0$ (which have supports in $overline{Omega}$) modeling the local distribution of the small bodies and their geometries, respectively. In particular, if the distributed bodies have a uniform spherical shape then the equivalent medium is isotropic while for general shapes it might be anisotropic (i.e. $mathbf{C}_0$ might be a matrix). In addition, if the background density $rho$ is variable in $Omega$ and $rho =1$ in $mathbb{R}^3setminus{overline{Omega}}$, then if we remove from $Omega$ appropriately distributed small bodies then the equivalent medium will be equal to $omega^2 I_3$ in $mathbb{R}^3$, i.e. the obstacle $Omega$ characterized by $rho$ is approximately cloaked at the given and fixed frequency $omega$." @default.
• W810583080 created "2016-06-24" @default.
• W810583080 creator A5031058881 @default.
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• W810583080 date "2016-10-18" @default.
• W810583080 modified "2023-09-23" @default.
• W810583080 title "The equivalent medium for the elastic scattering by many small rigid bodies and applications" @default.
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• W810583080 doi "https://doi.org/10.1093/imamat/hxw042" @default.
• W810583080 hasPublicationYear "2016" @default.
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