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(Color) (a) Schematic of the hybrid design, (b) densities and (c) bulk moduli composing each TASL layer are given as a function of radius from the core’s center for a 10-layer lattice; high-density sub-layers are shown in blue, low-density sub-layers in green. Bar-height away from 1 indicates magnitudes normalized to water (ρw ,Bw ). Solid lines show the ideal material properties required for maximal scattering reduction based on Eq. (1), open circles give the value taken by each composite layer.
(Color) (a)-(f) Near field intensity maps calculated at k = π/rc showing scattering from an Al cylinder of radius rc with: (a) bare cylinder; (b) SC shell of thickness 0.1rc ; (c) 1/3 TASL with b = 2rc , layer thickness δ = 0.1rc , and total thickness 10δ; (d) 1/3 TASL with b = 2rc , layer thickness δ = 0.05rc , and total thickness 20δ; (e) hybrid method with SC shell thickness 0.1rc and 10δ TASL with δ = 0.11rc ; (f) hybrid method with SC shell thickness 0.05rc and 20δ TASL with δ = 0.0525rc . (g) and (h) Form factors F(k) vs wavenumber k demonstrate the operational bandwidths of the methods in panels (a)-(f); (g) 10-layer SL and (h) 20-layer SL. Form factors are normalized to the bare Al cylinder at its maximal scattering amplitude.
(Color) (a) and (b) Parameter space showing the frequency-averaged F(k) for (a) a bare SC shell, and (b) a 20δ-hybrid SC shell (10δ is similar), as a function of the normalized density ρ/ρw and bulk modulus B/Bw of the shell. The average is taken over wavenumbers k = [π/10rc , π/2δ]. The color map is a linear scale, normalized to the average F(k) for a bare Al cylinder. (c) Reduction in F(k) with respect to a bare Al cylinder calculated at each k for the methods shown in Fig. 2(h). The black line shows an alternate hybrid design using material parameters slightly off the minimum in panel(b).
Density ρ, bulk modulus B, and sound speed c listed for water, Al, and the SC shells used in the simulations.
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