RESUMEN
Topological phases of matter have been extensively investigated in solid-state materials and classical wave systems with integer dimensions. However, topological states in non-integer dimensions remain almost unexplored. Fractals, being self-similar on different scales, are one of the intriguing complex geometries with non-integer dimensions. Here, we demonstrate fractal higher-order topological states with unprecedented emergent phenomena in a Sierpinski acoustic metamaterial. We uncover abundant topological edge and corner states in the acoustic metamaterial due to the fractal geometry. Interestingly, the numbers of the edge and corner states depend exponentially on the system size, and the leading exponent is the Hausdorff fractal dimension of the Sierpinski carpet. Furthermore, the results reveal the unconventional spectrum and rich wave patterns of the corner states with consistent simulations and experiments. This study thus unveils unconventional topological states in fractal geometry and may inspire future studies of topological phenomena in non-Euclidean geometries.
RESUMEN
Acoustic metamaterials are a class of artificially periodic structures with extraordinary elastic properties that cannot be easily found in naturally occurring materials and can be applied to regulate the sound propagation behavior. The fractal configuration can be widely found in the acoustic system, like characterizing the broadband or multi-band sound propagation. This work will engineer three-dimensional (3D) labyrinthine fractal acoustic metamaterials (LFAMs) to regulate the sound propagation on subwavelength scales. The dispersion relations of LFAMs are systematically analyzed by the Bloch theory and the finite element method (FEM). The multi-bands, acoustic modes, and isotropic properties characterize their acoustic wave properties in the low-frequency regime. The effective bulk modulus and mass density of the LFAMs are numerically calculated to explain the low-frequency bandgap behaviors in specific frequencies. The transmissions and pressure field distributions of 3D LFAMs have been used to measure the ability for sound suppression. Furthermore, when considering the thermo-viscous loss on the transmission properties, the high absorptions occur within the multi-band range for low-frequency sound. Hence, this research contributes to potential applications on 3D LFAMs for multi-bands blocking and/or absorption on deep-subwavelength scales.
RESUMEN
PURPOSE: The aim of this study was to investigate the optimal threshold for the functional lung (FL) definition of single-photon emission computed tomography (SPECT) lung perfusion imaging. PATIENTS AND METHODS: Forty consecutive stage III non-small-cell lung cancer patients underwent SPECT lung perfusion scans and PET/CT scans for treatment planning, and the images were coregistered. Total lung and perfusion lung volumes corresponding to 10, 20, , 60% of the maximum SPECT count were segmented automatically. The SPECT-weighted mean lung dose (SWMDx%) and the percentage of FL volume receiving more than 20 Gy (Fx%V20) of different thresholds were investigated using SPECT-weighted dose-volume histograms. Receiver-operator characteristic curves were used to identify SWMD and FV20 of different thresholds in predicting the incidence of radiation pneumonitis (RP). RESULTS: Eleven (27.5%) patients developed RP (grades 1, 2, 3, and 4 were 10.0, 7.5, 7.5, and 2.5%, respectively) after treatment. The largest area under the receiver-operator characteristic curve was 0.881 for the ability of SWMD to predict RP with 20% as the threshold and 0.928 for the ability of FV20 with 20% as the threshold. CONCLUSION: The SWMD20% and FV20 of FL using 20% of the maximum SPECT count as the threshold may be better predictors for the risk of RP.