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1.
《Wave Motion》2020
Acoustic properties of an additive-manufactured SiC scaffold with hexagonal symmetry fabricated by the robocasting method are studied both numerically and experimentally. The numerical analysis is based on the finite element method (FEM) using Bloch boundary conditions. The calculations show both angular and frequency dispersion of the acoustic waves with wavelengths comparable to the spacing between the rods, i.e., on a millimeter scale, indicating interesting acoustic properties in the MHz range. The dispersion character leads to focusing of the energy propagation into the directions of the rods of the hexagonal structure. This is illustrated by modal-based calculations of the propagation of longitudinal and out-of-plane shear wave packets with a dominant wavelength. The experimental analysis consists of two steps, the measurement of the resonant spectrum and shear wave propagation character. The measured resonant spectrum is in good agreement with the one calculated using numerically obtained low-frequency properties of the structure, also showing the quality of the overall manufactured structure. The time-domain measurement shows significant changes in the energy propagation between low and high frequencies, as predicted by FEM calculations. 相似文献
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This note is denoted to establishing sharp distortion theorems for subclasses of α-Bloch mappings defined in the unit ball of Cn with critical points.Furthermore,the estimates of Bloch constant with respect to these subclasses are given. 相似文献
4.
Radoslaw Kolkowski Justyna Szeszko Benjamin Dwir Eli Kapon Joseph Zyss 《Laser \u0026amp; Photonics Reviews》2016,10(2):287-298
Rectangular arrays of pyramidal recesses coated by silver film are investigated by means of polarization‐resolved nonlinear microscopy at 900 nm fundamental wavelength, demonstrating strong dependence of the dipole‐allowed SHG upon the lattice parameters. The plasmonic band gap causes nearly complete SHG suppression in arrays of 650 nm periodicity, whereas a sharp resonance at 550 nm periodicity is observed due to excitation of band edge Bloch states at fundamental frequency, accompanied by symmetry‐constrained interactions with similar modes at the second‐harmonic frequency. Additionally, coupling with modes at the bottom side of the silver film may lead to extraordinary optical transmission, opening a channel for SHG from the highly nonlinear GaAs substrate. Changing the lattice geometry enables SHG intensity modulation over three orders of magnitude, while the effective nonlinear anisotropy can be continuously switched between the two lattice directions, reaching values as high as ±0.96.
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K.S. Charak 《Journal of Mathematical Analysis and Applications》2009,353(1):43-48
We prove two normality criteria for a family of meromorphic functions satisfying a certain differential condition and provide a counterexample to the converse of the Bloch principle. 相似文献
7.
In this paper, we mainly study the (2+1)-dimensional Schrödinger–Maxwell–Blochequation (SMBE). We have constructed the generalized N-fold Darboux transformations (DT), and based on the plane wave solutions, the breather and rogue wave solutions are systematically generated, the dynamical features of those solutions are graphically represented. 相似文献
8.
MingSheng Liu 《中国科学A辑(英文版)》2009,52(1):87-93
The Bloch constants for quasiregular harmonic mappings and open planar harmonic mappings are considered. Better estimates
are obtained. The results, presented in this paper, improve the one made by Chen et al. and Grigoryan.
This work was supported by the Research Foundation for Doctor Programme (Grant No. 20050574002) and the National Natural Science
Foundation of China (Grant No. 10471048) 相似文献
9.
In this paper, we obtain a version of subordination lemma for hyperbolic disk relative to hyperbolic geometry on the unit disk D. This subordination lemma yields the distortion theorem for Bloch mappings f ∈ H(B^n) satisfying ||f||0 = 1 and det f'(0) = α ∈ (0, 1], where||f||0 = sup{(1 - |z|^2 )n+1/2n det(f'(z))[1/n : z ∈ B^n}. Here we establish the distortion theorem from a unified perspective and generalize some known results. This distortion theorem enables us to obtain a lower bound for the radius of the largest univalent ball in the image of f centered at f(0). When a = 1, the lower bound reduces to that of Bloch constant found by Liu. When n = 1, our distortion theorem coincides with that of Bonk, Minda and Yanagihara. 相似文献
10.
《Mathematische Nachrichten》2017,290(2-3):349-366
In this paper, we give a new characterization for the boundedness of weighted differentiation composition operator from logarithmic Bloch spaces to Bloch‐type spaces and calculate its essential norm in terms of the n‐th power of induced analytic self‐map on the unit disk. From which a sufficient and necessary condition of compactness of this operator follows immediately. 相似文献