Transmission of Water Waves under Multiple Vertical Thin Plates

The transmission of water waves under vertical thin plates, e.g., offshore floating breakwaters, oscillating water column wave energy converters, and so on, is a crucial feature that dominates the hydrodynamic performance of marine devices. In this paper, the analytical solution to the transmission of water waves under multiple 2D vertical thin plates is firstly derived based on the linear potential theory. The influences of relevant parameters on the wave transmission are discussed, which include the number of plates, the draft of plates, the distance between plates and the water depth. The analytical results suggest that the transmission of progressive waves gradually weakens with the growth of the number and draft of plates, and under the conditions of given number and draft of plates, the distribution of plates has significant influence on the transmission of progressive waves. The results of this paper contribute to the understanding of the transmission of water waves under multiple vertical thin plates, as well as the suggestion on optimal design of complex marine devices, such as a floating breakwater with multiple plates

The structural, mechanical, electronic, optical and thermodynamic properties of t-X3_{3}As4_{4} (X == Si, Ge and Sn) by first-principles calculations

The structural, mechanical, electronic, optical and thermodynamic properties of the t-X$_{\mathrm{3}}$As$_{\mathrm{4}}$ (X $=$ Si, Ge and Sn) with tetragonal structure have been investigated by first principles calculations. Our calculated results show that these compounds are mechanically and dynamically stable. By the study of elastic anisotropy, it is found that the anisotropic of the t-Sn$_{\mathrm{3}}$As$_{\mathrm{4}}$ is stronger than that of t-Si$_{\mathrm{3}}$As$_{\mathrm{4}}$ and t-Ge$_{\mathrm{3}}$As$_{\mathrm{4}}$. The band structures and density of states show that the t-X$_{\mathrm{3}}$As$_{\mathrm{4}}$ (Si, Ge and Sn) are semiconductors with narrow band gaps. Based on the analyses of electron density difference, in t-X$_{\mathrm{3}}$As$_{\mathrm{4}}$ As atoms get electrons, X atoms lose electrons. The calculated static dielectric constants, $\varepsilon_{1} (0)$, are 15.5, 20.0 and 15.1 eV for t-X$_{\mathrm{3}}$As$_{\mathrm{4}}$ (X $=$ Si, Ge and Sn), respectively. The Dulong-Petit limit of t-X$_{\mathrm{3}}$As$_{\mathrm{4}}$ is about 10 J mol$^{\mathrm{-1}}$K$^{\mathrm{-1}}$. The thermodynamic stability successively decreases from t-Si$_{\mathrm{3}}$As$_{\mathrm{4}}$ to t-Ge$_{\mathrm{3}}$As$_{\mathrm{4}}$ to t-Sn$_{\mathrm{3}}$As$_{\mathrm{4}}$.Comment: 14 pages, 10 figures, 6 table