Love waves in layered flexoelectric structures

Abstract

In this paper, the flexoelectric effect on Love waves propagating in a structure with a nanoscale piezoelectric guiding layer deposited on an isotropic elastic substrate is analytically investigated. Transcendental complex dispersion equations are obtained and solved numerically which are corresponding to the electrically open and short conditions at the free surface. A detailed discussion about the dispersion relations of the fundamental mode is subsequently presented. The results indicate that flexoelectricity has a substantial effect on Love wave propagation. The presence of flexoelectricity leads to a complex phase velocity with a negative/positive imaginary part, which means Love waves attenuate/grow over time. In addition, the phase velocity dispersion relations depend greatly on the thickness and flexoelectric coefficients of the guiding layer. The current work is the first attempt to explore the flexoelectric effect on the propagation characteristics of surface acoustic waves (SAWs). And the results would be beneficial to achieve a better performance of SAW devices.     

Dissociation of dimethyl ether at high temperatures

The decomposition of dimethyl ether (CH₃OCH₃) has been investigated behind incident shock waves in a diaphragmless shock tube using laser schlieren densitometry, LS (T = 1500–2450 K, P = 57 ± 4, 125 ± 5 and 253 ± 12 Torr). The LS density gradient profiles were simulated and excellent agreement was found between the simulations and experimental profiles. Rate coefficients for CH₃OCH₃ → CH₃O + CH₃ were obtained. They showed strong fall-off, and at the lower end of the experimental temperature range are close to the low pressure limit. First order rate coefficient expressions were determined over 1500 < T < 2450 K. k_57Torr = (3.10 ± 1.0) × 10⁷⁹T^?19.03 exp(?54417/T) s^?1, k_125Torr = (1.12 ± 0.3) × 10⁸³T^?19.94 exp(?55554/T) s^?1and k_253Torr = (1.02 ± 0.3) × 10⁷³T^?17.09 exp(?51500/T) s^?1. The effect of a roaming channel for decomposition of dimethyl ether was assessed and the best agreement was obtained with 1% dissociation of DME via the roaming path.     

Effects of Soret diffusion on the laminar flame speed and Markstein length of syngas/air mixtures

The effects of Soret diffusion on premixed syngas/air flames at normal and elevated temperatures and pressures are investigated numerically including detailed chemistry and transport. The emphasis is placed on assessing and interpreting the influence of Soret diffusion on the unstretched and stretched laminar flame speed and Markstein length of syngas/air mixtures. The laminar flame speed and Markstein length are obtained by simulating the unstretched planar flame and positively-stretched spherical flame, respectively. The results indicate that at atmospheric pressure the laminar flame speed of syngas/air is mainly reduced by Soret diffusion of H radical while the influence of H₂ Soret diffusion is negligible. This is due to the facts that the main reaction zone and the Soret diffusion for H radical (H₂) are strongly (weakly) coupled, and that Soret diffusion reduces the H concentration in the reaction zone. Because of the enhancement in the Soret diffusion flux of H radical, the influence of Soret diffusion on the laminar burning flux increases with the initial temperature and pressure. Unlike the results at atmospheric pressure, at elevated pressures the laminar flame speed is shown to be affected by the Soret diffusion of H₂ as well as H radical. For stretched spherical flame, it is shown that the Soret diffusion of both H and H₂ should be included so that the stretched flame speed can be accurately predicted. Similar to the laminar flame speed, the Markstein length is also reduced by Soret diffusion. However, the reduction is found to be mainly caused by Soret diffusion of H₂ rather than that of H radical. Moreover, the influence of Soret diffusion on the Markstein length is demonstrated to decrease with the initial temperature and pressure.     

Flame propagation of nano/micron-sized aluminum particles and ice (ALICE) mixtures

Flame propagation of aluminum–ice (ALICE) mixtures is studied theoretically and experimentally. Both a mono distribution of nano aluminum particles and a bimodal distribution of nano- and micron-sized aluminum particles are considered over a pressure range of 1–10 MPa. A multi-zone theoretical framework is established to predict the burning rate and temperature distribution by solving the energy equation in each zone and matching the temperature and heat flux at the interfacial boundaries. The burning rates are measured experimentally by burning aluminum–ice strands in a constant-volume vessel. For stoichiometric ALICE mixtures with 80 nm particles, the burning rate shows a pressure dependence of r_b = aPⁿ, with an exponent of 0.33. If a portion of 80 nm particles is replaced with 5 and 20 μm particles, the burning rate is not significantly affected for a loading density up to 15–25% and decreases significantly beyond this value. The flame thickness of a bimodal-particle mixture is greater than its counterpart of a mono-dispersed particle mixture. The theoretical and experimental results support the hypothesis that the combustion of aluminum–ice mixtures is controlled by diffusion processes across the oxide layers of particles.     

pH‐sensing nanostar probe using surface‐enhanced Raman scattering (SERS): theoretical and experimental studies

Local pH environment has been considered to be a potential biomarker for tumor diagnosis because solid tumors contain highly acidic environments. A pH‐sensing nanoprobe based on surface‐enhanced Raman scattering (SERS) using nanostars under near‐infrared excitation has been developed for potential biomedical applications. To theoretically investigate the effect of protonation state on SERS spectra of p‐mercaptobenzoic acid (pMBA), we used the density functional theory (DFT) with the B3LYP functional to calculate Raman vibrational spectra of pMBA‐Au/Ag complex in both protonated and deprotonated states. Vibrational spectral bands were assigned with DFT calculation and used to investigate SERS spectral changes observed from experiment when varying pH value between five and nine. The SERS peak position of pMBA at ~1580 cm⁻¹ was identified to be a novel pH‐sensing index, which has small but noticeable downshift with pH increase. This phenomenon is confirmed and well‐explained with theoretical simulation. The study demonstrates that SERS is a sensitive tool to monitor minor structural changes due to local pH environment, and DFT calculations can be used to investigate Raman spectra changes associated with minor differences in molecular structure. Copyright © 2013 John Wiley & Sons, Ltd.     

Spin-Hamiltonian parameters,defect model and defect structure for the tetragonal Mo5+ center in x-ray-irradiated α-ZnMoO4 crystals

ABSTRACT

The spin-Hamiltonian parameters (g factors g_i, hyperfine structure constants A_i (⁹⁵Mo⁵⁺) and A_i (⁹⁷Mo⁵⁺), i?=?// and ⊥) assigned to the tetragonal Mo⁵⁺ (4d¹) tetrahedral center in α-ZnMoO₄ crystal caused by a Mo⁶⁺(1) ion trapping an electron after x-ray irradiation are calculated from the high-order perturbation formulas resting on the two-mechanism model. The model takes account of both the effects of crystal-field (CF) mechanism concerning the CF excited states in the CF theory and that of the charge-transfer (CT) mechanism related to CT excited states. The calculated results are reasonably consistent with the experimental values, confirming this assignment (or defect model). The calculations also indicate that the effect of CT mechanism cannot be neglected. The defect structure (particularly, the angular distortion) and signs of constants A_i (⁹⁵Mo⁵⁺) and A_i (⁹⁷Mo⁵⁺) of this Mo⁵⁺ defect center are also decided from the calculations. The outcomes are discussed.     

Near-Subconvexlikeness in Vector Optimization with Set-Valued Functions

A new class of generalized convex set-valued functions, termed nearly-subconvexlike functions, is introduced. This class is a generalization of cone-subconvexlike maps, nearly-convexlike set-valued functions, and preinvex set-valued functions. Properties for the nearly-subconvexlike functions are derived and a theorem of the alternative is proved. A Lagrangian multiplier theorem is established and two scalarization theorems are obtained for vector optimization.     

REMARKS ON THE LIFESPAN FOR THE SOLUTION TO NONLINEAR WAVE EQUATIONS IN THREE SPACE DIMENSIONS

The authors consider the Cauchy problem for the following nonlinear wave equationswhere x ∈ R3, t ≥ 0, ε > 0 is a small parameter, and obtain the sharp bounds for the lifespan of solution to (0.1). Specially, it is proved that there exist two constants C1 and C2, which are independent of ε, then the lifespan T(ε) satisfies the folowing inequalities     

On the Upper Bound of Second Eigenvalues for Uniformly Elliptic Operators of any Orders

Abstract Let Ω R~m(m≥1)be a bounded domain with piecewise smooth boundary Ω.Let t and r bepositive integers with t>r+1. We consider the eigenvalue problems(1.1)and(12),and obtain Theorem 1and Theorem 2, which generalize the results in[1,2.5].     

Enhanced accuracy by post-processing for finite element methods for hyperbolic equations

We consider the enhancement of accuracy, by means of a simple post-processing technique, for finite element approximations to transient hyperbolic equations. The post-processing is a convolution with a kernel whose support has measure of order one in the case of arbitrary unstructured meshes; if the mesh is locally translation invariant, the support of the kernel is a cube whose edges are of size of the order of only. For example, when polynomials of degree are used in the discontinuous Galerkin (DG) method, and the exact solution is globally smooth, the DG method is of order in the -norm, whereas the post-processed approximation is of order ; if the exact solution is in only, in which case no order of convergence is available for the DG method, the post-processed approximation converges with order in , where is a subdomain over which the exact solution is smooth. Numerical results displaying the sharpness of the estimates are presented.