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AbstractThe free vibration characteristics of functionally graded cylindrical shells under magnetic and temperature fields are investigated. According to Donnell’s theory, the kinetic energy, deformation energy, and their variational expressions are obtained. Based on the electromagnetic elasticity theory, the eddy current electromagnetic and magnetization force models are established. Using Hamilton’s principle, the magneto-thermo-elastic free vibration partial differential equations are derived. The modal frequency differential matrix equation with diverse boundary conditions is derived from the Galerkin integral technique. Through numerical examples, the curves and three-dimensional surface diagrams depicting the variations for the natural frequency with diverse parameters are obtained. The feasibility of the proposed solution method in this paper is supported by literature examples. The influence of magnetic induction intensity, temperature, power-law index, wave number, and shell dimension on the natural frequencies are determined. [ABSTRACT FROM AUTHOR]

To investigate the relationship between upper airway morphology and the severity of obstructive sleep apnea (OSA) in patients with anatomically small retruded mandibles. Fifty-two patients with small retruded mandibles underwent polysomnography and airway computed tomography. The airway morphology parameters and sleep assessment were compared between the patients with or without OSA. Twenty-eight patients diagnosed with OSA, according to polysomnography, had a higher distance between the hyoid bone and mandibular plane (HMP), lateral dimension (LAT)/anteroposterior dimension (AP), but lower minimum cross-sectional area (mCSA), AP, surface area, volume, avgCSA, and airway uniformity (U). The apnea-hypopnea index had negative correlations with mCSA, AP, surface area, volume, avgCSA, and U, and had a positive correlation with HMP and LAT/AP. OSA is common among patients with small retruded mandibles and is associated with a more compressed upper airway shape and longer HMP. [ABSTRACT FROM AUTHOR]

In this article, an exponential wave integrator sine pseudospectral method is formulated and analysed for discretizing the coupled Schrödinger–Boussinesq system. Our method is based on the utilizations of sine pseudospectral discretization for spatial derivatives followed by exponential wave integrator for temporal derivatives in phase space. The scheme is fully explicit and very efficient due to discrete sine transform (DST), and it is of spectral accuracy in space and second-order accuracy in time. Numerical analysis of the proposed method is carried out and rigorous error estimates are established via discrete energy and induction argument method. The numerical results are reported to verify our theoretical analysis. [ABSTRACT FROM AUTHOR]

In this study, we propose an efficient split-step compact finite difference (SSCFD) method for computing the coupled Gross–Pitaevskii (CGP) equations. The coupled equations are divided into two parts, nonlinear subproblems and linear ones. Commonly, the nonlinear subproblems could be integrated directly and accurately, but it fails when the time-dependent potential cannot be integrated exactly. In this case, the midpoint and trapezoidal rules are applied approximately. At the same time, the split order is not reduced. For the linear ones, compact finite difference cannot be designed directly. To circumvent this problem, a linear transformation is introduced to decouple the system, which can make the split-step method be used again. Additionally, the proposed SSCFD method also holds for the coupled nonlinear Schrödinger (CNLS) system with time-dependent potential. Finally, numerical experiments for CGP equations and CNLS equations are well simulated, conservative properties and convergence rates are demonstrated as well. It is shown from the numerical tests that the present method is efficient and reliable. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the convergence of explicit finite difference schemes which contain a Richardson scheme and a leap-frog scheme for computing the coupled Gross--Pitaevskii equations in high space dimensions. We establish the optimal error estimates of our schemes at the order of O(τ² + h²) in the l∞-norm with the time step τ and the mesh size h. Besides the standard techniques of the energy analysis method, the key techniques in the analysis is to use the method of induction argument and order reduction. The numerical results are reported to confirm our theoretical analysis for the numerical methods. [ABSTRACT FROM AUTHOR]

In this article, a decoupled and linearized compact difference scheme is investigated to solve the coupled Schrödinger-Boussinesq equations numerically. We establish the convergence rates for the error at the order of in the -norm with the time step τ and mesh size h. The linear scheme is proved to conserve the total energy which is defined as a recursion relationship. Due to the difficulty in obtaining the priori estimate from the discrete energy, we utilize cut-off function technique to prove the convergence. The numerical results are reported to verify the theoretical analysis, and the numerical comparison between our scheme with previous methods are conducted to show the efficiency of our scheme. [ABSTRACT FROM AUTHOR]

Phosphorus-containing montmorillonite (P-MMT) was successfully prepared via intercalating resorcinol bis(diphenyl phosphate) (RDP) into montmorillonite (MMT) layers, and was utilized as a synergistic agent in the polypropylene/melamine pyrophosphate/pentaerythritol (PP/MPP/PER) intumescent flame retardant (IFR) system. The synergistic effect of P-MMT and IFR was investigated by dynamic mechanical analysis (DMA), thermogravimetry (TG), limiting oxygen index (LOI), UL-94 test, cone calorimeter test (CCT), and scanning electron microscopy (SEM). It was found that P-MMT could significantly improve the thermostability and flame retardancy of the PP/IFR composite. When 2.0 wt% P-MMT replaced the same amount of IFR in the composite, both the onset decomposition temperature (T onset) and the maximum-rate decomposition temperature (T max) of the PP/IFR composite were increased by more than 14°C. Meanwhile, the LOI value was increased from 29.5% to 32.5%, the UL-94 rating was enhanced from V-1 to V-0, and the heat release rate (HRR), total heat release (THR), and mass lose rate (MLR) were decreased dramatically, which proved that P-MMT had a good synergistic effect with IFR in flame retardant PP. [ABSTRACT FROM PUBLISHER]

A novel intumescent flame retardant (IFR), using thermoplastic polyurethane (TPU) as a carrier resin to encapsulate melamine pyrophosphate/pentaerythritol (MPP/PER), was adopted to flame retard polypropylene (PP). The effects of TPU encapsulation on the mechanical properties, flame retardancy, thermal stability, and water-resistance of flame retardant PP were investigated. It was found that the dispersion of the IFR particles and the compatibility between the IFR and PP matrix were improved, which was responsible for the enhanced mechanical properties and flame retardancy of the flame retardant PP. Moreover, the incorporation of TPU could effectively prevent the esterification reaction between MPP and PER during the processing of flame retardant PP, and prevent the IFR from leaching out of the PP matrix. It thus remarkably improved the thermal stability and water-resistance of the IFR. Furthermore, PP/TPU-encapsulated IFR composite showed better charring performance than that of PP/MPP/PER. [ABSTRACT FROM PUBLISHER]

Four copper(II) complexes of N , N '-bis(4-methoxysalicylidene)-1,2-diimino ethanemonohydrate ( 1 ), N , N '-bis(5-methoxysalicylidene)-1,2-diiminoethane ( 2 ), N , N '-bis(3-methoxysalicylidene)-2,2-dimethyl-1,3-diiminopropane ( 3 ) and N , N '-bis(4-methoxysalicylidene)-2,2-dimethyl-1,3-diiminopropane ( 4 ) have been prepared and characterized spectroscopically. The solid-state structures of the complexes were established by X-ray crystallography. Complexes 2 , 3 and 4 contain Cu(II) in a tetrahedrally distorted square planar environment with two phenolate O atoms being deprotonated. Complex 1 is five-coordinate and displays color isomerism. [ABSTRACT FROM AUTHOR]