Oscillation and non‐oscillation results for solutions of perturbed half‐linear equations

The purpose of this paper is to describe the oscillatory properties of second‐order Euler‐type half‐linear differential equations with perturbations in both terms. All but one perturbations in each term are considered to be given by finite sums of periodic continuous functions, while coefficients in the last perturbations are considered to be general continuous functions. Since the periodic behavior of the coefficients enables us to solve the oscillation and non‐oscillation of the considered equations, including the so‐called critical case, we determine the oscillatory properties of the equations with the last general perturbations. As the main result, we prove that the studied equations are conditionally oscillatory in the considered very general setting. The novelty of our results is illustrated by many examples, and we give concrete new corollaries as well. Note that the obtained results are new even in the case of linear equations.     

Novel low-dielectric constant and soluble polyimides from diamines containing fluorene and pyridine unit

Polyimides (PI's) with low-dielectric constant and excellent organic solubility have broad application prospects in the electronic field. Herein, this study designed a series of novel, low dielectric, organic soluble PI films by creatively introducing fluorene and pyridine ring into diamine monomers. Because of the noncoplanar structure of fluorenyl and the polarization of pyridine ring, PI films achieved a low-dielectric constant (2.22–3.09 at 10 MHz) and excellent organic solubility. Even in some organic solvents with low-boiling points, these PI films still exhibited outstanding solubility. In addition, all the films possessed high-tensile strength (≈120 MPa) and excellent optical transparency (>70%, 450 nm). It was worth noting that the glass transition temperature of films was all above 280°C and 5% weight loss temperature (T_5%) was at 486–553°C. In general, the novel high-performance low-dielectric PI films are expected to be used in the field of microelectronics.     

Optical and static dielectric study of a terminally fluorinated liquid crystalline compound

Optical and static dielectric studies on a terminally fluorinated liquid crystalline compound have been carried out. Measurements of temperature variation of refractive indices of the compound are done by using thin prism method. A four-parameter model is validated by fitting the experimentally measured values of refractive indices, birefringence and average refractive indices of the compound with the theoretical ones. Refractive index and density data are utilized for determination of orientational order parameter. The temperature variation of dielectric permittivities of the compound are measured by a LCR meter.     

光栅衍射实验中测量光栅常数的两种辅助方法

衍射光栅可以将不同波长的光在空间上分离开,在光谱分析领域中有广泛应用.利用光栅的衍射来测量光栅常数是大学物理实验中的一个典型实验,而本文介绍的正是光栅衍射实验中的两个有趣现象:一是旋转光栅时,谱线的偏转角存在一个最小值;二是光栅旋转到一定角度时,衍射光斑会逐渐消失在视野中.论文从理论上分析解释这两种现象,并设计出两种测量光栅常数的方法,在实验上进行验证.与传统的用最小偏转角测光栅常数的方法相比,本文重点分析了由判定最小偏转角位置偏差所带来的影响,并提出了对称旋转测量的方法来进一步减小误差.     

有耗介质层上多导体传输线的电磁耦合时域分析方法

目前,针对空间电磁场作用有耗介质层上传输线的电磁耦合,仍缺乏有效的数值分析方法.因此,本文提出一种高效的时域混合算法,很好地解决了有耗介质层上传输线电磁耦合建模难的问题.首先,对经典传输线方程进行改进,推导了适用于有耗介质层上多导体传输线电磁耦合分析的修正传输线方程.然后,结合时域有限差分方法和相应插值技术,求解修正传输线方程,获得多导线及其端接负载上的电压和电流响应,并实现空间电磁场辐射与多导线瞬态响应的同步计算.最后,通过相应计算实例的数值模拟,与CST软件的仿真结果进行对比,验证了时域混合算法的正确性和高效性.     

受限亚音速气流中倒置悬臂壁板静气弹稳定性的理论及实验研究

板壳结构在航空航天、高速列车、能量采集等诸多工程领域已经得到了广泛应用. 将悬臂壁板倒置于轴向气流中并在壁板周围流场中设置刚性壁面可有效地调控壁板的失稳速度, 是俘能器优化设计的重要措施之一. 但针对刚性壁面作用下亚音速气流中倒置悬臂壁板的失稳机制仍需要开展深入研究. 本文以受限亚音速气流中倒置的二维悬臂壁板为对象, 以理论分析及风洞实验为手段, 研究了单侧刚性壁面效应对倒置悬臂壁板静态失稳特性的影响规律. 在理论分析中, 首先应用镜像函数法来处理壁面约束条件, 基于算子理论研究获得了以Possio积分方程为表征的壁板气动力, 壁面效应实际表征为一包含移位Tricomi算子的复合算子; 然后将壁板失稳方程的求解问题转化为定区间上的函数逼近问题; 最后, 依据Wererstrass定理并利用最小二乘法求解该最优函数, 以获得系统的失稳临界参数. 在试验研究中依据压杆稳定原理设计了壁板静态失稳的测试方法并完成了风洞实验. 理论分析结果表明, 壁板会发生发散(静气动弹性)失稳, 临界动压随壁板与壁面间距的增加而增大并最终趋于稳定(无壁面情况); 通过理论与风洞实验结果的对比分析, 验证了本文气动力及理论分析的适用性及准确性. 针对倒置悬臂壁板结构的气动弹性失稳问题, 本文提出的方法不涉及系统方程的离散及特征值求解问题, 而是将其转化为了定区间上的函数逼近问题进行求解, 这为弹性结构静气动弹性失稳问题的研究提供了一个可行的新思路.      

Molecular dynamic study of dielectric polarization and ferroelectricity in a model polar polymer

Molecular dynamics simulations are used to explore the polarization response of a lamellar crystal consisting of folded chains of a highly simplified model polar polymer. The system is based on a united atom model of polyethylene with constrained bond lengths and bond angles, and it is endowed with artificial partial charges placed on the united atoms to give it a simple polar character. Simulations performed with various temperatures, electric field directions, and electric field application histories reveal a complicated sequence of reorientation processes, including pronounced ferroelectric behavior. The sequence includes a weak, temperature‐independent prompt response, and a slow‐rising delay regime with stretched exponential behavior and thermally‐activated reorientation parameters consistent with trans‐gauche (TG) barrier crossings in the amorphous phase. When the delay regime has progressed sufficiently, a primary large‐amplitude response due to organized rotation of large subsegments in the crystalline phase occurs in a rapid manner that requires relatively few TG barrier crossings. A final, extremely slow rise in residual polarization completes the sequence. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015 , 53, 740–759     

Crosslinkable high dielectric constant polymer dielectrics for low voltage organic field‐effect transistor memory devices

I n this study, we successfully synthesized water/methanol soluble random copolymers with a high dielectric constant, poly(n‐(hydroxymethyl) acrylamide‐co‐5‐(9‐(5‐(diethylamino)pentyl)?2‐(4‐vinylphenyl)?9H‐fluorene(P(NMA‐co‐F6NSt)), which contained chemical crosslinkable segment (NMA) and hole trapping building block (F6NSt). The feeding molar ratios of two monomers (NMA:F6NSt) were set as 100:0, 95:5, 80:20, and 67:33 for the copolymers of P1 , P2 , P3, and P4 , respectively. The crosslinked P(NMA‐co‐F6NSt) thin film could serve as both dielectric and charge storage layers in organic field‐effect transistor (OFET) memory device and exhibited high k (i.e., 4.91–6.47) characteristics, leading to a low voltage operation and a small power consumption. Devices based on the P1 ‐ P4 dielectrics showed excellent insulating properties and good charge storage performance under a low operating voltage in a range of ±5V because of tightly network structures and well‐dispersed trapping cites. In particular, P3 ‐based memory device exhibited a large memory window of 4.13 V with stable data retention stability over 10⁴ s, a large on/off ratio of 10⁴, and good endurance characteristics as high as 200 cycles. The above results suggested that a high‐performance OFET memory device could be facilely achieved using the novel crosslinkable high‐k copolymers. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2016 , 54, 3224–3236     

Where the rubber meets the hand: Unlocking the sensing potential of dielectric elastomers

Practice makes perfect to some extent. Research has shown that musicians who practice the piano for long periods of time can suffer a range of hand problems from loss of control to diminished speed. Now imagine a rubber keyboard that is springy, soft, and elastic. This is the new type of input device that dielectric elastomers (DE) can create. However their usage in large sensing systems is limited by a scalability challenge. Each DE sensor is married to a pair of connection cables and electronics, adding to the complexity of the background overheads. A new efficient multi‐frequency method is presented that is capable of detecting internal pressure changes from a difference in the DE's capacitance without the need for any additional wires or connections. This effectively segments the DE into smaller sections, achieving information from a single sensor equivalent to multiple sensors. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2016 , 54, 465–472     

Structural and Dielectric Properties of Polythiophene/Chrom(III) Acetylacetonate Composites

The dielectric and morphological properties of polythiophene (PT) filled with various mass fractions of chrom(III) acetylacetonate (Cr(acac)₃), synthesized via chemical oxidative polymerization, are described. Significant shifts of the absorption peak of the C-S bond in the Fourier transform infrared (FT-IR) spectra indicated that the metal cations mostly interacted with sulfur atoms. Thermal analyses performed by differential scanning calorimetry (DSC) indicated that the cold crystallization temperature (T_cc) of PT decreased with increasing doping level. Microstructural differences were observed between PT and its composites in scanning electron microscopy (SEM) images. Dielectric measurements showed that the conductivity of the PT significantly increased with increasing doping level, from ?10^?7 S/m to ?10^?4 S/m at 10 kHz and 300 K.