Error estimates for the interpolating moving least-squares method in n-dimensional space

In this paper, the interpolating moving least-squares (IMLS) method is discussed in details. A simpler expression of the approximation function of the IMLS method is obtained. Compared with the moving least-squares (MLS) approximation, the shape function of the IMLS method satisfies the property of Kronecker δ function. Then the meshless method based on the IMLS method can overcome the difficulties of applying the essential boundary conditions. The error estimates of the approximation function and its first and second order derivatives of the IMLS method are presented in n-dimensional space. The theoretical results show that if the weight function is sufficiently smooth and the order of the polynomial basis functions is big enough, the approximation function and its partial derivatives are convergent to the exact values in terms of the maximum radius of the domains of influence of nodes. Then the interpolating element-free Galerkin (IEFG) method based on the IMLS method is presented for potential problems. The advantage of the IEFG method is that the essential boundary conditions can be applied directly and easily. For the purpose of demonstration, some selected numerical examples are given to prove the theories in this paper.     

Stochastic delay fractional evolution equations driven by fractional Brownian motion

In this paper, we consider a class of stochastic delay fractional evolution equations driven by fractional Brownian motion in a Hilbert space. Sufficient conditions for the existence and uniqueness of mild solutions are obtained. An application to the stochastic fractional heat equation is presented to illustrate the theory. Copyright © 2014 John Wiley & Sons, Ltd.     

On edge connectivity and parity factor

By Petersen's Theorem, a bridgeless cubic graph has a 2-factor. Fleischner(Discrete Math.,101, 33–37(1992)) has extended this result to bridgeless graphs of minimum degree at least three by showing that every such graph has an even factor without isolated vertices. Let me 0 be even and mo 0 be odd. In this paper, we prove that every m e-edge-connected graph with minimum degree at least me + 1 contains an even factor with minimum degree at least m e and every(m o + 1)-edge-connected graph contains an odd factor with minimum degree at least m o, which further extends Fleischner's result. Moreover, we show that our results are best possible.     

Ab initio studies of the structural,elastic, electronic and thermal properties of NiTi2 intermetallic

First principles calculations were performed in the framework of the density functional theory (DFT) using the Full Potential–Linear Augment Plane Wave method (FP–LAPW) within the generalized gradient approximation (GGA) to predict the structural, electronic, elastic and thermal properties of NiTi₂ intermetallic compound. By using the Wien2k all-electron code, calculations of the ground state and electronic properties such as lattice constants, bulk modulus, presure derivative of bulk modulus, total energies and density of states were also included. The elastic constants and mechanical properties such as Poisson’s ratio, Young’s modulus and shear modulus are estimated from the calculated elastic constants of the single crystal. Through the quasi-harmonic Debye model, the preasure and temperature dependences of the linear expansion coefficient, bulk modulus and heat capacity have been investigated. Finally, the Debye temperature has been estimated from the average sound velocity according to the predicted polycrystal bulk properties and from the single crystal elastic constants.     

Effect of Li2CO3 addition on the structural,optical, ferroelectric,and electric-field-induced strain of lead-free BNKT-based ceramics

In this work, we reported the effect of Li₂CO₃ addition on the structural, optical, ferroelectric properties and electric-field-induced strain of Bi_0.5(Na,K)_0.5TiO₃ (BNKT) solid solution with CaZrO₃ ceramics. Both rhombohedral and tetragonal structures were distorted after adding Lithium (Li). The band gap values decreased from 2.91 to 2.69 eV for 5 mol% Li-addition. The maximum polarization and remanent polarization decreased from 49.66 μC/cm² to 27.11 μC/cm² and from 22.93 μC/cm² to 5.35 μC/cm² for un-doped and 5 mol% Li- addition BNKT ceramics, respectively. The maximum S_max/E_max value was 567 pm/V at 2 mol% Li₂CO₃ access. We expected this work will help to understand the role of A-site dopant in lead-free ferroelectric BNKT materials.     

Silver-coated LiVPO4F composite with improved electrochemical performance as cathode material for lithium-ion batteries

Nano-structured LiVPO₄F/Ag composite cathode material has been successfully synthesized via a sol–gel route. The structural and physical properties, as well as the electrochemical performance of the material are compared with those of the pristine LiVPO₄F. X-ray diffraction (XRD) and scanning electron microscopy (SEM) reveal that Ag particles are uniformly dispersed on the surface of LiVPO₄F without destroying the crystal structure of the bulk material. An analysis of the electrochemical measurements show that the Ag-modified LiVPO₄F material exhibits high discharge capacity, good cycle performance (108.5 mAh g⁻¹ after 50th cycles at 0.1 C, 93% of initial discharge capacity) and excellent rate behavior (81.8 mAh g⁻¹ for initial discharge capacity at 5 C). The electrochemical impedance spectroscopy (EIS) results reveal that the adding of Ag decreases the charge-transfer resistance (R_ct) of LiVPO₄F cathode. This study demonstrates that Ag-coating is a promising way to improve the electrochemical performance of the pristine LiVPO₄F for lithium-ion batteries cathode material.     

利用自发布里渊散射测量液体声速

为了克服共振干涉法在液体的热力学声速和高频声速测量方面精度不高的问题, 本文建立了一种基于自发布里渊散射原理的测定液体声速的实验装置. 利用法布里-珀罗干涉仪对散射光进行扫描滤波, 数据采集卡结合光子计数器对散射光进行探测, 设计了一种散射光信息采集分析方法. 该实验方法有效的解决了传统布里渊散射方法中信号失真的问题, 显著地提升了液体声速测量精度. 对308.6–906.2 MHz内298.15 K饱和液相CCl₄声速进行了测量, 测量结果与文献值具有较好一致性. 利用法布里-珀罗干涉仪周期性扫描的滤波原理, 通过在测量得到的布里渊频移上加减整数倍个自由波谱区, 得到了更大频率的波谱信息, 进而设计一种测定介质高频声速的方法. 对CCl₄在5406.1–5521.0 MHz频段内的声速进行了测量. 实验结果显示, CCl₄的热力学声速随频率无明显变化, 而高频声速随频率的增大呈增大趋势且远大于热力学声速, 证实CCl₄具有色散现象.     

折射率正负梯度交替表面的研究

利用不均匀材料提出了一种折射率正负梯度交替表面, 并利用几何光学法和电磁场数值仿真方法对其机理进行了研究与验证, 发现其可以操控电磁波的传播: 在一定的参数下, 其可以将空间中的入射电磁波一直束缚在介质中, 或在介质中传播一定距离后再实现电磁波的释放; 同时该结构具有宽带、极化无关等特性. 利用该结构可引导能流, 减小后向散射截面, 可用作隐身表面.     

高能电子辐照绝缘厚样品的表面电位动态特性

采用数值计算和实验测量相结合的方法, 阐明了高能电子束照射下绝缘厚样品的表面电位和电子产额动态特性. 结果表明: 由于电子在样品内部的散射和输运, 沿着深度方向, 空间电位先缓慢下降到最小值, 然后逐渐升高并趋近于零; 随着电子束照射, 样品的表面电位逐渐下降, 可至负千伏量级, 电子总产额逐渐增大至一个接近于1的稳定值; 电子束停止照射后, 长时间放置下, 表面电位将逐渐升高, 但带电并不会消除; 表面电位随电子束能量的升高近似线性下降, 随入射角的增大而升高, 而随样品厚度的增大仅略有下降.