Stochastic response of van der Pol oscillator with two kinds of fractional derivatives under Gaussian white noise excitation

This paper aims to investigate the stochastic response of the van der Pol(VDP) oscillator with two kinds of fractional derivatives under Gaussian white noise excitation.First,the fractional VDP oscillator is replaced by an equivalent VDP oscillator without fractional derivative terms by using the generalized harmonic balance technique.Then,the stochastic averaging method is applied to the equivalent VDP oscillator to obtain the analytical solution.Finally,the analytical solutions are validated by numerical results from the Monte Carlo simulation of the original fractional VDP oscillator.The numerical results not only demonstrate the accuracy of the proposed approach but also show that the fractional order,the fractional coefficient and the intensity of Gaussian white noise play important roles in the responses of the fractional VDP oscillator.An interesting phenomenon we found is that the effects of the fractional order of two kinds of fractional derivative items on the fractional stochastic systems are totally contrary.     

Accurate, high-order representation of complex three-dimensional surfaces via Fourier continuation analysis

We present a new method for construction of high-order parametrizations of surfaces: starting from point clouds, the method we propose can be used to produce full surface parametrizations (by sets of local charts, each one representing a large surface patch – which, typically, contains thousands of the points in the original point-cloud) for complex surfaces of scientific and engineering relevance. The proposed approach accurately renders both smooth and non-smooth portions of a surface: it yields super-algebraically convergent Fourier series approximations to a given surface up to and including all points of geometric singularity, such as corners, edges, conical points, etc. In view of their C^∞ smoothness (except at true geometric singularities) and their properties of high-order approximation, the surfaces produced by this method are suitable for use in conjunction with high-order numerical methods for boundary value problems in domains with complex boundaries, including PDE solvers, integral equation solvers, etc. Our approach is based on a very simple concept: use of Fourier analysis to continue smooth portions of a piecewise smooth function into new functions which, defined on larger domains, are both smooth and periodic. The “continuation functions” arising from a function f converge super-algebraically to f in its domain of definition as discretizations are refined. We demonstrate the capabilities of the proposed approach for a number of surfaces of engineering relevance.     

<Emphasis Type="Italic">p</Emphasis>-Nuclearity in a New Perspective

In this Letter we try to settle some confused points concerning the use of the notion of p-nuclearity in the mathematical and physical literature, pointing out that the nuclearity index in the physicists’ sense vanishes for any p> 1. Our discussion of these issues suggests a new perspective, in terms of ε-entropy and operator spaces, which might permit connections to be drawn between phase space criteria and quantum energy inequalities.Mathematics Subject Classification (2000): 81T05, 47B10, 47L25.     

An Efficient Numerical Model for Planar Spiral Inductor On-Chip

In this paper, a very useful numerical technique has been developed for analyzing the transient characteristics of a planar-spiral inductor on-chip. A locally conformal technique and an alternating-direction implicit scheme are applied to the finite-difference time-domain method. A formulation for solving three dimensional Maxwell’s equations is proposed. Using the proposed method, various parameters of the planar-spiral inductors have been analyzed and an equivalent circuit, which includes frequency-independent circuit elements, has been introduced. Highly computational efficiency is implemented. Numerical results show excellent agreement with the measured data over a wide frequency range.     

基于优化核极限学习机的风电功率时间序列预测

针对时间序列预测,在单隐层前馈神经网络的基础上,基于进化计算的优化策略,提出了一种优化的核极限学习机(optimized kernel extreme learning machine,O-KELM)方法.与极限学习机(extreme learning machine,ELM)方法相比,核极限学习机(kernel extreme learning machine,KELM)方法无须设定网络隐含层节点的数目,以核函数表示未知的隐含层非线性特征映射,通过正则化最小二乘算法计算网络的输出权值,它能以极快的学习速度获得良好的推广性.在KELM的基础上,分别将遗传算法、模拟退火、微分演化三种进化算法用于模型的结构输入选择、正则化系数以及核参数的优化选取,以进一步提高网络的性能.将O-KELM方法应用于标准Mackey-Glass混沌时间序列预测及某地区的风电功率时间序列预测实例中,在同等条件下,还与优化的极限学习机(optimized extreme learning machine,O-ELM)方法进行比较.实验结果表明,所提出的O-KELM方法在预测精度上优于O-ELM方法,表明了其有效性.     

A data-analysis method for identifying differential effects of time-delayed feedback forces and periodic driving forces in stochastic systems

In this work a method is developed for analyzing time series of periodically driven stochastic systems involving time-delayed feedback. The proposed data-analysis method yields dynamical models in terms of stochastic delay differential equations. On the basis of these dynamical models differential effects of driving forces and time-delayed feedback forces can be identified.     

Rapidly convergent series for high-accuracy calculation of the Voigt function

A rapidly convergent series, based on Fourier expansion of the exponential multiplier, is presented for highly accurate approximation of the Voigt function (VF). The corresponding algorithm enables the rapid calculation, required for its implementation as a subprogram in an interpolation approach. The numerical analysis of this VF approximation suggests that it may be more accurate than 10⁻⁹ in the Humlí?ek regions 3 and 4.     

Direct numerical simulation methods of hypersonic flat-plate boundary layer in thermally perfect gas

High-temperature effects alter the physical and transport properties of air such as vibrational excitation in a thermally perfect gas,and this factor should be considered in order to compute the flow field correctly.Herein,for the thermally perfect gas,a simple method of direct numerical simulation on flat-plat boundary layer is put forward,using the equivalent specific heat ratio instead of constant specific heat ratio in the N-S equations and flux splitting form of a calorically perfect gas.The results calculated by the new method are consistent with that by solving the N-S equations of a thermally perfect gas directly.The mean flow has the similarity,and consistent to the corresponding Blasius solution,which confirms that satisfactory results can be obtained basing on the Blasius solution as the mean flow directly in stability analysis.The amplitude growth curve of small disturbance is introduced at the inlet by using direct numerical simulation,which is consistent with that obtained by linear stability theory.It verified that the equation established and the simulation method is correct.     

高光谱成像仪等效焦面装调模组设计

高光谱成像仪CCD组件在装调时,纵向需要满足20 μm焦深要求,横向需要实现光谱维、空间维的对准。为了避免检测时对昂贵的CCD频繁安装、拆除,设计了一种等效焦面装调模组。等效模组按照CCD组件的实测尺寸精密制造,提供了可供显微镜观察的模拟光谱像。通过测量实际光谱像和模拟光谱像的位置差别能够获取修磨垫的修整量,并实现光谱像和CCD像元的横向对准。试验表明,存在工具显微镜测量误差、修磨垫加工误差、互换性误差时,光谱像面各处离焦量均小于焦深。试验中仅用3次迭代即达到MTF为0.3的要求,提高了装调效率和操作安全性。     

铁电液晶光寻址空间光调制器性能分析

针对氢化非晶硅/铝/铁电液晶结构的光寻址空间光调制器（OASLM）,依据其等效电路模型,利用Pspice和Matlab软件对其分辨率、响应速度、对比度及灰度响应等性能进行了分析。结果表明:在铁电液晶（FLC）层厚度一定的情况下,减小光敏感层（a-Si:H层）的厚度可以提高FLC-OASLM的调制传递函数,从而提高分辨率;在其他参量一定的情况下,FLC-OASLM的响应速度随写入光光强增大而增大（写入光从0.08 mW/cm2增大到10 mW/cm2,延迟时间减小110 s,上升时间减小154 s）,随擦除光光强增大而减小（擦除光从0增大到1 mW/cm2,延迟时间增大41 s,上升时间仅增加3 s）;FLC-OASLM的对比度随控制光光强增大而增大,最终趋于一个稳定值21∶1;在其他参量不变时,随着擦除光光强的增大,输出光响应呈现等级下降,且发现当擦除光光强达到一定值（3 mW/cm2）后,擦除光的改变主要影响下降时间而对上升时间几乎无影响;合理设计激励源信号波形,可以得到超过十级灰度输出,表明擦除光具有实现FLC OASLM的灰度响应的功能。