Optimal control problem of the uncertain second‐order circuit based on first hitting criteria

First hitting criteria of a system are to initially achieve some performance indeces of the target state set. This paper primarily investigates the optimal control problem of the uncertain second‐order circuit based on first hitting criteria. First, considering time efficiency and different from the ordinary expected utility criterion over an infinite time horizon, two first hitting criteria which are reliability index and reliable time criteria are innovatively proposed. Second, assuming the circuit output voltage as an uncertain variable when the historical data is lacking, we better model the real circuit system with the uncertain second‐order differential equation which is essentially the uncertain fractional‐order differential equation. Then, based on the first hitting time theorem of the uncertain fractional‐order differential equation, the distribution function of the first hitting time under the second‐order circuit system is proposed and the uncertain second‐order circuit optimal control model (reliability index and reliable time‐based model) is transformed into corresponding crisp optimal problem. Lastly, analytic expressions of the optimal control for the reliability index model are obtained. Meanwhile, sufficient condition and guidance for parameters for the optimal solution of the reliable time‐based model are derived, and corresponding numerical examples are also given to demonstrate the fluctuation of our optimal solution for different parameters.     

双势垒磁性隧道结中量子阱共振隧穿效应的第一性原理理论

磁性隧道结材料中自旋相关的量子阱态所导致的共振隧穿现象具有很重要的研究和应用价值，文章介绍了最近在Fe（001）／MgO／Fe／MgO／Fe双势垒磁性隧道结中存在的量子阱共振隧穿效应的理论研究工作，通过量子阱态的第一性原理的计算以及结合对中间Fe薄膜孤岛结构所导致Coulomb阻塞效应的分析，证实了最近Nozaki等人（Nozaki T et al．Phys．Rev．Lett．，2006，96：027208）实验中得到的振荡效应确实来源于中间Fe层多数自旋电子在Г点处形成的△1对称性的量子阱态．Coulomb阻塞效应的存在正是导致实验中低温下量子阱共振隧穿效应不够明显的主要原因．     

平面波经小圆环衍射轴上光强特性分析

从标量衍射理论出发,采用瑞利-索末菲衍射边界条件,通过求解第一类瑞利-索末菲衍射积分得到平面波经圆环衍射后轴上的波函数,进而分析轴上的光强特性以及光强极值数量、位置和大小与衍射圆环内外孔径的关系.比较用传统的光强定义和精确定义得到的光强公式的偏差,以及偏差与内外半径的关系.并将圆环衍射向内半径为零和外半径为无穷大两个方向进行推广,即对圆孔和圆形障碍物两种情况下的衍射情况进行讨论.     

MgO-decorated carbon nanotubes for CO2 adsorption: first principles calculations

The global greenhouse effect makes it urgent to deal with the increasing greenhouse gases.In this paper the performance of MgO-decorated carbon nanotubes for CO 2 adsorption is investigated through first principles calculations.The results show that the MgO-decorated carbon nanotubes can adsorb CO 2 well and are relatively insensitive to O 2 and N 2 at the same time.The binding energy arrives at 1.18 eV for the single-MgO-decorated carbon nanotube adsorbing one CO 2 molecule,while the corresponding values for O 2 and N 2 are 0.55 eV and 0.06 eV,respectively.In addition,multi-molecule adsorption is also proved to be very satisfactory.These results indicate that MgO-decorated carbon nanotubes have great potential applications in industrial and environmental processes.     

boldmath Broadband water window supercontinuum generation with a ω+3ω/2 multicycle two-colour pulse

We propose a method to generate a high-efficiency broadband water window supercontinuum with a ω+3ω/2 multicycle two-colour pulse. Our results reveal that the 3ω/2 laser pulse can simultaneously modulate the acceleration step and the ionization step, which not only broadens the bandwidth but also enhances the yield of the generated supercontinuum. An ultra-broadband supercontinuum from 290 eV to 555 eV covering the whole water window is generated. Using this method, we expect that an isolated 62-as pulse with a minor pre-pulse can be directly obtained.     

三维各向异性耦合谐振子哈密顿量的对角化

根据物理量的可测实在性,应用二次型理论,一般地解决了3个质量与3个频率均不相同、坐标和动量各自具有全耦合谐振子系统的哈密顿量的可对角化问题,并具体给出了哈密顿量对角化的标准形.     

Growth and characterization of L-phenylalanine nitric acid (LPN) and tris L-(phenylalanine)-phenylalanininum nitrate (TPLPN) as second and third order nonlinear optical materials

We synthesized noncentrosymmetric single crystals of L-phenylalanine nitrate (LPN) and tris L-(phenylalanine) L-phenylalaninium nitrate (TPLPN) by slow solvent evaporation technique. Both crystallized in monoclinic system with different acentric space groups namely P2₁ (LPN) and C2 (TPLPN) respectively. The IR and Raman spectral investigation was done for LPN and TPLPN and discussed. The UV-vis-studies accomplished the excitation wavelength of the grown crystals suitable to exhibit second harmonic generation signal. From the absorption data, remarkable optical properties such as direct band gap energy, Urbach energy, extinction coefficient were evaluated. The mechanical strength of the grown crystal was examined by Vickers micro hardness test. The temperature of decomposition was confirmed by TG/DSC analysis. Fluorescence emission spectrum of LPN and TPLPN were recorded and lifetime was also studied. The dielectric constant and dielectric loss of LPN and TPLPN has been determined as a function of frequency and temperature. Also the surface topologies of the crystallized salts were assessed by SEM studies. The third-order nonlinearities of LPN and TPLPN were determined by Z-scan technique with Nd: YAG at 532?nm and thereby from closed and open Z-scan data, third-order susceptibilities were calculated to be χ⁽³⁾?=?8.826?×?10^?6 esu for LPN and χ⁽³⁾?=?2.552?×?10^?7 esu for TPLPN.     

Mean first passage time of active Brownian particle in one dimension

We investigate the mean first passage time of an active Brownian particle in one dimension using numerical simulations. The activity in one dimension is modelled as a two state model; the particle moves with a constant propulsion strength but its orientation switches from one state to other as in a random telegraphic process. We study the influence of a finite resetting rate r on the mean first passage time to a fixed target of a single free active Brownian particle and map this result using an effective diffusion process. As in the case of a passive Brownian particle, we can find an optimal resetting rate r* for an active Brownian particle for which the target is found with the minimum average time. In the case of the presence of an external potential, we find good agreement between the theory and numerical simulations using an effective potential approach.     

Concentrated second‐harmonic generation from a single Al‐covered ZnS nanobelt

Here we report on the hybrid nanostructures where a single ZnS nanobelt was half‐covered with an aluminum (Al) film, which is an ideal platform for studying the second‐harmonic generation (SHG) enhancement effects of the Al coating. It was fabricated by the lift‐off process and allowed for the accurate comparison of the SHG intensity between the Al‐covered and the same bare ZnS nanobelt under consistent test conditions. The results indicate that the Al coating in the hybrid nanostructures not only confines the pumping laser in the ZnS effectively, but also concentrates the emitted SHG signal greatly, increasing the signal collection efficiency. By the combination of these two effects, ∼60 times enhancement of the SHG intensity is achieved at the optimized geometry size (width and thickness) of the ZnS nanobelts. The Al‐based hybrid nanostructures open up new possibilities for low‐cost, highly efficient and directional coherent nanolight sources at short wavelengths.

     

第一性原理对(NaP3)n(n=1～5)团簇的几何结构和性质的研究

本文采用第一性原理研究了(NaP3)n(n=1～5)团簇的几何结构、能隙、电荷分布以及态密度.研究结果表明: NaP3团簇为线型结构,是(NaP3)n(n=1～5)团簇中的基本单元,随着n增大,团簇转变为环状结构和空间结构,; (NaP3)3团簇的能隙出现峰值, 表明该团簇较其他团簇有较高的稳定性; (NaP3)3团簇中对于高能量区域的态密度是由Na 3s和P 3p轨道贡献,其中在费米附近的能量主要由P 3p轨道贡献, 对于低能量区域的态密度主要由Na 3s轨道贡献; (NaP3)n(n=1～5)团簇中的Na原子电荷分布均为正值, 表明电荷总体上是从Na原子转移到P原子.