UV-Vis Spectrum and the Third-order Nonlinear Optical Properties of the Chiral Camphorderived β-diketonate Platinum Complexes

UV-Vis spectrum and the third-order nonlinear optical properties of the chiral camphor-derived β-diketonate have been studied at the B3LYP/6-31G* level. The results showed that the introduction of electron-drawing group-CF3 and-C3F7 on β-diketonate made the strongest absorption peak red-shift and the lowest energy absorption blue-shied. Introduction of-OC2H5 on the benzene or pyridine ring made the lowest energy absorption blue-shift. When the-C2H3 was introduced on the benzene or pyridine ring, the lowest energy absorption was red-shifted. Introduction of electron-donating group on β-diketonate can enlarge their nonlinear optical properties. On the contrary, the introduction of electron-drawing group dropped it down.     

基于偶氮苯衍生物的三阶非线性光开关性能的调控

偶氮苯衍生物因其具有特殊的共轭体系常用作光开关特性的三阶非线性光学（NLO）开关材料,但有部分带有特殊基团的偶氮类分子在一般条件下无法显示其性能.然而,这类分子在被调节之后能展示出优异的光控的NLO开关性能.以无光控的NLO开关性能的5-（N-4-偶氮苯基）氨甲基间苯二甲酸为研究对象,并对其潜在的光控NLO开关性能进行调控.经过调节后的这类分子在光照条件下能顺利地经历可逆的顺反异构化反应,且产生三阶非线性性能的转换.其Z-扫描实验结果显示处于反式构型的材料展示出反饱和吸收和自散焦特性;在光照之后,这类材料转化为顺式构型并展现出饱和吸收和自聚焦行为.三阶NLO性能的转换是由于材料的结构发生转变其内部电子产生重排,使得它们在激光刺激下产生不同的响应机制.     

Tracking problem under a time-varying topology

This paper studies the multi-agent tracking problem of a third-order maneuvering target under uncertain communication environments. Each tracking agent is assumed to be a third-order system and can only use its own and neighbors＇ position, velocity, and acceleration information to design its control input. In this work, the uncertain communication environments are modelled by a finite number of constant Laplacian matrices together with their corresponding scheduling functions. Sufficient conditions for the existence of a tracking strategy have been expressed in terms of the solvability of linear matrix inequalities. Finally, a numerical example is employed to demonstrate the effectiveness of the proposed tracking strategy.     

三阶色散影响下二阶孤子间互作用及抑制

在色散位移光纤中，研究了三阶色散影响下同相和反相二阶孤子之间的互作用，分析了同相和反相二阶孤子对衰变后时域波形和频域频移的变化，发现三阶色散使二阶孤子分裂出一大一小两个不同振幅的基阶孤子，并彼此分离，但孤子对中心频率频移量却减小。通过采用非线性增益控制的方法可以有效抑制二阶孤子间的互作用，使孤子保型传输而不发生衰变。同时通过周期性改变三阶色散系数，可以减小三阶色散的不利影响，抑制孤子中心频率的频移，使孤子对不偏离原来时间槽，稳定孤子传输。     

Gaussian Limiting Behavior of the Rescaled Solution to the Linear Korteweg–de Vries Equation with Random Initial Conditions

We analyze the asymptotic behavior of the rescaled solution to the linear Korteweg–de Vries equation when the initial conditions are supposed to be random and weakly dependent. By means of the method of moments we prove the Gaussianity of the limiting process and we present its correlation function. The same technique is applied to the analysis of another third-order heat-type equation.     

Large near resonance third order nonlinearity in GaN

We have studied third order nonlinearities, including two-photon absorption coefficient and nonlinear refractive index n ₂, of GaN in below bandgap ultraviolet (UV) wavelength regime by using UV femtosecond pulses. Two-photon absorption was investigated by demonstrating femtosecond UV pulsewidth autocorrelation in a GaN thin film while femtosecond Z-scan measurements revealed information for both n ₂ and . The distribution of n ₂ versus wavelength was found to be consistent with a model described by the quadratic Stark effect, which is the dominant factor contributed to the nonlinear refractive index near the bandgap. Large on the order of 10 cm/GW and large negative n ₂ with a magnitude on the order of several 10^–12 cm²/W were obtained. The at near mid-gap infrared (IR) wavelength was also found to be on the order of several cm/GW by using two-photon-type autocorrelations in a GaN thin film. Taking advantage of the large two-photon absorption at mid-gap wavelengths, we have demonstrated excellent image quality on two-photon confocal microscopy, including two-photon-scanning-photoluminescence imaging and two-photon optical-beam-induced current microscopy, on a GaN Hall measurement sample and an InGaN green light emitting diode.     

A CSP and tabulation-based adaptive chemistry model

We demonstrate the feasibility of a new strategy for the construction of an adaptive chemistry model that is based on an explicit integrator stabilized by an approximation of the Computational Singular Perturbation (CSP)-slow-manifold projector. We examine the effectiveness and accuracy of this technique first using a model problem with variable stiffness. We assess the effect of using an approximation of the CSP-slow-manifold by either reusing the CSP vectors calculated in previous steps or from a pre-built tabulation. We find that while accuracy is preserved, the associated CPU cost was reduced substantially by this method. We used two ignition simulations – hydrogen–air and heptane–air mixtures – to demonstrate the feasibility of using the new method to handle realistic kinetic mechanisms. We test the effect of utilizing an approximation of the CSP-slow-manifold and find that its use preserves the order of the explicit integrator, produces no degradation in accuracy, and results in a scheme that is competitive with traditional implicit integration. Further analysis on the performance data demonstrates that the tabulation of the CSP-slow-manifold provides an increasing level of efficiency as the size of the mechanism increases. From the software engineering perspective, all the machinery developed is Common Component Architecture compliant, giving the software a distinct advantage in the ease of maintainability and flexibility in its utilization. Extension of this algorithm is underway to implement an automated tabulation of the CSP-slow-manifold for a detailed chemical kinetic system either off-line, or on-line with a reactive flow simulation code.     

三阶两点边值问题变号解的多重性

主要研究一类三阶两点边值问题变号解的存在性和多重性,利用不动点指数和拓扑度理论等得到了新的结论.     

一类三阶微分方程边值问题的单调迭代法

用单调迭代法研究一类三阶微分方程边值问题解的存在性,不仅证明了该问题解的存在性,而且得到了其迭代格式.