一种提高极值点处收敛精度的三阶WENO-Z格式

为了提高三阶WENO-Z格式在极值点处的计算精度，通过理论推导给出三阶WENO格式满足收敛精度的充分条件。采用泰勒级数展开的方式，推导给出所构造格式非线性权重的计算公式，并综合权衡计算精度和计算稳定性确定所构造格式的参数。通过两个典型的精度测试，验证了改进格式在光滑流场极值点区域逼近三阶精度。进一步选用激波与熵波相互作用和Richtmyer-Meshkov不稳定性等经典算例，证实了本文提出的改进格式WENO-PZ3相较其他格式（WENO-JS3和WENO-Z3）不仅具有较高的精度，而且降低了格式的耗散，提高了对流场结构的分辨率。     

Heterobimetallic Cluster-Based Coordination Polymers: Assembly,Structures and Third-Order Nonlinear Optical Properties

Reactions of (NH₄)₂WS₄ with CuCN, CuCN/1,2-bis(4-pyridyl)propane (bppa) or [Cu(MeCN)₄]PF₆/bppa under different reaction conditions afforded a set of two- or three-dimensional W/Cu/S cluster-based coordination polymers including {[Et₄N]₂[WS₄Cu₄(μ-CN)₂(μ-I)₂]}_n ( 1 ), [WS₄Cu₄(μ-CN)₂(bppa)₂]_n ( 2 ) and {[WS₄Cu₄(bppa)₄](PF₆)₂}_n ( 3 ), respectively. Compound 2 can be readily formed from reaction of 1 with bppa under solvothermal conditions. Compounds 1 and 2 feature two-dimensional networks with a “sql” topology, while 3 possesses a two-fold interpenetrated three-dimensional net with a rare “reo” topology. Compounds 1 – 3 in DMF exhibited different third-order nonlinear optical responses, and they all showed a reverse saturable absorption while 2 held a strong self-focusing effect.     

关于一类电-力振动模型的建模与分析

从电学、力学的基本原理出发,通过数学方法建立和分析了一种电-力振动模型。这是一种较复杂的电力混合作用的线性振动系统,由模型的特殊结构(类扬声器结构)作者确立了两种磁场,即感生磁场和外磁场两者正交独立,并规定了电学、力学两种不同物理量的坐标取向关系。该模型需要求得三阶正系数常微分方程的收敛解,再求得包含暂态、稳态项的完整解。另外,文章从能量和做功的角度,通过对电压电流间的相位差分析,对所建模型的正确性作了论证,同时也为这类建模引荐了一种论证手段。     

一个奇摄动微分方程非线性混合边值问题

研究了一个三阶半线性微分方程的奇摄动非线性混合边值问题.利用边界层函数法构造了该问题的形式渐近解,并采用微分不等式理论证明了解的存在性,给出了渐近解的误差估计,最后得出了边界层函数指数型衰减的结论.     

Peristaltic motion of a third-order fluid in a planar channel

In order to determine the characteristics of the peristaltic transport of shear thinning non-Newtonian materials, the motion of a third-order fluid in a planar channel having walls that are transversely displaced by an infinite, harmonic traveling wave of large wavelength and negligibly small Reynolds number was analyzed using a perturbation expansion in terms of a variant of the Deborah number. Within the range of validity of this analysis, we found the pumping rate of a shear-thinning fluid is less than that for a Newtonian fluid having a shear viscosity the same as the lower-limiting viscosity of the nonNewtonian material. Also, the space of variables for which trapping of a bolus of fluid occurs is reduced for the shear-thinning fluid investigated here.     

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.     

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.     

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.     

Conditional linearizability criteria for a system of third-order ordinary differential equations

We provide linearizability criteria for a class of systems of two third-order ordinary differential equations that is cubically nonlinear in the first derivative, by differentiating a system of second-order quadratically nonlinear ordinary differential equations and using the original system to replace the second derivatives. The procedure developed splits into two cases: those for which the coefficients are constant and those for which they are variables. Both cases are discussed and examples given.     

Novel mesophases in fluorine substituted banana-shaped mesogens

A new homologous series of achiral banana-shaped mesogens ('Dn') has been synthesized and studied by the classical techniques (optical microscopy, differential scanning calorimetry, X-ray diffraction, miscibility studies and electro-optic investigations). The short homologues (D6-D8) exhibit a two-dimensional phase 'B1_x' different from a B1 phase with a rectangular lattice. The longer homologues (D9-D14) present a mesophase which displays the defects of the B7 phase of the PIMB-NO₂ compounds. Nevertheless the D9-D14 mesophase is not miscible with the B7 phase, and contrary to B7, exhibits a bistable behaviour ('ferroelectric' type) suggesting at least a B7 variant.