Hereditary optimal control problems: Numerical method based upon a padé approximation

In this paper, we consider a particular approximation scheme which can be used to solve hereditary optimal control problems. These problems are characterized by variables with a time-delayed argumentx(t – ). In our approximation scheme, we first replace the variable with an augmented statey(t) x(t - ). The two-sided Laplace transform ofy(t) is a product of the Laplace transform ofx(t) and an exponential factor. This factor is approximated by a first-order Padé approximation, and a differential relation fory(t) can be found. The transformed problem, without any time-delayed argument, can then be solved using a gradient algorithm in the usual way. Four problems are solved to illustrate the validity and usefulness of this technique.This research was supported in part by the National Aeronautics and Space Administration under NASA Grant NCC-2-106.     

The projection operator approach to the Fokker-Planck equation. II. Dichotomic and nonlinear Gaussian noise

Two models for the Freedericksz transition in a fluctuating magnetic field are considered: one is based on a dichotomic and the other on a nonlinear Gaussian noise. Both noises are characterized by a finite correlation time. It is shown that the linear response assumption leading to the best Fokker-Planck approximation in the dichotomic and nonlinear Gaussian cases can be trusted only up to the order ¹ and ⁰, respectively. The role of the corrections to the linear response approximation is discussed and it is shown how to replace the non-Fokker-Planck terms stemming from these corrections with equivalent terms of standard type. This technique is shown to produce perfect agreement with the exact analytical results (dichotomic noise) and to satisfactorily fit the results of analog simulation (nonlinear Gaussian noise).     

Stochastic modeling of a billiard in a gravitational field: Power law behavior of Lyapunov exponents

We consider the motion of a point particle (billiard) in a uniform gravitational field constrained to move in a symmetric wedge-shaped region. The billiard is reflected at the wedge boundary. The phase space of the system naturally divides itself into two regions in which the tangent maps are respectively parabolic and hyperbolic. It is known that the system is integrable for two values of the wedge half-angle ₁ and ₂ and chaotic for ₁<< ₂. We study the system at three levels of approximation: first, where the deterministic dynamics is replaced by a random evolution; second, where, in addition, the tangent map in each region is, replaced by its average; and third, where the tangent map is replaced by a single global average. We show that at all three levels the Lyapunov exponent exhibits power law behavior near ₁ and ₂ with exponents 1/2 and 1, respectively. We indicate the origin of the exponent 1, which has not been observed in unaccelerated billiards.     

非线性光学材料──水草酸铵

一水草酸铵（简称ＡＯＭ）是一种优良的电光晶体￣［１］。文献￣［１，２］报道了该晶体的晶体结构，化学式为（ＮＨ＿４）＿２Ｃ＿２Ｏ＿２·Ｈ＿２Ｏ，属正交晶系，Ｐ２２２空间群，晶胞参数ａ＝０．８０３５ｎｍ，ｂ＝１。０３１ｎｍ，ｃ＝０．３８０１ｎｍ，ｚ＝２。本文拟报道ＡＯＭ单晶生长，热化学分析，透过波段以及非线性光学性质的初步研究。     

Synthesis, Structure and Secondorder Nonlinear Optical Activities of a New Tungsten（0） Compound with Pyridine-2-thiolato Ligand, [Et4N][W（pyS）（CO）4] （pys = C5H4NS^-）

The reaction of W(CO)6 with pyOSNa (C5-H4NOSNa) and Et4NCl in MeCN affords a new tungsten(0) complex [Et4N][W(pyS)(CO)4] 1 (Mr.= 536.29).The crystal and molecular structures have been determined by X-ray single-crystal diffraction.Complex 1 crystallizes in the orthorhombic system,space group P212121 with a = 8.2429(5),b = 9.1045(4),c =26.8851(14) (A),β = 90.00°,V= 2017.66(18) (A)3,Z = 4,Dc.= 1.765 g/cm3,μ = 58.51 cm-1,F(000) =1048,the final R = 0.0204 and wR = 0.0400 for 4432 observed reflections with I ＞ 2σ(I).X-ray structure analysis revealed that the molecule is acentric and has large first-order hyperpolarizability (7.2 × 10-30 esu),so it could be an IR second-order nonlinear optical candidate material.     

一种主链含非线性光学活性基团聚合物的合成

把非线性光学(NLO)发色基团引入到聚合物主链中,既可以增大聚合物中NLO基团的含量,从而提高聚合物的宏观NLO系数,又能够提高NLO聚合物的极化稳定性。本文报道一种由酚酞环氧树脂(PPh)与对硝基苯胺(NA)得到的NLO聚合物的合成及其极化松弛。 所用酚酞环氧树脂系自制,环氧值0.427。对硝基苯胺北京化工厂产,分析纯。N,N-二甲基甲酰胺为中国医药公司售品,化学纯,用前减压蒸馏精制,乙醇、丙酮均为北京化工厂生产,分析纯。在氮气保护下将等当量的PPh与NA溶于DMF中于150℃反应6～8小时后,倒     

含吩噻嗪金属配合物的合成及非线性光学性质研究

本文报道了一种新的配体:10-乙基-3-甲酰吩噻嗪缩肼基二硫代甲酸甲酯(HL)及其金属配合物的合成。采用了元素分析、质谱、核磁共振、红外光谱对配体及其金属配合物进行了表征。此外,并应用紫外、荧光和Z-扫描技术,测定了配体及其金属配合物的荧光最佳发射波长(λ_max^em)、荧光量子产率(Φ_f)、寿命(τ)和非线性光学性质。结果表明它们在DMF溶液中都能发射出较强的橄榄色荧光,配体及其金属配合物都有双光子吸收,并且金属配合物的非线性光学效应比配体明显增强。用半经验量子化学方法(RHF/PM3)计算结果与实验值较为吻合。     

Tree-gel and loop-gel conversions in nonlinear polymerization

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Fabrication of ultrathin films with large third-order nonlinear optical properties.

An ultrathin composite film containing anionic Ag-His complexes (His: L-Histidine) and oppositely charged BH-PPV was fabricated by means of the electrostatic layer-by-layer self-assembly technique. UV/Vis spectra showed a continuous deposition process of Ag-His complexes and BH-PPV. The film structure was characterized by using small-angle X-ray diffraction, AFM, and SEM. The nonlinear optical properties of the ultrathin film were studied by using the Z-scan technique with a laser duration of 8 ns at a wavelength of 532 nm. The film sample exhibited a strong nonlinear saturated absorption, with an alpha2 value of -3.9 x 10(-5) mW(-1) and a self-defocusing effect with an n2 value of -4.78 x 10 (-12) m2W(-1).     

聚酰胺酸及其接枝衍生物的三阶非线性光学性能研究

设计合成了苯代三聚氰胺与均苯四酸二酐缩聚物, 及不同侧链的p-π共轭缩聚物, 并以量子化学PM3/CIS方法为基础, 利用完全态求和(SOS)公式, 对不同侧链取代的聚酰胺酸的分子进行了几何构型优化, 并计算了其三阶非线性光学系数γ. 研究了不同侧链对聚合物三阶非线性性能的影响. 这些结果对合成具有优良加工性能的三阶非线性光学材料是有一定的指导作用.