A trajectory-following method for unconstrained optimization

A trajectory-following method with interesting properties is considered for solving unconstrained nonlinear programming problems. The trajectory is defined by a special system of ordinary differential equations. This system uses only the gradient of the objective function. Numerical examples are given.The work of the second author was supported by the DFG Schwerpunkt Anwendungs-bezogene Optimierung and Steuerung.     

Determination of the optimal initial function and the parameters for nonlinear time-delay systems

This paper deals with dynamic systems described by nonlinear differential-difference equations of retarded type. The problem considered is to determine the initial function and certain system parameters which minimize a given cost functional. A computational method is presented and some convergence results are given. Numerical examples of linear and nonlinear systems are also included.     

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。     

Tree-gel and loop-gel conversions in nonlinear polymerization

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Crystal Structure of Dimethylamine 3,5-Dinitrobenzoic Acid Organic Adduct

1 INTRODUCTION Nonlinear optics (NLO) is at the forefront of cur- rent researches because of its importance in provi- ding the key functions of frequency shifting, optical modulation, optical switching, optical logic and op- tical memory for the emerging …     

Two-photon absorption in quadrupolar pi-conjugated molecules: influence of the nature of the conjugated bridge and the donor-acceptor separation

Quadrupolar-type substitution of pi-conjugated chromophores with donor and acceptor groups has been shown to increase their two-photon absorption (TPA) response by up to two orders of magnitude. Here, we apply highly correlated quantum-chemical calculations to evaluate the impact of the nature of conjugated bridge and the charge-transfer distance on that enhancement. We compare chromophores with phenylenevinylene-, thienylenevinylene-, polyene-, and indenofluorene-type backbones substituted by dimethylamino and cyano groups. In all compounds, we find a strongly TPA-active A(g) state (either 2A(g) or 3A(g)) in the low-energy region, as well as a higher lying TPA-active state (mA(g)) at close to twice the energy of the lowest lying one-photon allowed state; the smaller energy detuning in the mA(g) states results in very large TPA cross sections delta. We also investigate the influence of the degree of ground-state polarization on TPA. Independent of the nature of the backbone and the donor-acceptor separation, delta displays the same qualitative evolution with a maximum before the cyanine-like limit; the highest TPA cross sections are calculated for distirylbenzene- and polyene-based systems.     

Determination of molecular orientation distribution of a stable paramagnetic probe in oriented 4-cyano-4’-<Emphasis Type="Italic">n</Emphasis>-pentylbiphenyl

The molecular orientation distribution function of a stable radical 4-hydroxy-2,2,6,6-tetramethylpiperidine-1-oxyl in magnetic-field oriented 4-cyano-4’-n-pentylbiphenyl was determined from the angular dependence of the ESR spectra. The preferred molecular orientation of radical species in the liquid crystal matrix was determined. The temperature evolution of the orientation distribution function was studied.__________Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 1, pp. 190–195, January, 2005.     

Coherent anti-Stokes Raman Scattering Microscopy.

Coherent anti-Stokes Raman scattering (CARS) microscopy is presented as a new nonlinear optical technique. The combination of vibrational spectroscopy and microscopy allows highly sensitive investigations of unlabelled samples. CARS is an ideal tool for studying a broad variety of samples. The main drawback of the technique is its non-zero-background nature, which implies that the signal has to be detected against a nonresonant background. The need to solve this problem is reflected in the rapid technological developments that have been observed during the last decade. Recent results show that CARS microscopy has the potential to become an important complementary technique that can be used with other well-established microscopic methods. Although it has some limitations, it offers unique access to many problems that cannot be tackled with conventional techniques. For this reason, it can be expected that the impressive growth of the field will continue.     

2-苯基苯并咪唑衍生物非线性光学性质的从头算研究

采用HF／6-31G^*方法优化分子构型，在此基础上用CPHF方法系统地研究了多种基团取代的2-苯基苯并咪唑衍生物的二阶非线性光学系数βvec，并对βvdc的影响因素进行了探讨，为进一步设计综合性能优良的有机非线性光学材料提供理论指导．