Statistical Properties of Stimulated Raman Scattering in a Nonlinear Regime

Statistical properties of the Raman scattering of an intense step pulse are investigated by numerical solution of the equations of a semi-classical theory with assignment of a random Gaussian distribution of the initial polarization over the sample. The probability density functions of the intensity, energy, delay time, and width of a Stokes pulse and also of the position, height, and width of the spectral peaks of the first incidental Stokes component with the preservation of the phase memory of scattering centers are calculated. The influence of collisional dephasing on the fluctuation of these characteristics is considered.     

On the numerical determination of optimal inputs

The design of optimal inputs for linear and nonlinear system identification involves the maximization of a quadratic performance index subject to an input energy constraint. In the classical approach, a Lagrange multiplier is introduced whose value is an unknown constant. In recent papers, the Lagrange multiplier has been determined by plotting a curve of the Lagrange multiplier as a function of the critical interval length or a curve of input energy versus the interval length. A new approach is presented in this paper in which the Lagrange multiplier is introduced as a state variable and evaluated simultaneously with the optimal input. Numerical results are given for both a linear and a nonlinear dynamic system.     

Statistical mechanics of money: how saving propensity affects its distribution

We consider a simple model of a closed economic system where the total money is conserved and the number of economic agents is fixed. Analogous to statistical systems in equilibrium, money and the average money per economic agent are equivalent to energy and temperature, respectively. We investigate the effect of the saving propensity of the agents on the stationary or equilibrium probability distribution of money. When the agents do not save, the equilibrium money distribution becomes the usual Gibb's distribution, characteristic of non-interacting agents. However with saving, even for individual self-interest, the dynamics becomes cooperative and the resulting asymmetric Gaussian-like stationary distribution acquires global ordering properties. Intriguing singularities are observed in the stationary money distribution in the market, as functions of the marginal saving propensity of the agents. Received 2 May 2000     

绿光抽运准周期光学超晶格产生红光与蓝光的研究

使用一块准周期LiTaO3光学超晶格晶体,利用准相位匹配技术,通过光参变产生与和频两个非线性过程,将一束532nm绿色抽运光转变成666nm红光与443nm蓝光。具体过程为,通过参变过程获得红色信号光和红外闲频光,再通过绿色抽运光与红外闲置光和频获得蓝光,两个过程在同一块准周期光学超晶格中实现,准周期超晶格的两个倒易矢量分别补偿这两个过程中的相位失配。抽运光的脉宽为40ps,重复频率为10Hz,在平均功率为0．5mW时,测得红光和蓝光功率分别0．15mW和16．6μW,转换效率达到34％和3％。这一方法,提供了一种用一块超晶格晶体同时获得三原色输出的有效途径。     

Conditional Symmetries and Solutions to a Class of Nonlinear Diffusion-Convection Equations

The present paper discusses a class of nonlinear diffusion-convection equations with source. The method that we use is the conditional symmetry method. It is shown that the equation admits certain conditional symmetries for coefficient functions of the equations. As a consequence, solutions to the resulting equations are obtained.     

Nonlinear corrector for Reynolds-averaged Navier-Stokes equations

The scope of this paper is to present a nonlinear error estimation and correction for Navier-Stokes and Reynolds-averaged Navier-Stokes equations. This nonlinear corrector enables better solution or functional output predictions at fixed mesh complexity and can be considered in a mesh adaptation process. After solving the problem at hand, a corrected solution is obtained by solving again the problem with an added source term. This source term is deduced from the evaluation of the residual of the numerical solution interpolated on the h/2 mesh. To avoid the generation of the h/2 mesh (which is prohibitive for realistic applications), the residual at each vertex is computed by local refinement only in the neighborhood of the considered vertex. One of the main feature of this approach is that it automatically takes into account all the properties of the considered numerical method. The numerical examples point out that it successfully improves solution predictions and yields a sharp estimate of the numerical error. Moreover, we demonstrate the superiority of the nonlinear corrector with respect to linear corrector that can be found in the literature.     

L1-type smoothness indicators based weighted essentially nonoscillatory scheme for Hamilton-Jacobi equations

This article presents an improved fifth-order finite difference weighted essentially nonoscillatory (WENO) scheme to solve Hamilton-Jacobi equations. A new type of nonlinear weights is introduced with the construction of local smoothness indicators on each local stencil that are measured with the help of generalized undivided differences in L¹-norm. A novel global smoothness measurement is also constructed with the help of local measurements from its linear combination. Numerical experiments are conducted in one- and two-dimensions to demonstrate the performance enhancement, resolution power, numerical accuracy for the proposed scheme, and compared it with the classical WENO scheme.     

Two-Photon Absorption Enhancement by the Inclusion of a Tropone Ring in Distorted Nanographene Ribbons

A new family of distorted ribbon-shaped nanographenes was designed, synthesized, and their optical and electrochemical properties were evaluated, pointing out an unprecedented correlation between their structural characteristics and the two-photon absorption (TPA) responses and electrochemical band gaps. Three nanographene ribbons have been prepared: a seven-membered-ring-containing nanographene presenting a tropone moiety at the edge, its full-carbon analogue, and a purely hexagonal one. We have found that the TPA cross-sections and the electrochemical band gaps of the seven-membered-ring-containing compounds are higher and lower, respectively, than those of the fully hexagonal polycyclic aromatic hydrocarbon (PAH). Interestingly, the inclusion of additional curvature has a positive effect in terms of non-linear optical properties of those ribbons.     

Elastic constants of sodium chlorate from 77 K to 350 K

The elastic constantsC ₁₁,C ₁₂ andC ₄₄ of sodium chlorate single crystal have been evaluated using 10 MHz ultrasonic pulse echo superposition technique. The values areC ₁₁=4.90,C ₁₂=1.39,C ₄₄=1.17 (× 10¹⁰ N/m ²) at 298 K and 6.15, 2.16, 1.32 (×10¹⁰ N/m ²) at 77 K. The data agree well with the values measured earlier up to 223 K. Brief mention is also made of the low temperature bonding problems in these soft crystals.