Curvature investigation in tapered fibers and its application to sensing and mode conversion

Non-adiabatic tapered fibers are basic photonic components used in a wide range of applications. Here we investigate a way to increase their utility through the controllable bending of one of their tapered sections. The experiments carried out explain, for the first time, the mechanics of this approach showing how these tapers can be used to build more sensitive sensors. Their use as highly efficient mode converters is also discussed.     

A priori tests of a stochastic mode reduction strategy

Several a priori tests of a systematic stochastic mode reduction procedure recently devised by the authors [Proc. Natl. Acad. Sci. 96 (1999) 14687; Commun. Pure Appl. Math. 54 (2001) 891] are developed here. In this procedure, reduced stochastic equations for a smaller collections of resolved variables are derived systematically for complex nonlinear systems with many degrees of freedom and a large collection of unresolved variables. While the above approach is mathematically rigorous in the limit when the ratio of correlation times between the resolved and the unresolved variables is arbitrary small, it is shown here on a systematic hierarchy of models that this ratio can be surprisingly big. Typically, the systematic reduced stochastic modeling yields quantitatively realistic dynamics for ratios as large as 1/2. The examples studied here vary from instructive stochastic triad models to prototype complex systems with many degrees of freedom utilizing the truncated Burgers–Hopf equations as a nonlinear heat bath. Systematic quantitative tests for the stochastic modeling procedure are developed here which involve the stationary distribution and the two-time correlations for the second and fourth moments including the resolved variables and the energy in the resolved variables. In an important illustrative example presented here, the nonlinear original system involves 102 degrees of freedom and the reduced stochastic model predicted by the theory for two resolved variables involves both nonlinear interaction and multiplicative noises. Even for large value of the correlation time ratio of the order of 1/2, the reduced stochastic model with two degrees of freedom captures the essentially nonlinear and non-Gaussian statistics of the original nonlinear systems with 102 modes extremely well. Furthermore, it is shown here that the standard regression fitting of the second-order correlations alone fails to reproduce the nonlinear stochastic dynamics in this example.     

Investigation and optimization of the covering power and coloristic properties of paint coatings of complex composition

A method for finding the optimum sizes of pigment particles, their volume concentration, and the paint coating thickness that provide the covering power and the required coloristic characteristics of reflected light for the minimum flow rate of pigments is based on using a four-flow approximation of the solution to the equation of radiation transfer in dispersion media and is extended to coatings of complex composition. The capabilities of the method are demonstrated by examples of coatings of mixtures of hematite and rutile particles in a binder with n=1.5 for variations of the modal size and the half-width of the size distribution of the pigment particles. B. I. Stepanov Institute of Physics, Academy of Sciences of Belarus, 70, F. Skorina Ave., Minsk, 220072, Belarus. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 64, No. 1, pp. 90–96, January–February, 1997.     

A computational strategy for multiscale systems with applications to Lorenz 96 model

Numerical schemes for systems with multiple spatio-temporal scales are investigated. The multiscale schemes use asymptotic results for this type of systems which guarantee the existence of an effective dynamics for some suitably defined modes varying slowly on the largest scales. The multiscale schemes are analyzed in general, then illustrated on a specific example of a moderately large deterministic system displaying chaotic behavior due to Lorenz. Issues like consistency, accuracy, and efficiency are discussed in detail. The role of possible hidden slow variables as well as additional effects arising on the diffusive time-scale are also investigated. As a byproduct we obtain a rather complete characterization of the effective dynamics in Lorenz model.     

输入输出共轴的三弯曲型TM01-TE11模式转换器

 通过采用相位重匹配技术，设计了一种输入输出共轴的三弯曲型TM₀₁-TE₁₁模式转换器，该转换器由三段常曲率弯曲波导和两段直波导组成。用模式耦合理论建立了该类模式转换器的数值计算和优化设计方法，并设计了一个中心频率为7.0 GHz的模式转换器。该转换器的TM₀₁-TE₁₁转换效率在中心频率上大于99％，在6.5~7.5 GHz的频率范围内大于90％。应用时域有限差分法和有限元方法对所设计的模式转换器进行了仿真，仿真结果验证了设计理论和设计结果。     

Convergence rate of the best-r-point-average estimator for the maximizer of a nonparametric regression function

The best-r-point-average (BRPA) estimator of the maximizer of a regression function, proposed in Changchien (in: M.T. Chao, P.E. Cheng (Eds.), Proceedings of the 1990 Taipei Symposium in Statistics, June 28–30, 1990, pp. 63–78) has certain merits over the estimators derived through the estimation of the regression function. Some of the properties of the BRPA estimator have been studied in Chen et al. (J. Multivariate Anal. 57 (1996) 191) and Bai and Huang (Sankhya: Indian J. Statist. Ser. A. 61 (Pt. 2) (1999) 208–217). In this article, we further study the properties of the BRPA estimator and give its convergence rate under some quite general conditions. Simulation results are presented for the illustration of the convergence rate. Some comparisons with existing estimators such as the Müller estimator are provided.     

荧光光度法直接测定高纯氧化钕中的痕量镨和铈

使用Ｐ－ＥＬＳ５０荧光光谱仪，在盐酸介质中，用同一激发波长激发，分别测定Ｐｒ（Ⅲ）（ｎｍ）和Ｃｅ（Ⅲ）（３５６ｎｍ）发射峰强度。     

高纯度植酸的制备

高纯度植酸的制备孙定光胡佩廖显威（四川师范大学化学系成都６１００６６）关键词植酸制备高纯试剂中图分类号Ｏ６２９．９植酸（ＰｈｙｔｉｃＡｃｉｄ）又名肌醇六磷酸酯，分子式：Ｃ６Ｈ１８Ｏ２４Ｐ６，结构为植酸是中等强度的有机酸，因其结构特殊，具极强的螯合作用...     

化学光谱法测定5N氧化钆中14个稀土杂质元素

报道了化学光谱法测定５Ｎ高纯氧化钆中１４个稀土杂质元素，在Ｐ５０７萃淋树脂色层柱上分离氧化钆中稀土杂质元素，分别采用定量分离Ｌａ－Ｓｍ及Ｔｂ－Ｌｕ＋Ｙ和部份分离Ｅｕ的方法，并相应地采用碳粉吸附法和碳粉粉末法进行光谱测定。分离时间为３．５ｈ，测定下限为１．２μｇ／ｇ（ＲＥ）。     

Determination of the Enantiomeric Purity of l-Carnitine and Acetyl-l-Carnitine by Chiral Liquid Chromatography

A chiral liquid chromatographic method for determination of the enantiomeric purity of both l-carnitine and acetyl-l-carnitine is described. Separation of the enantiomers of dl-carnitine and acetyl-dl-carnitine was achieved on a commercial chiral column (Chiralcel OD-R) after derivatization with (alpha-bromo)methyl phenyl ketone. Introduction of this lipophilic UV chromophoric group to the carnitine and acetylcarnitine molecules improved their retention, resolution, and UV detection. The mobile phase was 74:26 (v/v) 0.5 mol L^-1 sodium perchlorate–acetonitrile, pH 3.8, and the flow rate was 0.4 mL min^-1. Detection was performed at 235 nm. The method is selective and reliable for determination of the enantiomeric purity of bulk drug substances l-carnitine and acetyl-l-carnitine.