Femtosecond second-order solitons in optical fiber transmission

A propagation of the femtosecond second-order solitons in an optical fiber is studied. We show that a generalized nonlinear Schrödinger equation well describes the propagation of the second-order soliton even containing only a few optical cycles. The propagations of a 50 fs and a 10 fs second-order soliton in an optical fiber are numerically simulated. It is found that, for the case of 10 fs second-order soliton, the soliton decay is dominated by the third-order dispersion, in contrast to the case of 50 fs second-order solitons, where the soliton decay is dominated by the delayed Raman response. It is also found that the exact delayed Raman response form must be used for the propagation of the 50 fs or less than 50 fs second-order soliton.     

The Use of Multi-Pass Time-of-Flight Mass Analyzers for Nuclear-Decay Spectroscopy of Mass Identified Nuclei

The masses of ions of some keV can be determined in multi-pass time-of-flight mass analyzers [1,2] with high precision. The mass accuracies thus achieved are sufficient to determine the proton and neutron numbers for most short-lived and stable nuclei [3,5]. Recording α- or γ-radiation of the investigated nuclei in delayed coincidence to the ion arrival, one thus can perform nuclear spectroscopy of selected nuclei. This revised version was published online in July 2006 with corrections to the Cover Date.     

High-Order Leap-Frog Based Discontinuous Galerkin Method for the Time-Domain Maxwell Equations on Non-Conforming Simplicial Meshes

A high-order leap-flog based non-dissipative discontinuous Galerkin timedomain method for solving Maxwell's equations is introduced and analyzed. The proposed method combines a centered approximation for the evaluation of fluxes at the interface between neighboring elements, with a Nth-order leap-frog time scheme. Moreover, the interpolation degree is defined at the element level and the mesh is refined locally in a non-conforming way resulting in arbitrary level hanging nodes. The method is proved to be stable under some CFL-like condition on the time step. The convergence of the semi-discrete approximation to Maxwell's equations is established rigorously and bounds on the global divergence error are provided. Numerical experiments with highorder elements show the potential of the method.     

Complexity of Body Movements during Sleep in Children with Autism Spectrum Disorder

Recently, measuring the complexity of body movements during sleep has been proven as an objective biomarker of various psychiatric disorders. Although sleep problems are common in children with autism spectrum disorder (ASD) and might exacerbate ASD symptoms, their objectivity as a biomarker remains to be established. Therefore, details of body movement complexity during sleep as estimated by actigraphy were investigated in typically developing (TD) children and in children with ASD. Several complexity analyses were applied to raw and thresholded data of actigraphy from 17 TD children and 17 children with ASD. Determinism, irregularity and unpredictability, and long-range temporal correlation were examined respectively using the false nearest neighbor (FNN) algorithm, information-theoretic analyses, and detrended fluctuation analysis (DFA). Although the FNN algorithm did not reveal determinism in body movements, surrogate analyses identified the influence of nonlinear processes on the irregularity and long-range temporal correlation of body movements. Additionally, the irregularity and unpredictability of body movements measured by expanded sample entropy were significantly lower in ASD than in TD children up to two hours after sleep onset and at approximately six hours after sleep onset. This difference was found especially for the high-irregularity period. Through this study, we characterized details of the complexity of body movements during sleep and demonstrated the group difference of body movement complexity across TD children and children with ASD. Complexity analyses of body movements during sleep have provided valuable insights into sleep profiles. Body movement complexity might be useful as a biomarker for ASD.     

Parameter accuracy analysis of weak-value amplification process in the presence of noise

We theoretically introduce the statistical uncertainty of photon number and phase error to discuss the precision of parameters to be measured based on weak measurements. When the photon counting scheme is used, we discuss the relative accuracy of the system in the presence of phase error by using the orthogonal and nonorthogonal pre-and postselected states, respectively. When using the measurement scheme of pointer shift, we discuss the measurement accuracy in the presence of phase error, pointer resolution, and statistical uncertainty. These results give a guide way to get the smallest relative precision and deepen our understanding about weak measurement.     

Sharp Estimates of Bounded Solutions to Some Second-order Forced Dissipative Equations

Résumé A l’aide d’inégalités différentielles, on établit une estimation proche de l’optimalité pour la norme dans de l’unique solution bornée de u′′ + cu′ + Au = f(t) lorsque A = A ^* ≥ λ I est un opérateur borné ou non sur un espace de Hilbert réel H, V = D(A ^1/2) et λ, c sont des constantes positives, tandis que . By using differential inequalities, a close-to-optimal bound of the unique bounded solution of u′′ + cu′ + Au = f(t) is obtained whenever A = A ^* ≥ λ I is a bounded or unbounded linear operator on a real Hilbert space H, V = D(A ^1/2) and λ, c are positive constants, while .

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Modelling of inhomogeneous turbulence in the absence of mean velocity gradients

In this paper we propose a new rational model for turbulent transport of Reynolds stresses and dissipation. For this purpose we first analyse some properties of diffused turbulence i.e. turbulence where dissipation is balanced by turbulent diffusion arising from inhomogeneity. Then we use some of these results to deduce some mathematical requirements that must be satisfied by any rational model and we show that they are not verified by available models. Consequently we derive a more general model taking into account the various properties of diffused turbulence.     

13顶点金属碳硼烷结构和非线性光学性质的DFT研究

采用量子化学密度泛函理论(DFT)B3LYP/6-31G(d)方法,对4,1,6-MC2B10H1213顶点金属碳硼烷几何构型进行优化,结合有限场(FF)方法计算了它们的极化率和二阶非线性光学(NLO)系数.结果表明,十个13顶点金属碳硼烷分子中1a～6a的二阶NLO系数与其构型纵向扩张呈现相同的规律.分子的前线分子轨道能级差越小,其二阶NLO系数越大.对于不同自旋态的同种金属碳硼烷分子,其偶极矩值为高自旋态大于相应的低自旋态,极化率和二阶NLO系数与自旋多重度没有一致的对应规律,自旋多重度对NLO性质影响不大.     

A study of the precision and accuracy of peak quantification in comprehensive two-dimensional liquid chromatography in time

Simulated chromatographic data were used to determine the precision and accuracy in the estimation of peak volumes (i.e., peak sizes) in comprehensive two-dimensional liquid chromatography in time (LC × LC). Peak volumes were determined both by summing the areas in the second dimension chromatograms and by fitting the second dimension areas to a Gaussian peak. The Gaussian method is better at predicting the peak volume than the moments method provided there are at least three second dimension injections above the limit of detection (LOD). However, when only two of the second dimension signals are substantially above baseline, the accuracy and precision of the Gaussian fit method become quite poor because the results from the fitting algorithm become indeterminate. Based on simulations in which the modulation ratio (M_R = 4¹σ/t_s) and sampling phase (?) were varied, we conclude for well-resolved peaks that the optimum precision in peak volumes in 2D separations will be obtained when the M_R is between two and five, such that there are typically four to ten second dimension peaks recorded over the eight σ width of the first dimension peak. This sampling rate is similar to that suggested by the Murphy–Schure–Foley criterion. This provides an RSD of approximately 2% for the signal-to-noise ratio used in the present simulations. The precision of the peak volume of experimental data was also assessed, and RSD values were in the range of 4–5%. We conclude that the poorer precision found in the LC × LC experimental data as compared to LC may be due to experimental imprecision in sampling the effluent from the first dimension column.     

标准镜的高精度柔性支撑镜框的优化设计

为了实现干涉仪标准镜中光学元件的高精度定位,设计了一种柔性支撑镜框,研究了该结构的力学模型、结构参数、定位精度和透镜变形。首先,根据材料力学原理将柔性镜框等效为一个弹簧系统;根据力学方程和几何关系,建立了透镜中心位置与柔性结构的挠度之间的二元方程。然后,分析了安装位置、温度、结构参数对透镜位置以及作用力的影响。最后,应用有限元仿真分析了所设计结构的力学性能,并进行对比验证。结果表明,数值仿真分析的结果与有限元仿真结果基本相同,柔性镜框的柔性结构厚度最优值为1.5 mm。该设计方案完全满足干涉仪标准镜对镜框在定位精度、稳定性方面的要求。