AN INTEGRATION METHOD WITH FITTING CUBIC SPLINE FUNCTIONS TO A NUMERICAL MODEL OF 2ND-ORDER SPACE-TIME DIFFERENTIAL REMAINDER——FOR AN IDEAL GLOBAL SIMULATION CASE WITH PRIMITIVE ATMOSPHERIC EQUATIONS

In this paper,the forecasting equations of a 2nd-order space-time differential remainder are deduced from the Navier-Stokes primitive equations and Eulerian operator by Taylor-series expansion.Here we introduce a cubic spline numerical model(Spline Model for short),which is with a quasi-Lagrangian time-split integration scheme of fitting cubic spline/bicubic surface to all physical variable fields in the atmospheric equations on spherical discrete latitude-longitude mesh.A new algorithm of"fitting cubic spline—time step integration—fitting cubic spline—……"is developed to determine their first-and2nd-order derivatives and their upstream points for time discrete integral to the governing equations in Spline Model.And the cubic spline function and its mathematical polarities are also discussed to understand the Spline Model’s mathematical foundation of numerical analysis.It is pointed out that the Spline Model has mathematical laws of"convergence"of the cubic spline functions contracting to the original functions as well as its 1st-order and 2nd-order derivatives.The"optimality"of the 2nd-order derivative of the cubic spline functions is optimal approximation to that of the original functions.In addition,a Hermite bicubic patch is equivalent to operate on a grid for a 2nd-order derivative variable field.Besides,the slopes and curvatures of a central difference are identified respectively,with a smoothing coefficient of 1/3,three-point smoothing of that of a cubic spline.Then the slopes and curvatures of a central difference are calculated from the smoothing coefficient 1/3 and three-point smoothing of that of a cubic spline,respectively.Furthermore,a global simulation case of adiabatic,non-frictional and"incompressible"model atmosphere is shown with the quasi-Lagrangian time integration by using a global Spline Model,whose initial condition comes from the NCEP reanalysis data,along with quasi-uniform latitude-longitude grids and the so-called"shallow atmosphere"Navier-Stokes primitive equations in the spherical coordinates.The Spline Model,which adopted the Navier-Stokes primitive equations and quasi-Lagrangian time-split integration scheme,provides an initial ideal case of global atmospheric circulation.In addition,considering the essentially non-linear atmospheric motions,the Spline Model could judge reasonably well simple points of any smoothed variable field according to its fitting spline curvatures that must conform to its physical interpretation.

Nonlinear Random Motion Analysis of Coupled Heave-Pitch Motions of a Spar Platform Considering lst-Order and 2nd-Order Wave Loads

In this study, the coupled heave-pitch motion equations of a spar platform were established by considering lst-order and 2nd-order random wave loads and the effects of time-varying displacement volume and transient wave elevation. We generated random wave loads based on frequency-domain wave load transfer functions and the Joint North Sea Wave Project （JONSWAP） wave spectrum, designed program codes to solve the motion equations, and then simulated the coupled heave-pitch motion responses of the platform in the time domain. We then calculated and compared the motion responses in different sea conditions and separately investigated the effects of 2nd-order random wave loads and transient wave elevation. The results show that the coupled heave-pitch motion responses of the platform are primarily dominated by wave height and the characteristic wave period, the latter of which has a greater impact. 2nd-order mean wave loads mainly affect the average heave value. The platform＇s pitch increases after the 2nd-order low frequency wave loads are taken into account. The platform＇s heave is underestimated if the transient wave elevation term in the motion equations is neglected.

Distributed analysis of forward stimulated Brillouin scattering for acoustic impedance sensing by extraction of a 2nd-order local spectrum

Distributed fiber sensors based on forward stimulated Brillouin scattering(F-SBS)have attracted special attention because of their capability to detect the acoustic impedance of liquid material outside fiber.However,the reported results were based on the extraction of a 1st-order local spectrum,causing the sensing distance to be restricted by pump depletion.Here,a novel post-processing technique was proposed for distributed acoustic impedance sensing by extracting the 2nd-order local spectrum,which is beneficial for improving the sensing signal-to-noise ratio(SNR)significantly,since its pulse energy penetrates into the fiber more deeply.As a proof-of-concept,distributed acoustic impedance sensing along~1630 m fiber under moderate spatial resolution of~20 m was demonstrated.

Solving (2+1)-dimensional sine-Poisson equation by a modified variable separated ordinary differential equation method

By introducing a more general auxiliary ordinary differential equation （ODE）, a modified variable separated ordinary differential equation method is presented for solving the （2 ＋ 1）-dimensional sine-Poisson equation. As a result, many explicit and exact solutions of the （2 ＋ 1）-dimensional sine-Poisson equation are derived in a simple manner by this technique.

三偏心混沌混凝土振动台振动特性分析

针对雷尔密特理论单一的激振频率只能对应一定粒径范围的骨料从而造成混凝土密实度不高的问题,建立了三偏心混沌激振器与双质体振动系统相结合的四自由度振动台力学模型,根据其在有势力和耗散力作用下的第二类Lagrange方程,推导出系统的动力学微分方程,通过Ode45(R-K)算法对振动过程进行仿真,利用得到的相轨图、Poincare图、功率谱图定性和最大Lyapunov指数定量表征振动台的振动特性,结果表明:振动台的振动为混沌振动,具有很宽的振动频率,能够对应混凝土骨料中不同粒径的共振频率。最后运用PFC 2D颗粒流分析软件对混凝土密实成型过程进行仿真验证,对比表明混沌振动台相比普通单一频率振动台混凝土密实度提高了6.32%,为工程实际中混凝土密实成型提供了理论依据。

2nd-order spline wavelet convolution method in resolving chemical overlapped peaks

A 2nd-order spline wavelet convolution method in resolving overlapped peaks is developed. It determines the number of peaks, peak positions and width through wavelet? convolution, then uses spline function to construct the resoluter, which is used to resolve overlapped peaks. Theoretical proof is given, and the selections of wavelets and parameters are discussed. It is proven that baseline separation can be achieved after processed, the relative errors of peak position and area are less than 0.2% and 4.0% respectively. It can be directly applied to seriously overlapped signals, noisy signals and multi-component signals, and the results are satisfactory. It is a novel effective method for resolution.

Single-to-Multiple Channel Wavelength Conversions and Tuning of Picosecond Pulses in Quasi-Phase-Matched Waveguides

We report the single-to-multiple channel wavelength conversions of 1.57-ps pulses based on cascaded secondharmonic generation and difference frequency generation in quasi-phase-matched periodically poled lithium hiebate waveguides. For single-to-single channel wavelength conversion, no external cavity laser is required with use of a fibre ring laser. The conversion efficiency is about -21.44 dB. The converted idler wavelength can be tuned from 1526.4nm to 1537.5nm as the lasing pump wavelength is varied from 1566.1 nm to 1555.0nm. By employing several input pumps, tunable single-to-dual and single-to-triple channel wavelength conversions are experimentally demonstrated.

Third Order Adjoint Sensitivity and Uncertainty Analysis of an OECD/NEA Reactor Physics Benchmark: III. Response Moments

The (180)3 third-order mixed sensitivities of the leakage response of a polyethylene-reflected plutonium (PERP) experimental benchmark with respect to the benchmark’s 180 microscopic total cross sections have been computed in accompanying works [1] [2]. This work quantifies the contributions of these (180)3 third-order mixed sensitivities to the PERP benchmark’s leakage response distribution moments (expected value, variance and skewness) and compares these contributions to those stemming from the corresponding first- and second-order sensitivities of the PERP benchmark’s leakage response with respect to the total cross sections. The numerical results obtained in this work reveal that the importance of the 3rd-order sensitivities can surpass the importance of the 1st- and 2nd-order sensitivities when the parameters’ uncertainties increase. In particular, for a uniform standard deviation of 10% of the microscopic total cross sections, the 3rd-order sensitivities contribute 80% to the response variance, whereas the contribution stemming from the 1st- and 2nd-order sensitivities amount only to 2% and 18%, respectively. Consequently, neglecting the 3rd-order sensitivities could cause a very large non-conservative error by under-reporting the response variance by a factor of 506%. The results obtained in this work also indicate that the effects of the 3rd-order sensitivities are to reduce the response’s skewness in parameter space, rendering the distribution of the leakage response more symmetric about its expected value. The results obtained in this work are the first such results ever published in reactor physics. Since correlations among the group-averaged microscopic total cross sections are not available, only the effects of typical standard deviations for these cross sections could be considered. Due to this lack of correlations among the cross sections, the effects of the mixed 3rd-order sensitivities could not be quantified exactly at this time. These effects could be quantified only when correlations among the group-averaged microscopic total cross sections would be obtained experimentally by the nuclear physics community.

Fifth-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Nonlinear Systems (5th-CASAM-N): I. Mathematical Framework

This work presents the mathematical framework of the “Fifth-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Nonlinear Systems (5th-CASAM-N),” which generalizes and extends all of the previous works performed to date on this subject. The 5th-CASAM-N enables the exact and efficient computation of all sensitivities, up to and including fifth-order, of model responses to uncertain model parameters and uncertain boundaries of the system’s domain of definition, thus enabling, inter alia, the quantification of uncertainties stemming from manufacturing tolerances. The 5th-CASAM-N provides a fundamental step towards overcoming the curse of dimensionality in sensitivity and uncertainty analysis.