中国三峡地区汛期降水量的正态性研究

为了分析三峡地区降水量序列的正态性和谱结构,对降水量的常见各种变换进行试验性研究。试验包括单站降水量、降水量的平方根、立方根和Γ分布概率值等非线性变换,以及级别变换。研究区域多站平均降水量、区域降水量的主分量、区域降水量的非线性变换后的主分量和区域降水量的级别变换后的主分量等序列。研究发现三峡地区单站降水量的各种变换不改变序列原始谱结构,仅影响概率分布的偏度和峰度,使其较好地遵从正态分布,其中以Γ分布的变换以及级别变换在分布的偏度上为最好。 区域降水量的各种变换的综合指数(区域平均值和主分量)正态性及谱结构分析表明,除区域平均值变换后不改变原单站序列的谱结构外,主分量的综合指数能改变原单站序列的谱结构,同时也影响概率分布的偏度和峰度,使其能较好地遵从正态分布。其中以降水量的立方根和Γ分布概率变换以及级别变换,在分布的偏度上有较好的效果。     

非线性观测值函数的协方差和协因数传播及其权倒数

将非线性观测值函数在其近似值处泰勒级数展开，取至二次项，得到线性－二次项形式。利用线性空间［Ｌ，Ｑ］＾Ｎ的概念和性质，将它表示成［α，β］的向量形式。定义广义协方差算子和广义协因数算子，导出了线性－二次项的非线性观测值函数的广义协方差和广义协因数传播律。在此基础上，给出了非线性平差值函数和未知数函数的权倒数公式。     

QN—模型及其在覆盖区资源靶区预测中的应用

本文把数量化理论Ⅲ与Ｑ－型非线性映射在机地结合在一起，定义了一种新的数学模型－ＱＮ－模型。详细地介绍了该模型的基本原理和计算步骤，给出了模型在覆盖区资源靶区以预测中应用的实例。     

Intermittent chaos in nonlinear wave–wave interactions in space plasmas

There is increasing observational evidence of nonlinear wave–wave interactions in space and astrophysical plasmas. We first review a number of theoretical models of nonlinear wave–wave interactions which our group has developed in the past years. We next describe a nonlinear three-mode truncated model of Alfvén waves, involving resonant interactions of one linearly unstable mode and two linearly damped modes. We construct a bifurcation diagram for this three-wave model and investigate the phenomenon of intermittent chaos. The theoretical results presented in this paper can improve our understanding of intermittent time series frequently observed in space and astrophysical plasmas.     

Modified Rindler acceleration as a nonlinear electromagnetic effect

The model proposed originally by Mannheim and Kazanas for fitting the shapes of galactic rotation curves has recently been considered by Grumiller to describe gravity of a central object at large distances. Herein we employ the same geometry within the context of nonlinear electrodynamics (NED). Pure electrical NED model is shown to generate the novel Rindler acceleration term in the metric which explains anomalous behaviors of test particles/satellites. Remarkably a pure magnetic model of NED yields flat rotation curves that may account for the missing dark matter. Weak and strong energy conditions are satisfied in such models of NED.     

Modeling nonlinear wave–wave interactions with the elliptic mild slope equation

An approach is developed to simulate wave–wave interactions using nonlinear elliptic mild-slope equation in domains where wave reflection, refraction, diffraction and breaking effects must also be considered. This involves the construction of an efficient solution procedure including effective boundary treatment, modification of the nonlinear equation to resolve convergence issues, and validation of the overall approach. For solving the second-order boundary-value problem, the Alternating Direction Implicit (ADI) scheme is employed, and the use of approximate boundary conditions is supplemented, for improved accuracy, with internal wave generation method and dissipative sponge layers. The performance of the nonlinear model is investigated for a range of practical wave conditions involving reflection, diffraction and shoaling in the presence of nonlinear wave–wave interactions. In addition, the transformation of a wave spectrum due to nonlinear shoaling and breaking, and nonlinear resonance inside a rectangular harbor are simulated. Numerical calculations are compared with the results from other relevant nonlinear models and experimental data available in literature. Results show that the approach developed here performs reasonably well, and has thus improved the applicability of this class of wave transformation models.     

Investigation of directional hydraulic fracturing based on true tri-axial experiment and finite element modeling

The initiation and propagation of directional hydraulic fracturing (DHF) was investigated based on true tri-axial experiment and finite element modeling. The influences of notch angle, notch length and injection rate on the DHF were investigated. The initiation and propagation of DHF was modeled by a 3D nonlinear finite element method. A comparison between experimental investigation and numerical modeling results indicates that there is a good correlation between unbalanced force (UF) and fracturing. UF can be used to predict the hydraulic fracture initiation and propagation.     

相对湿度和PM2.5浓度对大气能见度的影响研究:基于小时资料的多站对比分析

为了全面分析浙江省不同区域能见度变化基本特征及影响机理,基于杭州、宁波、温州3个国家基本气象站2013-2014年逐时能见度观测资料,比较分析了3市能见度变化的基本特征。发现3市不同等级能见度出现频率基本一致,随着能见度等级的提高,出现频率逐渐降低;从能见度的日变化来看,07时（北京时）前后最低,之后缓慢上升,14-15时达到最高,随后逐渐下降;全年有两个能见度较低时段,分别出现在12月-次年2月和5-6月;总体而言,宁波能见度最优,杭州和温州大体相当。功率谱分析结果表明,3市能见度均有显著的日周期,高频波段呈现出多个显著谱峰,低频波段存在若干显著谱峰。进一步开展机理分析,发现相对湿度和PM_2.5浓度是调制大气能见度的关键因子,相对湿度增大、PM_2.5浓度升高导致能见度降低。在同一相对湿度等级下,初始阶段能见度随PM_2.5浓度的升高迅速降低,到达“拐点”之后降低速率趋于缓慢。在同一PM_2.5浓度水平下,相对湿度越大,能见度越低,说明水汽对能见度也有重要影响。基于相对湿度和PM_2.5浓度两个因子,采用非线性拟合方案构建了大气能见度定量统计模型,总体而言模型拟合效果较好。最后针对研究中存在的不足和未来值得进一步发掘的科学问题进行了讨论。     

CONDITIONAL NONLINEAR OPTIMAL PERTURBATIONS: APPLICATION IN TROPICAL CYCLONE FORECASTS

Considering the feature of tropical cyclones (TCs) that strong positive vorticity exists in the lower layers of troposphere, this study proposed to use vorticity at 850 hPa as cost function to find the conditional nonlinear optimal perturbation (CNOP), which was largely different from those previous studies using total energy of perturbed forecast variables. The CNOP was obtained by an ensemble-based approach. All of the sensitive areas determined by CNOP with vorticity at 850 hPa as cost function for the three cases were located over the TC core region and its vicinity. The impact of the CNOP-based adaptive observations on TC forecasts was evaluated with three cases via observational system simulation experiments (OSSEs). Results showed obvious improvements in TC intensity or track forecasts due to the CNOP-based adaptive observations, which were related to the main error source of the verification area, i.e., intensity error or location error.     

System identification for nonlinear maneuvering of large tankers using artificial neural network

This paper deals with the application of nonparametric system identification to a nonlinear maneuvering model for large tankers using artificial neural network method. The three coupled maneuvering equations in this model for large tankers contain linear and nonlinear terms and instead of attempting to determine the parameters (i.e. hydrodynamic derivatives) associated with nonlinear terms, all nonlinear terms are clubbed together to form one unknown time function per equation which are sought to be represented by the neural network coefficients. The time series used in training the network are obtained from simulated data of zigzag maneuvers and the proposed method has been applied to these data. The neural network scheme adopted in this work has one middle or hidden layer of neurons and it employs the Levenberg–Marquardt algorithm. Using the best choices for the number of hidden layer neurons, length of training data, convergence tolerance etc., the performance of the proposed neural network model has been investigated and conclusions drawn.