二阶后牛顿光线方程

近来相继提出一系列的空间天体测量计划，要求考虑在多参考系中二阶后牛顿部分对光线传播的贡献，也就是说，必须讨论在最近完成的扩展的DSX体系下的二阶后牛顿(2PN)光线方程．DSX体系是在20世纪90年代初建立的，用来讨论对N个任意形状和组成、自转可变形物体的一套完整的一阶后牛顿(1PN)天体力学理论．在此建议采用迭代的方法来推导2PN光线方程．从度规和Christoffel记号出发推导太阳系中的2PN光线方程．当忽略掉更高阶的项时，2PN光线方程将回到在很多教科书中广泛出现的1PN光线方程．利用这套方程就可以计算太阳系的光线传播．     

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三电平逆变器驱动的IPMSM模型预测电流控制系统研究

三电平逆变器拓扑结构简单、所用器件较少且每个功率管所承受的电压应力小,适用于高电压、大容量的场合.相比于传统两电平逆变器,三电平逆变器输出电平的数量从2变成3,输出的电压电流谐波含量低,波形正弦度更好.本文提出内置式永磁同步电机模型预测电流控制算法,以提高控制系统电流动态响应速度,并针对该算法在控制系统中产生的时间延迟,引入二阶延迟补偿策略.对以上内容建立系统仿真模型,仿真结果表明：三电平逆变器相比两电平逆变器输出电流波形谐波含量更小、电机的动态及稳态性能更好.     

蛙跳格式的替代方案及其在大气环流模式中的应用

蛙跳（Leapfrog）时间差分格式采用AsselinRobert时间滤波方案去除计算解能够降低原始方程组的时间差分格式的计算精度,采用二阶Runge-Kutta格式构造欧拉前差方案可弥补蛙跳格式的不足。即在不存在计算解的条件下去除滤波影响,更大程度保持方程组的计算准确性。作者基于NCAR CAM3.0(Community Atmosphere Model 3.0)完善的软件平台,将原模式的三时间层蛙跳时间差分方案修改为两时间层二阶Runge-Kutta时间差分格式,对与重力波有关项使用中央差隐式处理,以此构建半隐式大气环流谱模式。通过斜压波实验比较不同格式在保持初值稳定性上的表现,从而发现,二阶Runge-Kutta方案能够更好的保证方案的初值稳定性。同时在纬向对称平衡场中加入扰动的情况下,二阶Runge-Kutta方案模拟的斜压波动发展演变的特征具有良好的收敛性,对波动发展的描述能力更强。存在这种优势的可能原因可归结为格式自身的优势和摆脱了时间滤波的负面影响,通过加入不同滤波系数的比较实验可以看到,滤波的平滑作用对模式结果的影响显著,但格式自身的优势也是改进模拟结果的主要因素。通过非绝热条件下20 年（1980～1999年）气候态全模式模拟考察模式在气候模拟中的表现,结果表明,此方案在长期的气候模拟中同样可降低预报变量及诊断变量的模拟误差,具有更好的模拟能力。     

SECOND-ORDER ANALYSIS OF POINT PATTERNS: THE CASE OF CHICAGO AS A MULTI-CENTER URBAN REGION *

A comprehensive approach to the analysis of point patterns demonstrates the usefulness of second-order methods by exploring population distribution in the Chicago region. The methods are based on the development of a distribution of all interpoint distances representing the total covariation in a pattern. Clustering and inhibition models are explored with regard to the population pattern. Some evidence supports a multi-center city hypothesis for the region.     

A conservative, unconditionally stable, second-order three-point differencing scheme for the diffusion–convection equation

A three-point differencing scheme for the diffusion–convection equation is presented that offers all the advantages of both the central and the one-sided ('upwind') differencing scheme without suffering from their drawbacks. Specifically, the scheme is conservative, unconditionally stable, and second-order-accurate in space. It is free of oscillations and over- or undershoots, simple to code, and requires essentially no more computing time than the one-sided scheme. Although known for a relatively long time in numerical mathematics, the scheme apparently has not received sufficient attention from modellers of hydrothermal systems or contaminant transport in the geosciences. In order to fill this gap a comparison is made between this scheme and the widely used one-sided scheme for the transient diffusion–convection equation in different time discretizations. The results are discussed taking into account other approaches towards minimizing numerical diffusion.     

层化海洋中二阶多色波对可渗透结构的绕射问题

可渗透结构具有使波浪作用减弱的效应,而海水的层化及水波的非线性使结构的波绕射产生多层复杂机制。将可渗透结构应用于复杂海况条件中,海水的层化性、波浪的非线性及结构的透空性构成了波绕射的一个十分复杂的数学问题。该问题存在理论研究的必要性,而文章则着重探讨其数学分析的可能性。通过引入二层海的层化海模式及Stokes二阶波的非线性波模式,给出了二阶多色波对透空结构的波绕射的定解问题提法,提出了复合形式的二阶多色波辐射条件式及可渗透结构的二阶物面条件式,应用特征函数解法与积分法推导了多色波对结构绕射的一阶势解与二阶作用的耦合积分解式,并讨论了解式所涉及无穷积分的算法。     

Second-Order Potentials and Forces for Two-Dimensional Diffraction Problem of Finite Water Depth

-In this paper, an analytical solution in the outer region of finite water depth is derived for the second-order diffraction potential, which gives a clear physical meaning of the wave transmission and reflection characteristics in the far field. A numerical method-simple Green's function technique-for calculating the second-order diffraction potential in the inner region is also described. Numerical results are provided for the second-order wave forces on a semi-submerged cylinder. It is found that the contribution of second-order diffraction potential to second-order wave forces is important. The effect of water depth and submerged depth on the wave force is also discussed.     

GRIB码的二级压缩

ＧＲＩＢ码是目前世界气象组织建议使用的二进制比特流压缩代码，适用于表示数值天气预报产品的格点场数据，该文在ＧＲＩＢ码一级压缩原理等内容简介的基础上，着重讨论了ＧＲＩＢ码二级压缩的概念，原理和方法。     

含二阶起伏体的模拟岩体节理试样剪切特性试验研究

利用规则的小尺寸锯齿构造二阶起伏体,对不同二阶起伏体高度的人工节理进行常法向应力下的直剪试验,研究了节理剪切力学特性。对节理的剪切强度、变形特征进行了分析,并对破坏特征做出解释。试验结果表明：二阶起伏体对节理剪切力学特性有重要影响,含二阶起伏体节理的剪切力学特性与只含有一阶起伏体节理的剪切力学特性不同,只含一阶起伏体的节理剪应力只有一个峰值,含二阶起伏体的节理会出现波浪状的剪胀曲线和多峰值剪应力,且峰值剪应力随剪切位移增大依次出现并逐个减小;随着二阶起伏体高度增大,节理峰值剪切强度增大,节理依次出现磨损破坏、多次性剪断破坏、一次性剪断破坏。