Theory of Basin Scale Dynamics of a Stratified Rotating Fluid

The dynamics of a stratified fluid contained in a rotating rectangular box is described in terms of the evolution of the lowest moments of its density and momentum fields. The first moment of the density field also gives the position of the fluids centre-of-mass. The resulting low-order model allows for fast assessment both of adopted parameterisations, as well as of particular values of parameters. In the ideal fluid limit (neglect of viscous and diffusive effects), in the absence of wind, the equations have a Hamiltonian structure that is integrable (non-integrable) in the absence (presence) of differential heating. In a non-rotating convective regime, dynamically rich behaviour and strong dependence on the single (lumped) parameter are established. For small values of this parameter, in a self-similar regime, further reduction to an explicit map is discussed in an Appendix. Introducing rotation in a nearly geostrophic regime leads through a Hopf bifurcation to a limit cycle, and under the influence of wind and salt to multiple equilibria and chaos, respectively.     

Relationships among some locally conservative discretization methods which handle discontinuous coefficients

This paper presents the relationships between some numerical methods suitable for a heterogeneous elliptic equation with application to reservoir simulation. The methods discussed are the classical mixed finite element method (MFEM), the control-volume mixed finite element method (CVMFEM), the support operators method (SOM), the enhanced cell-centered finite difference method (ECCFDM), and the multi-point flux-approximation (MPFA) control-volume method. These methods are all locally mass conservative, and handle general irregular grids with anisotropic and heterogeneous discontinuous permeability. In addition to this, the methods have a common weak continuity in the pressure across the edges, which in some cases corresponds to Lagrange multipliers. It seems that this last property is an essential common quality for these methods. T.F. Russell: Partially supported by the National Science Foundation Grant Nos. DMS-0084438 and DMS-0222300.     

非等步长GM(1,1)模型及其在大堤沉降监测的应用

针对非等步长数据,传统GM方法是构造等步长序列,生成1-AGO序列,再建立等步长GM(1,1)模型。考虑到变形观测序列非等步长特性,以相邻观测时间间隔为权,直接生成1-WAGO序列,建立非等步长GM(1,1)模型。将GM(1,1)模型应用于堤防工程沉降观测分析与预报,得到了有益的结论。     

VLL方法在自动获取建筑物高程中的应用

铅垂线轨迹法(VLL,Vertical Line Locus)是一种直接解求高程的方法,将该方法加以改进,并将其应用在建筑物高程信息的获取中,实现了自动批量获取建筑物高程信息的目的,并具有一定的精度。实验表明,该方法效率较高,可靠性较好。     

基于多GPU的Harris角点检测并行算法

提出了一种基于多图形处理器(graphic processing unit,GPU)设计思想的Harris角点检测并行算法,使用众多线程将计算中耗时的影像高斯卷积平滑滤波部分改造成单指令多线程(single instruction multi-ple thread,SIMT)模式,并采用GPU中共享存储器、常数存储器和锁页内存机制在统一计算设备架构(com-pute unified device archetecture,CUDA)上完成影像角点检测的全过程。实验结果表明,基于多GPU的Har-ris角点检测并行算法比CPU上的串行算法可获得最高达60倍的加速比,其执行效率明显提高,对于大规模数据处理呈现出良好的实时处理能力。     

基于二元关系的GIS实体拓扑关系的粗糙表达

利用二元关系和粗糙集的一些性质来研究GIS实体之间关系,发现在基于二元关系的广义近似空间下GIS实体的前继领域、后继领域算子、上、下继领域包含了比它自身更广的一个集合定义。同样基于粗糙集,我们发现二元关系GIS实体的上、下近似比Pawlark粗糙集的定义更广泛。在二元关系的广义近似空间下,一个GIS单点集的上近似等于它的前继领域,同样等于它后继领域的逆。     

直升机电力巡检中电力线的自动提取

结合电力线在直升机航拍影像中的成像特性,提出了一种复杂自然背景中电力线的自动提取方法。首先,利用Ratio算子从复杂背景中检测出电力线边缘;然后把边缘转化成直线段,对出现断裂与欠连接的直线进行连接与合并;最后,从这些直线段中采样一些点集,利用随机一致性抽样算法(Ransac)从中选择尽可能少但足够的点来拟合成一根完整的电力线,并通过实验证明了该方法的有效性。     

Duality properties of Gorringe–Leach equations

In the category of motions preserving the angular momentum direction, Gorringe and Leach exhibited two classes of differential equations having elliptical orbits. After enlarging slightly these classes, we show that they are related by a duality correspondence of the Arnold–Vassiliev type. The specific associated conserved quantities (Laplace–Runge–Lenz vector and Fradkin–Jauch–Hill tensor) are then dual reflections of each other.     

Analytical solutions for the equations of motion of a space vehicle during the atmospheric re-entry phase on a 2-D trajectory

A practical and important problem encountered during the atmospheric re-entry phase is to determine analytical solutions for the space vehicle dynamical equations of motion. The author proposes new solutions for the equations of trajectory and flight-path angle of the space vehicle during the re-entry phase in Earth’s atmosphere. Explicit analytical solutions for the aerodynamic equations of motion can be effectively applied to investigate and control the rocket flight characteristics. Setting the initial conditions for the speed, re-entering flight-path angle, altitude, atmosphere density, lift and drag coefficients, the nonlinear differential equations of motion are linearized by a proper choice of the re-entry range angles. After integration, the solutions are expressed with the Exponential Integral, and Generalized Exponential Integral functions. Theoretical frameworks for proposed solutions as well as, several numerical examples, are presented.     

Solution of Lane-Emden type equations using Bernstein operational matrix of differentiation

The purpose of this paper is to propose an efficient numerical method for solving Lane-Emden type equations arising in astrophysics using Bernstein polynomials. First Bernstein operational matrix of differentiation is derived using Bernstein polynomials and then applied to solve the linear and nonlinear differential equations of Lane-Emden type. Some illustrative examples are given to demonstrate the efficiency and validity of the proposed algorithm.