Stress Tensor Fluctuations and Passive Quantum Gravity

The quantum fluctuations of the stress tensor of a quantum field are discussed, as are the resulting space-time metric fluctuations. Passive quantum gravity is an approximation in which gravity is not directly quantized, but fluctuations of the space-time geometry are driven by stress tensor fluctuations. We discuss a decomposition of the stress tensor correlation function into three parts, and consider the physical implications of each part. The operational significance of metric fluctuations and the possible limits of validity of semiclassical gravity are discussed.     

Dispersion analysis of the least‐squares finite‐element shallow‐water system

The frequency or dispersion relation for the least‐squares mixed formulation of the shallow‐water equations is analysed. We consider the use of different approximation spaces corresponding to co‐located and staggered meshes, respectively. The study includes the effect of Coriolis, and the dispersion properties are compared analytically and graphically with those of the mixed Galerkin formulation. Numerical solutions of a test problem to simulate slow Rossby modes illustrate the theoretical results. Copyright © 2003 John Wiley & Sons, Ltd.     

重力输水管道优化设计方法研究

针对重力输水管道设计中存在的问题，文章以管道造价最小为目标，应用动态规划，提出了一种新的重力输水管道优化设计方法，对输水管的当量管径、流量分配、连接管设置与可靠性校核计算等问题作了探讨。该方法可用于沿线有节点流量流出的并联输水管道优化设计，能明显节省投资，有良好的实用性     

宇宙学常数疑难

当代天文学的一系列观测事实都支持应该存在一个非零的正的宇宙学常数，但是，人们发现当前宇宙学常数值太小，而且宇宙学常数即真空能量密度与现在的物质密度巧合地具有相同的量级，然而现有物理学理论还无法给出合理的解释，因此宇宙学常数问题成为物理学和天文学上最重大的疑难之一。文章综述了近年来宇宙在加速膨胀这一重大的天文发现和宇宙学常数的观测结果以及当前理论物理学在宇宙学常数问题上的一些尝试。     

Reformulation of the support set selection problem in the logical analysis of data

The paper is concerned with the problem of binary classification of data records, given an already classified training set of records. Among the various approaches to the problem, the methodology of the logical analysis of data (LAD) is considered. Such approach is based on discrete mathematics, with special emphasis on Boolean functions. With respect to the standard LAD procedure, enhancements based on probability considerations are presented. In particular, the problem of the selection of the optimal support set is formulated as a weighted set covering problem. Testable statistical hypothesis are used. Accuracy of the modified LAD procedure is compared to that of the standard LAD procedure on datasets of the UCI repository. Encouraging results are obtained and discussed.     

Stochastic modeling of a billiard in a gravitational field: Power law behavior of Lyapunov exponents

We consider the motion of a point particle (billiard) in a uniform gravitational field constrained to move in a symmetric wedge-shaped region. The billiard is reflected at the wedge boundary. The phase space of the system naturally divides itself into two regions in which the tangent maps are respectively parabolic and hyperbolic. It is known that the system is integrable for two values of the wedge half-angle ₁ and ₂ and chaotic for ₁<< ₂. We study the system at three levels of approximation: first, where the deterministic dynamics is replaced by a random evolution; second, where, in addition, the tangent map in each region is, replaced by its average; and third, where the tangent map is replaced by a single global average. We show that at all three levels the Lyapunov exponent exhibits power law behavior near ₁ and ₂ with exponents 1/2 and 1, respectively. We indicate the origin of the exponent 1, which has not been observed in unaccelerated billiards.     

改变飞艇重心位置控制纵向运动

本文针对目前平流层飞艇的运动控制效率较低的问题,重点研究了改变平流层飞艇重心的轴向位置来控制飞艇的纵向运动。首先讨论了考虑飞艇重心位置的力和力矩平衡,并利用德国斯图加特大学风洞试验的数据,进行了算例分析。然后和常用的升降舵控制进行效率比较,得出了在空气密度较低的平流层采用改变重心位置比舵面控制具有优越性的结论。最后提出了改变飞艇重心位置的方法。     

Moving grid method for numerical simulation of stratified flows

We develop a second‐order accurate Navier–Stokes solver based on r‐adaptivity of the underlying numerical discretization. The motion of the mesh is based on the fluid velocity field; however, certain adjustments to the Lagrangian velocities are introduced to maintain quality of the mesh. The adjustments are based on the variational approach of energy minimization to redistribute grid points closer to the areas of rapid solution variation. To quantify the numerical diffusion inherent to each method, we monitor changes in the background potential energy, computation of which is based on the density field. We demonstrate on a standing interfacial gravity wave simulation how using our method of grid evolution decreases the rate of increase of the background potential energy compared with using the same advection scheme on the stationary grid. To further highlight the benefit of the proposed moving grid method, we apply it to the nonhydrostatic lock‐exchange flow where the evolution of the interface is more complex than in the standing wave test case. Naive grid evolution based on the fluid velocities in the lock‐exchange flow leads to grid tangling as Kelvin–Helmholtz billows develop at the interface. This is remedied by grid refinement using the variational approach. Copyright © 2012 John Wiley & Sons, Ltd.     

考虑重力因素的断溶体储层“井-洞-缝”模型试井解释方法

顺北油田属于大型断裂构造运动形成的断溶体储层，纵向裂缝系统和垂向分布的溶洞是主要的储集体空间.本文提出溶洞中的压力变化是由流动和波动共同产生的，依此把能量守恒方程与试井理论相结合，建立考虑重力因素的断溶体储层试井解释方法.定义无量纲量，并对无量纲方程进行Laplace变换，得到Laplace空间上的井底压力.由Stehfest数值反演算法得到试井分析所需的图版曲线.对重力因素进行敏感性分析表明：重力因素只影响双对数曲线的末期，当重力因素很明显时，曲线特征类似于定压边界.对新疆油田的某井进行分析，解释了曲线后期下掉原因，并给出溶洞体积以及波动相关参数等，分析结果与生产实际情况相吻合.     

Conditions of stability and instability for a pair of arbitrarily stratified compressible fluids in an arbitrary non-uniform gravity field

The work continues and develops authors’ previous investigation of stability in the small for a two-layer system of inhomogeneous compressible fluids in the uniform gravity field. Here we present a solution of a similar problem in the case of arbitrary non-uniform potential gravity field. The equilibrium stratification of both density and elastic properties of the fluids is supposed arbitrary, as well as the shape of open on top reservoir filled by the fluids. The problem of stability of equilibrium is analyzed as the corresponding problem for the non-linearly elastic bodies, basing on the static energy criterion with regard for the boundary conditions at all parts of the boundary. The crucial element of the analysis is conversion of the quadratic functional of second variation of total potential energy of the system into a “canonical” form that enables to determine its sign. Making use of this canonical form, we obtain almost coinciding with each other necessary and sufficient conditions for stability (those being valid also for an arbitrary number of layers).