川藏公路培龙沟路段堆积物的分形特征及其地质意义

川藏公路培龙沟路段有多种不同类型的堆积物。本文应用分形理论,探讨了培龙沟路段泥石流堆积物、冰碛堆积物、冲洪积堆积物以及坡积或者残坡积物的分形特征。通过粒度分析法计算出不同类型堆积物的粒度分维,得到泥石流堆积物分维最大,冰碛堆积物分维较大,坡积或者残坡积堆积物较小,冲积物或者洪积物分维最小的规律。最后系统论述了堆积物粒度分维的地质意义,认为堆积物粒度分维是对堆积物物质组成的复杂性和自组织性、堆积物形成过程和形成时间以及泥石流、冰川、河流和洪水等搬运能力和运动过程的反映和度量。该研究为野外不同类型堆积物的区分、成因、形成过程等研究提供了一种新的方法,具有一定参考价值。     

GLOBAL ATTRACTOR FOR HASEGAWA-MIMA EQUATION

The long time behavior of solution of the Hasegawa-Mima equation with dissipation term was considered. The global attractor problem of the Hasegawa-Mima equation with initial periodic boundary condition was studied. Applying the uniform a priori estimates method, the existence of global attractor of this problem was proved, and also the dimensions of the global attractor was estimated.     

欧拉流体力学数值方法中的界面计算

本文所提算法适用于二维和三维多介质流体力学两步欧拉数值方法中输运计算的混合网格(包括自由面网格)界面处理。在一个混合网格中，界面被近似地看作直线(二维)或平面(三维)。整个方法分为三步：(1)第一步，用混合网格周围的八个网格的介质面积份额(二维)或二十六个网格的介质体积份额(三维)确定界面的法线方向；第二步，用混合网格的本身的介质面积份额(二维)或体积份额(三维)确定界面的方程(位置)；第三步，用此直线方程求出通过网格边界的流以及下一时刻网格的面积份额(二维)或体积份额(三维)。最后给出了用此方法所做的一些数值计算及与SLIC算法的比较。     

高维线性插值方法及其在3维温度场计算中的应用

通过分析1维和2维线性插值可以推导出任意斜角直线坐标系下n维线性插值的一般计算公式以及有唯一解的条件,这一结论能够应用于三维温度场计算。可以将n维插值问题归结如下:已知n 1维空间中的n 1个点的坐标以及第n 2个点的n个坐标分量xn 2,1,x n 2,2,,xn 2,n,求解该点的第n 1个坐标分量xn 2,n 1。根据线性插值定义,第n 2个点位于前n 1个点所确定的n维超平面上。根据这一条件列写方程、求解方程可得到插值xn 2,n 1。n维插值问题有唯一解的条件是已知的n 1个点在n维空间中构成的多面体的体积不为0。推导过程在斜角直线坐标系中完成,因而结论具有较大普适性。     

等达因图象的自动采集与识别

文中提出了一种机机械扫描系统．小功率激光器、图象板、相移元件、微机和程序软件组成的等达因图象自动采集与处理系统，用灰度值比较的思想实现了等达因图象的跟踪采集。提出了四幅图象相移法实现等达因图象的自动识别。系统能快速、实时、精确和全自动地实现等达因图象的记录和分析。给出与物体内各点应力状态一一对应的位相图。并用来研究了其他实验方法困难的局部三维效应问题。     

An Iterative Method of Point Mapping under Cell Reference for the Global Analysis: Theory and a Multiscale Reference Technique

In iterative method of Point Mapping under Cell Reference, a cell co-ordinate system, called cell reference, is built to identify the subregions (cells) in the state space. When the cell reference is equipped with the so-called characteristic functions, it can work as an inspector or a recorder to derive the local dynamics of the subregions from the information provided by the trajectories passing through them. This method can retain the accuracy of the Point Mapping Method but greatly reduce the computational work. In this paper, the theoretic basis for this method is first discussed and a multiscale reference technique is then devised which can select an optimal cell reference and make the method more practicable. Finally, an example for application is presented. It is shown that the present method cannot only accurately and efficiently depict the basins of attraction of a dynamical system but also potentially detect other characteristics of the system.     

Pure liquids described as concentrated cluster dispersions

The Fulcher-Tammann-Hesse-Vogel equation, ln = A + B/(T – T ₀ ), is shown to be equivalent to the general viscosity-composition relationship, ln _r =k f /(1 – f ), for binary mixtures. The Cailletet-Mathias law of the Rectilinear Diameter is rearranged to represent a density mixture formula for two components. Temperature-independent viscosities and densities can then be calculated for dense, solid cluster fractions, dispersed in a low-density, low-viscosity non-clustered continuous phase. The cluster fraction decreases with temperature. The value ofT ₀ is shown to be related to the liquid- or solid-like behavior of the clusters. For liquids with a vapor pressure < 1 mm Hg at the melting point, the calculated cluster volume fraction suggests close packing of clusters, ranging in shape from monodisperse spheres to polydisperse non-spherical particles. Examples are given for molecular liquids, molten metals, and molten salts. The size of the clusters is estimated from the heat of evaporation.     

On Determining the Percolation Reynolds Number and the Characteristic Linear Dimension for Ideal and Fictitious Porous Media

Various versions of representations of the percolation Reynolds number for porous media with isotropic and anisotropic flow properties are considered. The formulas are derived and the variants are analyzed with reference to model porous media with a periodic microstructure formed by systems of capillaries and packings consisting of spheres of constant diameter (ideal and fictitious porous media, respectively). A generalization of the Kozeny formula is given for determining the capillary diameter in an ideal porous medium equivalent to a fictitious medium with respect to permeability and porosity and it is shown that the capillary diameter is nonuniquely determined. Relations for recalculating values of the Reynolds number determined by means of formulas proposed earlier are given and it is shown that taking the microstructure of porous media into account, as proposed in [1, 2], makes it possible to explain the large scatter of the numerical values of the Reynolds number in processing the experimental data.     

Two lower bounds for the Stanley depth of monomial ideals

Let be two monomial ideals of the polynomial ring . In this paper, we provide two lower bounds for the Stanley depth of . On the one hand, we introduce the notion of lcm number of , denoted by , and prove that the inequality holds. On the other hand, we show that , where denotes the order dimension of the lcm lattice of . We show that I and satisfy Stanley's conjecture, if either the lcm number of I or the order dimension of the lcm lattice of I is small enough. Among other results, we also prove that the Stanley–Reisner ideal of a vertex decomposable simplicial complex satisfies Stanley's conjecture.