Dual models of pore spaces

We present a model for pore spaces that consists of two parts related by duality: (1) a decomposition of an open polyhedral pore space into open contractible pore bodies separated by relatively open interfaces and (2) a pore network that is homotopy equivalent to the pore space. The dual model is unique and free of parameters, but it relies on regularity conditions for the pore space. We show how to approximate any pore space by the interior of a polyhedral complex such that the regularity conditions are fulfilled. Thus, we are able to calculate the dual model from synthetic porous media and images of real porous media. The pore bodies are unions of relatively open Delaunay cells with respect to the corners of the pore boundary, and the pore network consists of certain at most two-dimensional (2D) Voronoi cells with respect to the corners of the pore boundary. The pore network describes the neighborhood relations between the pore bodies. In particular, any relatively open 2D Delaunay face f separating two pore bodies has a unique (relatively open) dual network edge. In our model, f is a pore throat only if it is hit by its dual network edge. Thus, as opposed to widespread intuition, any pore throat is convex, and adjacent pore bodies are not necessarily separated by pore throats. Due to the duality between the pore network and the decomposition of the pore space into pore bodies it is straightforward to store the geometrical properties of the pore bodies [pore throats] as attributes of the dual network vertices [edges]. Such an attributed network is used to perform 2D drainage simulations. The results agree very well with those from a pore-morphology based modeling approach performed directly on the digital image of a porous medium. Contractibility of the pore bodies and homotopy equivalence of the pore space and the pore network is proven using discrete Morse theory and the nerve theorem from combinatorial topology.     

WAVE-CISK对称不稳定谱点分布的半圆定理

采用滞弹性近似研究了WAVE-CISK下对称性扰动的谱点分布,得到了WAVE-CISK下对称不稳定扰动谱点分布的半圆定理,用其可估计该对称不稳定增长率的上界.发现存在WAVE-CISK时加热反馈和层结参数对该不稳定的增长率均有重要影响.WAVE-CISK加热反馈越强、基流的垂直切变越大,扰动的垂直结构越简单则该不稳定增长率的上界就越大.存在WAVE-CISK时滞弹性近似下的对称不稳定发生的条件也较Boussinesq近似下的更苛刻.     

关于气象灾害笼罩面积与出现概率的一个定理

从气象图表(如天气图)上可以得到某气象灾害(如暴雨、高温,也可以是一般气象现象、要素、变量等)所笼罩的面积占总面积的百分比F,从气象资料中可以得到该气象现象的出现概率p。本文证明:F对时间的平均值等于p对天气图面积的平均值。本文初步讨论了这个定理的应用,还指出对这类问题的深入分析会引出分布函数概念和熵气象学。     

采样过程和模数转换对记录的影响及“真实地面运动”获取——地震学上用的数字信号处理的基本原理和实例(讲座3)

通过采样过程和模数转换对记录影响的分析,讨论了数字地震仪记录的动态范围,以及如何使用谱分析方法去除仪器对最终记录的影响,以便获取“真实地面运动”的近似。     

G-凸空间内的连续选择定理和重合点定理

在G-凸空间内得到了一些新的连续选择定理,并利用连续选择定理证明了非紧G-凸空间内及乘积G-凸空间内的重合点定理.这些定理改进并推广了最近文献中的一些已知结果.     

点态性质与一致性质的一个新关系

为了研究点态性质和一致性质之间的关系,应用紧性性质在拓扑意义下得到逐点有界性质蕴含一致有界性质的结论,并将其推广到连续函数族的情况.基于Baire定理,得到完备度量空间中的逐点收敛性质可导出一致有界性质的结论.     

Mohr-Coulomb准则下基于滑动面深度的边坡参数反分析方法

利用上限定理与强度折减法,提出了一种新的边坡反分析方法。该方法基于边坡的滑动面形状,不需要位移、应力等监测数据。分析边坡的临界滑动面位置与强度参数的关系,可以发现,当边坡的几何形状、土体重度以及孔隙水压力分布确定,则临界滑动面的形状只与土体黏聚力c、内摩擦角φ的关系式c/tanφ有关,并在此基础上引入边坡的无量纲系数c,λcφ。利用极限分析上限定理与强度折减法,得到了边坡临界滑动面方程,提出了其深度的计算公式,建立了边坡c,λcφ值与滑动面深度的关系。通过已有边坡的反分析实例,验证了方法的正确性和有效性。     

Quantitative perturbation theory by successive elimination of harmonics

We revisit some results of perturbation theories by a method of successive elimination of harmonics inspired by some ideas of Delaunay. On the one hand, we give a connection between the KAM theorem and the Nekhoroshev theorem. On the other hand, we support in a quantitative fashion a semi-numerical method of analysis of a perturbed system recently introduced by one of the authors.     

椭球面上绘制大地线的算法

针对传统二维线划图无法表达大区域地理要素的问题,该文提出了一种在椭球面上绘制大地线的算法。以等间距内插空间直线逼近空间曲线这一思想作为基础,通过Bessel大地主题正、反算及克莱劳方程,实现大地线内插与绘制的综合分析与解算。实验结果表明,该方法较好地解决了在参考椭球面上难以精确绘制大地线的问题,对传统地图向三维椭球面线划图的转换与应用具有一定的参考价值。