Dual models of pore spaces     

Roland Glantz  Markus Hilpert 《Advances in water resources》2007

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.  相似文献   

Solution to the Stokes Boundary-Value Problem on an Ellipsoid of Revolution   总被引：1，自引：0，他引：1  

Martinec  Z.  Grafarend  E. W. 《Studia Geophysica et Geodaetica》1997,41(2):103-129

We have constructed Green's function to Stokes's boundary-value problem with the gravity data distributed over an ellipsoid of revolution. We show that the problem has a unique solution provided that the first eccentricity e₀ of the ellipsoid of revolution is less than 0·65041. The ellipsoidal Stokes function describing the effect of ellipticity of the boundary is expressed in the E-approximation as a finite sum of elementary functions which describe analytically the behaviour of the ellipsoidal Stokes function at the singular point = 0. We prove that the degree of singularity of the ellipsoidal Stokes function in the vicinity of its singular point is the same as that of the spherical Stokes function.  相似文献   

Hamiltonian perturbation theory on a manifold     

Francesco Fassò 《Celestial Mechanics and Dynamical Astronomy》1995,62(1):43-69

This paper deals with Hamiltonian perturbation theory for systems which, like Euler-Poinsot (the rigid body with a fixed point and no torques), are degenerate and do not possess a global system of action-angle coordinates. It turns out that the usual methods of perturbation theory, which are essentially local being based on the construction of normal forms within the domain of a local coordinate system, are not immediately usable to study perturbations of these systems, since degeneracy makes impossible to control that the system does not fall into a singularity of the coordinates. To overcome this difficulty, we develop a global formulation of Hamiltonian perturbation theory, in which the normal forms are globally defined on the phase space manifold. The key for this study lies in the geometry of the fibration by the invariant tori of an integrable degenerate Hamiltonian system, which is described by some generalizations of the Liouville-Arnol'd theorem and is reviewed in the paper. As an application, we provide a global formulation of Nekhoroshev's theorem on the stability for exponentially long times.  相似文献   

Applicability of a Backprojection Algorithm to Reconstruct Images of Subsurface Horizontal Planes for Laboratory Experiments in Electrical Resistance Tomography     

Josep Jordana  Ramon Pallàs-Areny 《Mathematical Geology》2004,36(1):127-141

This paper describes the use of a backprojection algorithm to reconstruct subsurface images of the electrical resistivity in horizontal planes parallel to the surface. The algorithm can be applied to detect buried objects such as tanks or pipes and possible leakages from them. Two imaging strategies are compared: juxtaposition of vertical planes, and 3D reconstruction from the sensitivity matrix corresponding to the entire volume whose surface is explored. The electrode arrays used for voltage measurement are the dipole–dipole array and a modified Schlumberger array. A personal computer controls current injection, electrode switching, and voltage detection. The system injects 1 kHz, 20 V peak-to-peak square waveforms, thus avoiding electrode polarization effects. Experimental laboratory measurements show that the algorithm detects localized objects such as an insulating sphere and a conductive cylinder immersed in water. Furthermore, covering half of the cylinder by a rubber sleeve to simulate a nonconductive leak, yields a distinct image for the leak. The backprojection algorithm does not need any regularization parameter and it is very fast in inverting the sensitivity matrix because it approximates the inverse matrix by its transposed. The dipole–dipole array usually yields a lower overall pixel error than the modified Schlumberger array but both allow the detection of simulated underground leaks.  相似文献   

矢量地形图拓扑等问题的研究与实践     

赵明  王庆  陈昕  鞠建荣  张凤梅 《现代测绘》2004,27(5):44-45,48

对矢量地图生产过程中常见的图形拓扑、数据冗余问题进行分析和研究；在此基础上结合生产实践，提出了相应的解决办法。研制了基于AutoCAD2000平台的相关程序。  相似文献   

地图扫描采样分辨率的研究   总被引：8，自引：2，他引：6  

林宗坚 《测绘科学》2000,25(1):13-15

本文提醒注意在当前国内生产中常被忽视的地图扫描采样分辨率问题 ,从理论上分析了采样分辨率过低所造成的成果质量问题 ,并提出工程实践中可操作的方法建议。  相似文献   

ArcGIS在矢量测绘数据质量控制中的应用     

谭福初  裴亚波  李广兰 《北京测绘》2007,(4):45-47

GIS应用和信息化测绘发展对测绘数据质量提出更高要求,本文通过对矢量测绘数据质量要素控制的简单分析,详细介绍了实际工作中运用ArcGIS对主要的质量要素进行控制检查的方法和步骤,对实施矢量测绘数据的质量控制具有实际意义。  相似文献   

Macrodynamics of α2 dynamos     

Glenn R. Ierley 《地球物理与天体物理流体动力学》2013,107(1-4):143-173

Abstract

Two distributions of the α-effect in a sphere are considered. The inviscid limit is approached both by direct numerical solution and by solution of a simpler nonlinear eigenvalue problem deriving from asymptotic boundary layer analysis for the case of stress-free boundaries. The inviscid limit in both cases is dominated by the need to satisfy the Taylor constraint which states that the integral of the Lorentz force over cylindrical (geostrophic) contours in a homogeneous fluid must tend to zero. For a small supercritical range in α, this condition can only be met by magnetic fields which vanish as the viscosity goes to zero. In this range, the agreement of the two approaches is excellent. In a portion of this range, the method of finite amplitude perturbation expansion is useful, and serves as a guide for understanding the numerical results. For larger α, evidence from the nonlinear eigenvalue problem suggests both that the Taylor state exists, and that the transition from small to large amplitude can require a finite amplitude (oscillatory) instability in accord with the findings of Soward and Jones (1983). However, solutions of the full equations have not been found which are independent of viscosity at larger values of α.  相似文献   

Land cover classification by an artificial neural network with ancillary information     

Giles M. Foody 《International journal of geographical information science》2013,27(5):527-542

Abstract

Remote sensing is an important source of land cover data required by many GIS users. Land cover data are typically derived from remotely–sensed data through the application of a conventional statistical classification. Such classification techniques are not, however, always appropriate, particularly as they may make untenable assumptions about the data and their output is hard, comprising only the code of the most likely class of membership. Whilst some deviation from the assumptions may be tolerated and a fuzzy output may be derived, making more information on class membership properties available, alternative classification procedures are sometimes required. Artificial neural networks are an attractive alternative to the statistical classifiers and here one is used to derive a fuzzy classification output from a remotely–sensed data set that may be post–processed with ancillary data available in a GIS to increase the accuracy with which land cover may be mapped. With the aid ancillary information on soil type and prior knowledge of class occurrence the accuracy of an artificial neural network classification was increased by 29–93 to 77–37 per cent. An artificial neural network can therefore be used generate a fuzzy classification output that may be used with other data sets in a GIS, which may not have been available to the producer of the classification, to increase the accuracy with which land cover may be classified.  相似文献   

点态性质与一致性质的一个新关系     

蔡龙生  吴定平  史沧红 《成都信息工程学院学报》2014,(2):195-198

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.  相似文献