Related papers: Local one-side porosity and pretangent spaces
We define and study the completely strongly porous at 0 subsets of R^{+}. Several characterizations of these subsets are obtained, among them the description via an universal property and structural one.
A scaling theory is developed for diffusion-limited cluster aggregation in a porous medium, where the primary particles and clusters stick irreversibly to the walls of the pore space as well as to each other. Three scaling regimes are…
Porosity and dimension are two useful, but different, concepts that quantify the size of fractal sets and measures. An active area of research concerns understanding the relationship between these two concepts. In this article we will…
The paper discusses local porosity theory and its relation with other geometric characterization methods for porous media such as correlation functions and contact distributions. Special emphasis is placed on the charcterization of…
Local porosity distributions for a three-dimensional porous medium and local porosity distributions for a two-dimensional plane-section through the medium are generally different. However, for homogeneous and isotropic media having finite…
A quantitative comparison of the pore space geometry for three natural sandstones is presented. The comparison is based on local porosity theory which provides a geometric characterization of stochastic microstructures. The characterization…
Partially ordered sets (posets) play a universal role as an abstract structure in many areas of mathematics. For finite posets, an explicit enumeration of distinct partial orders on a set of unlabelled elements is known only up to a…
We introduce a multiscale test statistic based on local order statistics and spacings that provides simultaneous confidence statements for the existence and location of local increases and decreases of a density or a failure rate. The…
Scaling describes how a given quantity $Y$ that characterizes a system varies with its size $P$. For most complex systems it is of the form $Y\sim P^\beta$ with a nontrivial value of the exponent $\beta$, usually determined by regression…
We apply a probabilistic approach to study the computational complexity of analog computers which solve linear programming problems. We analyze numerically various ensembles of linear programming problems and obtain, for each of these…
We present a first procedure that can estimate -- with statistical consistency guarantees -- any local-maxima of a density, under benign distributional conditions. The procedure estimates all such local maxima, or $\textit{modal-sets}$, of…
A stronger foundation for earlier work on the effects of number scaling, and local mathematics is described. Emphasis is placed on the effects of scaling on coordinate systems. Effects of scaling are represented by a scalar field, $\theta,$…
In cluster analysis, a common first step is to scale the data aiming to better partition them into clusters. Even though many different techniques have throughout many years been introduced to this end, it is probably fair to say that the…
We introduce local iterated function systems and present some of their basic properties. A new class of local attractors of local iterated function systems, namely local fractal functions, is constructed. We derive formulas so that these…
The most common statistic used to analyze large-scale structure surveys is the correlation function, or power spectrum. Here, we show how `slicing' the correlation function on local density brings sensitivity to interesting non-Gaussian…
The introduced notion of locally-periodic two-scale convergence allows to average a wider range of microstructures, compared to the periodic one. The compactness theorem for the locally-periodic two-scale convergence and the…
We show how to use numerical methods within the framework of successive scaling to analyse the microstructure of turbulence, in particular to find inertial range exponents and structure functions. The methods are first calibrated on the…
In this paper, we extend our previous work on the study of local scales of a function to studying local scales on curves and surfaces. In the case of a function f, the local scales of f at x is computed by measuring the deviation of f from…
We construct a family of closeness functions on the space of finite volume Lorentzian geometries using the abundance of discrete intervals in the underlying random causal sets. Although strictly weaker than a Lorentzian Gromov-Hausdorff…
In a companion paper, equations for partially molten media were derived using two-scale homogenization theory. One advantage of homogenization is that material properties, such as permeability and viscosity, readily emerge. A caveat is that…