Showing papers by "Volker Schmidt published in 2008"

Stochastic 3D Modeling of the GDL Structure in PEMFCs Based on Thin Section Detection

Abstract: We propose a mathematical model to describe the microstructure of the gas diffusion layer (GDL) in proton exchange membrane fuel cells (PEMFCs) based on tools from stochastic geometry. The GDL is considered as a stack of thin sections. This assumption is motivated by the production process and the visual appearance of relevant microscopic images. The thin sections are modeled as planar [two-dimensional (2D)] random line tessellations which are dilated with respect to three dimensions. Our 3D model for the GDL consists of several layers of these dilated line tessellations. We also describe a method to fit the proposed model to given GDL data provided by scanning electron microscopy images which can be seen as 2D projections of the 3D morphology. In connection with this, we develop an algorithm for the segmentation of such images which is necessary to obtain the required structural information from the given grayscale images.

Simulation algorithm of typical modulated Poisson-Voronoi cells and application to telecommunication network modelling

Abstract: We consider modulated Poisson-Voronoi tessellations, intended as models for telecommunication networks on a nationwide scale. By introducing an algorithm for the simulation of the typical cell of the latter tessellation, we lay the mathematical foundation for such a global analysis. A modulated Poisson-Voronoi tessellation has an intensity which is spatially variable and, hence, is able to provide a broad spectrum of model scenarios. Nevertheless, the considered tessellation model is stationary and we consider the case where the modulation is generated by a Boolean germ-grain model with circular grains. These circular grains may either have a deterministic or random but bounded radius. Furthermore, based on the introduced simulation algorithm for the typical cell and on Neveu’s exchange formula for Palm probability measures, we show how to estimate the mean distance from a randomly chosen location to its nearest Voronoi cell nucleus. The latter distance is interpreted as an important basic cost characteristic in telecommunication networks, especially for the computation of more sophisticated functionals later on. Said location is chosen at random among the points of another modulated Poisson process where the modulation is generated by the same Boolean model as for the nuclei. The case of a completely random placement for the considered location is thereby included as a special case. The estimation of the cost functional is performed in a way such that a simulation of the location placement is not necessary. Test methods for the correctness of the algorithm based on tests for random software are briefly discussed. Numerical examples are provided for characteristics of the typical cell as well as for the cost functional. We conclude with some remarks about extensions and modifications of the model regarded in this paper, like modulated Poisson—Delaunay tessellations.

An investigation of the spatial correlations for relative purchasing power in Baden–Württemberg

Abstract: The relative purchasing power—i.e., the purchasing power per inhabitant—is one of the key characteristics for businesses deciding on site selection. Apart from that it also plays a major role in regional planning, pricing policy and market research. In this study we investigate the spatial correlations for relative purchasing power of the townships in Baden–Wurttemberg. In particular, changes in relative purchasing power are analysed for three different time intervals, 1987–1993, 1993–1998 and 1998–2004, by means of distance-dependent characteristics like the mark–correlation function, the Simpson indices α(r) and β(r) and by tests on random labelling. It is shown that there are positive correlations for small distances between different townships but that these positive correlations become weaker over the years until they are almost nonexistent (in the sense that hypotheses of random labelling are no longer rejected). A conclusion from this loss of spatial correlations with time is that the relative purchasing power might become more and more purely random. This means that the relative purchasing power in a township is less and less influenced by the relative purchasing power of townships nearby. We further analysed these changes in the Bodensee–Oberschwaben and Stuttgart regions to compare the development of the relative purchasing power in both urban and rural environments.

The Laplacian in a stochastic model for spatiotemporal reaction systems

Abstract: We demonstrate how the Laplace operator can be combined with a stochastic jump process to describe the evolution of a polymer network. Growth processes in polymer networks can proceed through the transfer of rather large oligomeric subunits from a pool of soluble molecules into the laments forming the network. In such a situation stochastic jump processes are a natural tool for the description of network formation at the nanometer scale. However, modeling of the reaction system in high spatiotemporal resolution also needs to capture the evolution of the soluble lament precursor molecules, which controls local properties of the growth process. We illustrate how this may be achieved by combining a deterministic di usion equation with a stochastic jump process within the setting of a piecewise-deterministic Markov process. Since in many applications the di usion equation will be considered with periodic boundary conditions, we apply the theory of bilinear forms to prove existence and uniqueness of a solution, which is also shown to be positive, mass-preserving, and convergent to an equilibrium.

Wiley Series in Probability and Statistics Established by Walter A. Shewhart and Samuel S. Wilks

Abstract: The Wiley Series in Probability and Statistics is well established and authoritative. It covers many topics of current research interest in both pure and applied statistics and probability theory. Written by leading statisticians and institutions, the titles span both state-of-the-art developments in the field and classical methods. Reflecting the wide range of current research in statistics, the series encompasses applied, methodological and theoretical statistics, ranging from applications and new techniques made possible by advances in computerized practice to rigorous treatment of theoretical approaches. This series provides essential and invaluable reading for all statisticians, whether in academia, industry, government, or research.

Three-dimensional analysis of the intermediate filament network using SEM-tomography

Abstract: Pancreatic cancer is characterized by its early infiltration of adjacent tissue. There is a correlation between the keratin filament network structure and the migration ability of cells [1]. In earlier papers we quantitatively investigated two-dimensional images of the three-dimensional keratin network [2]. It is the goal of our ongoing research to expand these studies to three-dimensional datasets. We investigated, therefore, intermediate filaments from detergent-extracted cells by SEM-tomography.