Showing papers by "Volker Schmidt published in 2009"

The effect of three-dimensional morphology on the efficiency of hybrid polymer solar cells

Abstract: The efficiency of polymer solar cells critically depends on the intimacy of mixing of the donor and acceptor semiconductors used in these devices to create charges and on the presence of unhindered percolation pathways in the individual components to transport holes and electrons. The visualization of these bulk heterojunction morphologies in three dimensions has been challenging and has hampered progress in this area. Here, we spatially resolve the morphology of 2%-efficient hybrid solar cells consisting of poly(3-hexylthiophene) as the donor and ZnO as the acceptor in the nanometre range by electron tomography. The morphology is statistically analysed for spherical contact distance and percolation pathways. Together with solving the three-dimensional exciton-diffusion equation, a consistent and quantitative correlation between solar-cell performance, photophysical data and the three-dimensional morphology has been obtained for devices with different layer thicknesses that enables differentiating between generation and transport as limiting factors to performance.

Local Structural Characteristics of Pore Space in GDLs of PEM Fuel Cells Based on Geometric 3D Graphs

Abstract: Physical properties affecting transport processes inside the gas diffusion layer (GDL) in polymer electrolyte membrane (PEM) fu cells mainly depend on the microstructure of its pore space. The presented characterization of the complex structure of the po space is based on geometric three-dimensional (3D) graphs, which are marked to display transport-related properties such as po diameters. This representation of the open volume allows for an investigation of local structural characteristics by considering local tortuosity characteristics, pore sizes, and connectivity characteristics, respectively. The notion of local shortest path leng through the pore space of the GDL is introduced and the probability distribution of this random variable is computed. Its mean value is related to the (physical) tortuosity, which is given by the ratio of the mean effective path length through the GDL and i thickness. The developed methods are applied to simulated and to real (experimentally measured) 3D data. The used stochastic 3 model for the GDL is an extended version of the multilayer model proposed by Thiedmann et al. [J. Electrochem. Soc., 155, B39 (2008)], including a more flexible modeling of binder. The numerical results show the sensitivity of the proposed local chara teristics to varying binder modeling.

Distributional properties of euclidean distances in wireless networks involving road systems

Abstract: Stochastic models for hierarchical telecommunication networks are considered, which can be applied to the analysis and planning of large wireless networks. The network geometry is modelled by random geometric graphs, and the locations of network nodes by point processes on the edges of these graphs. In particular, the locations of high-level components (HLC) are modeled by Cox processes concentrated on the edge sets of random graphs, where their serving zones are the cells of Voronoi tessellations induced by these Cox processes. The locations of low-level components (LLC) are either modeled by planar Poisson processes or by Cox processes concentrated on the same edge sets as the HLC. Distributional properties of distances between the locations of network nodes are closely related with the interference geometry and, consequently, the performance of wireless networks. Representation formulas are derived for the distribution function and density of the typical Euclidean connection distance between LLC and HLC. They lead to suitable estimators of these characteristics, which can be computed by Monte Carlo simulation of the typical serving zone and the typical segment system in it, respectively.

Structural analysis of dialect maps using methods from spatial statistics

Abstract: In 1898, Karl Haag (HAAG 1898) introduced a new method of displaying dialect differences on a map. In the maps that he drew, the thickness of a line between two places indicates how different the dialects spoken on both sides of the line are, thus summing up the data of several dialect feature maps, each of which provides the realisations of one linguistic feature in space. This was the first step towards a quantitative dialectology, going along with other linguistic disciplines such as lexicography, phonetics, or historical linguistics (cf. KÖHLER ET AL. 2005, BEST 2006). The dialectometrical approaches developed since then have put forth a wide range of methods, all of which are based on the measuring of dialect distance (the grade to which the dialects in two places differ), which is essential for all further dialectometrical investigation. Up to the 1970s, this was done exclusively by counting the dialectal differences between all neighbouring places, a method that Jean Séguy adapted from Haag for the Atlas linquistique et ethnographique de la Gascogne (SÉGUY 1965–1973), the first major dialectometrical project. In the 1970s, Hans Goebl was the first scholar to extend this method – the counting of differences – to all possible pairs of places, not only neighbours, and developed a broad spectrum of advanced methods of visual presentation and of analysis, such as different kinds of cluster analysis or coherence tests (see, for example, GOEBL 1994, 2001, 2006, 2007). The subsequent dialectometrical approaches are based on Goebl’s method (KELLE 1986, HUMMEL 1993, SCHILTZ 1996, and others). The next major step was made by John Nerbonne and Wilbert Heeringa, who introduced a new way to measure the dialectal distance into Goeblian dialectometry: they used an adapted version of the so-called Levenshtein-distance to measure phonetic distance and were thus the first to take into account gradual similarities between records, not only identity or non-identity, and they also greatly contributed new analysis methods such as multi-dimensional scaling or factor analysis (e.g. NERBONNE AND HEERINGA 1998, HEERINGA 2004, NERBONNE 2006). There are various other methods which are dialectometrical in the sense of ‘quantitative

On the Expected Surface Area of the Wiener Sausage

Abstract: For parallel neighborhoods of the paths of the d -dimensional Brownian motion, so-called Wiener sausages, formulae for the expected surface area are given for any dimension d ≥ 2. It is shown by means of geometric arguments that the expected surface area is equal to the first derivative of the mean volume of the Wiener sausage with respect to its radius (© 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Tropical cyclone hazard assessment using model-based track simulation

Abstract: A method is introduced for assessing the probabilities and intensities of tropical cyclones at landfall and applied to data from the North Atlantic. First, a recently developed model for the basin-wide Monte-Carlo simulation of tropical cyclone tracks is enhanced and transferred to the North Atlantic basin. Subsequently, a large number of synthetic tracks is generated by means of an implementation of this model. This synthetic data is far more comprehensive than the available historical data, while exhibiting the same basic characteristics. It, thus, creates a more sound basis for assessing landfall probabilities than previously available, especially in areas with a low historical landfall frequency.

Parametric distance distributions for fixed access network analysis and planning

Abstract: The access network displays the important particularity that the locations of the network components strongly depend on geometrical features such as road systems and city's architecture. This paper presents a model for access networks arising from stochastic geometry, which takes this geometric structure into consideration, and thus offers a relevant view on location-dependent characteristics such as point-to-point connections as shortest paths along the road system. Closed analytical formulas are derived for point-to-point distance distributions, explicitly depending on the morphology of this road system. Theoretical predictions are successfully compared to real data from fixed access networks deployed in dense urban areas.

Scaling limits for shortest path lengths along the edges of stationary tessellations - Supplementary material

Abstract: We consider spatial stochastic models, which can be applied e.g. to telecommunication networks with two hierarchy levels. In particular, we consider two Cox processes concentrated on the edge set of a random tessellation, where the points can describe the locations of low-level and high-level network components, respectively, and the edge set the underlying infrastructure of the network, like road systems, railways, etc. Furthermore, each low-level component is marked with the shortest path along the edge set to the nearest high-level component. We investigate the typical shortest path length of the resulting marked point process, which is an important characteristic e.g. in performance analysis and planning of telecommunication networks. In particular, we show that its distribution converges to simple parametric limit distributions if a certain scaling factor converges to zero and infinity, respectively. This can be used to approximate the density of the typical shortest path length by analytical formulae.

Statistical analysis of labelling patterns of mammary carcinoma cell nuclei on histological sections.

Abstract: It is of central interest for tumour biology to explore the mechanisms of tumour cell proliferation. In this study, methods of spatial statistics were used to study the spatial distribution of proliferating cells within tumour tissue quantitatively and objectively. Mammary cancer tissue was studied as an example. It was attempted to clarify whether cell division occurs entirely at random (random labelling), i.e. the process of division occurs at random, independently from the state of the neighbouring nuclei, or whether the spatial distribution of proliferation is more complex, e.g. in the form of actively proliferating clusters alternating with relatively silent zones. In the case of random labelling, the reduced second moment functions K(r) of the labelled and the unlabelled nuclei would be identical. The same would hold for the pair correlation functions g(r). The alternative hypothesis is that the second-order properties of the processes of the labelled and the unlabelled nuclei are different. Twenty cases of invasive ductal mammary carcinomas were studied. The nuclei of proliferating cells were stained immunohistochemically with the monoclonal antibody MIB-1, which detects specifically the proliferation-associated nuclear antigen Ki 67. The planar coordinates of the tumor cell nucleus profiles from two rectangular visual fields per case were recorded. For each visual field, the following investigations were performed: estimation of the explorative summary characteristics K(r) and g(r), fitting of the parameters of a stationary Strauss hard-core model to the observed point patterns, estimation of two distance-dependent Simpson indices and Monte Carlo tests of all individual patterns on the null hypothesis of random labelling. Significant differences between the mean K-functions and the mean g-functions of the labelled and the unlabelled nuclei were found. Moreover, the mean interaction parameter gamma of the stationary Strauss hard-core model was significantly higher for the labelled nuclei than for the unlabelled nuclei. The estimates of the two distance-dependent Simpson indices showed a tendency of points with the same label towards a positive spatial correlation. In the Monte Carlo tests, the null hypothesis of random labelling was rejected for the majority of the visual fields. These four lines of investigation led to the concordant conclusion that the labelling of mammary carcinoma nuclei by MIB-1 is not simply random. The data suggest that the second-order properties of the point process of the labelled nuclei are significantly different from those of the unlabelled nuclei. In particular, the process of the labelled nuclei shows a higher degree of clustering (increased strength of interaction) than the process of the unlabelled points.

Simulation of the typical Poisson–Voronoi–Cox–Voronoi cell

Abstract: We consider stationary Poisson–Voronoi tessellations (PVT) in the Euclidean plane and study the properties of Voronoi tessellations induced by linear Poisson processes on the edges of the PVT. We are especially interested in simulation algorithms for the typical cell. Two different simulation algorithms are introduced. The first algorithm directly simulates the typical cell, whereas the second algorithm simulates cells from which distributional properties of the typical cell can be obtained. This second algorithm can also be used for simulating the typical cell of other Cox–Voronoi tessellations. The implementation of both algorithms is tested for their correctness using random software tests. Then different cell characteristics are studied by simulation and compared with the typical cell of PVT and Cox–Voronoi tessellations based on linear Poisson processes on the lines of Poisson line processes. Our results can be applied, for example, in the analysis of telecommunication networks and vesicle paths on c...

Myc Regulates Embryonic Vascular Permeability and Remodeling

Abstract: Previous work has shown that c-Myc is required for adequate vasculogenesis and angiogenesis. To further investigate the contribution of Myc to these processes, we conditionally expressed c-Myc in embryonic endothelial cells using a tetracycline-regulated system. Endothelial Myc overexpression resulted in severe defects in the embryonic vascular system. Myc-expressing embryos undergo widespread edema formation and multiple hemorrhagic lesions. They die between embryonic days 14.5 and 17.5. The changes in vascular permeability are not caused by deficiencies in vascular basement membrane composition or pericyte coverage. However, the overall turnover of endothelial cells is elevated as is revealed by increased levels of both proliferation and apoptosis. Whole-mount immunohistochemical analysis revealed alterations in the architecture of capillary networks. The dermal vasculature of Myc-expressing embryos is characterized by a reduction in vessel branching, which occurs despite upregulation of the proangiogenic factors vascular endothelial growth factor-A and angiopoietin-2. Thus, the net outcome of an excess of vascular endothelial growth factor-A and angiopoietin-2 in the face of an elevated cellular turnover appears to be a defect in vascular integrity.

Kriged Road-Traffic Maps

Abstract: A kriging based on residuals is employed for spatial extrapolation of anisotropic directional road–traffic data. The set of data considered in the present paper includes, among others, the actual geographic positions and velocities of approximately 300 test vehicles in downtown Berlin. They are transmitted to a central station within regular time intervals. The main idea of the extrapolation technique is to interpret the recorded velocities as realizations of a random velocity field, which is sampled at selected points only. Structural properties of the resulting road–traffic maps are discussed combined with a statistical space–time analysis of polygonal traffic trajectories extracted from the original traffic data. Finally, a brief outlook to simulation and prediction of future traffic states is provided.

Palm calculus for stationary Cox processes on iterated random tessellations

Abstract: We investigate Cox processes of random point patterns in the Euclidean plane, which are located on the edges of random geometric graphs. Such Cox processes have applications in the performance analysis and strategic planning of both wireless and wired telecommunication networks. They simultaneously allow to represent the underlying infrastructure of the network together with the locations of network components. In particular, we analyze the Palm version X* of stationary Cox processes X living on random graphs that are built by the edges of an iterated random tessellation T. We derive a representation formula for the Palm version T* of T which includes the initial tessellation T 0 and the component tessellation T 1 of T as well as their Palm versions T* 0 and T* 1 . Using this formula, we are able to construct a simulation algorithm for X* if both T 0 , T 1 and their Palm versions T* 0 , T* 1 can be simulated. This algorithm for X* extends earlier results for Cox processes on simpler (non-iterated) tessellations. It can be used, for example, in order to estimate the probability densities of various connection distances, which are important performance characteristics of telecommunication networks. In a numerical study we consider the particular case that T 0 is a Poisson-Voronoi tessellation and T 1 is a Poisson line tessellation.

Modelling tree roots in mixed forest stands by inhomogeneous marked Gibbs point processes.

Abstract: The aim of the paper is to apply point processes to root data modelling. We propose a new approach to parametric inference when the data are inhomogeneous replicated marked point patterns. We generalize Geyer's saturation point process to a model, which combines inhomogeneity, marks and interaction between the marked points. Furthermore, the inhomogeneity influences the definition of the neighbourhood of points. Using the maximum pseudolikelihood method, this model is then fitted to root data from mixed stands of Norway spruce (Picea abies (L.) Karst.) and European beech (Fagus sylvatica L.) to quantify the degree of root aggregation in such mixed stands. According to the analysis there is no evidence that the two root systems are not independent.

Micro-Scale Transport in the Diffusion Media of Polymer Electrolyte Fuel Cells

Abstract: This paper reports our recent work on the stochastic-model-based reconstruction of the gas diffusion layer (GDL) of PEFCs and direct numerical simulation and presented the pore-level transport within GDLs of polymer electrolyte fuel cell (PEFC). The carbon-paper-based GDL is modeled as a stack of thin sections with each section described by planar 2D random line tessellations which are further dilated to three dimensions. The reconstruction of the GDL structure is based on given GDL data provided by scanning electron microscopy (SEM) images. Based on the stochastically constructed digital GDL, we further conduct the DNS of the coupled transport processes, including gas flow and species transport, electronic current conduction, and heat transfer. Results indicate remarkable distinction in tortuosities of gas diffusion passage and solid matrix. The numerical tool can be applied to investigate the GDL microstructure and internal pore-level transport in PEFCs.Copyright © 2009 by ASME