Volker Schmidt

Universität Ulm, Ulm, Baden-Württemberg, Germany

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Publications (136)301.89 Total impact

  • [Show abstract] [Hide abstract]
    ABSTRACT: In meteorology it is important to compute the probabilities of certain weather events occurring. There are a number of numerical and statistical methods for estimating the probability that a weather event occurs at a fixed location (a point). However, there are no widely applicable techniques for estimating the probability of such an event occurring in a geographical region (an area). In this paper, we propose a model-based approach for the computation of area probabilities using point probabilities. We develop this approach in the context of estimating the probability of the meteorological event ‘occurrence of precipitation’. We treat the point and area probabilities as coverage probabilities of a germ–grain model, where the grains can roughly be interpreted as precipitation cells. The germ–grain model is completely characterized by a sequence of local intensities and a grain size. We compute these model characteristics using available point probabilities. A non-negative least-squares approach is used to determine the local intensities and a semivariogram estimation technique is used to find the grain size. We are then able to determine area probabilities either analytically or by repeated simulation of the germ–grain model. We validate our model, using radar observations to assess the precision of the computed probabilities.
  • Gerd Gaiselmann, Rafal Kulik, Volker Schmidt
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    ABSTRACT: This paper deals with statistical inference on the parameters of a stochastic model, describing curved fibrous objects in three dimensions, that is based on multivariate autoregressive processes. The model is fitted to experimental data consisting of a large number of short independently sampled trajectories of multivariate autoregressive processes. We discuss relevant statistical properties (e.g. asymptotic behaviour as the number of trajectories tends to infinity) of the maximum likelihood (ML) estimators for such processes. Numerical studies are also performed to analyse some of the more intractable properties of the ML estimators. Finally the whole methodology, i.e., the fibre model and its statistical inference, is applied to appropriately describe the tracking of fibres in real materials.
    Australian &amp New Zealand Journal of Statistics 03/2015; 57(1). DOI:10.1111/anzs.12102 · 0.53 Impact Factor
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    ABSTRACT: Organic electronic devices are often made by solution processing a multi-component ink. During solution processing, for example, via spin coating, the solvent evaporates and the solid components deposit on the substrate. The morphology of this layer can range from well-mixed to extensively phase separated. To optimize device performance, it is essential to control the degree and dominant length scale of phase separation. Currently, the mechanism of phase separation induced by solvent evaporation is poorly understood. It has been shown that length scales are influenced by spin speed, drying time, final layer thickness and the ratio between the solid components, but a complete experimental dataset and consistent theoretical understanding are lacking. In this contribution, in situ measurements during spin coating and a simple numerical model are used to understand the drying process. In addition, an advanced image analysis of transmission electron micrographs of films processed under a wide range of processing conditions is carried out. A normalized drying rate is proposed as the key parameter that controls the dominant length scale of phase separation.
    Advanced Functional Materials 02/2015; 25(6):855-863. DOI:10.1002/adfm.201403392 · 10.44 Impact Factor
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    ABSTRACT: Mechanical stress-strain curves are estimated by means of numerical simulation in order to analyze and compare the mechanical properties of a real Strontium-modified Al-Si alloy with virtually designed materials. The virtual materials are generated by a competitive stochastic growth model of the 3D coral-like morphology of the eutectic Si in Al-Si alloys. The experimental data for the real material was acquired using FEB/SEM tomography. The numerical simulations are based on finite element methods. The effects of coarsening the mesh size and using different degrees of the finite elements are discussed. The simulations show that there is high conformity between the mechanical properties of the real and virtual materials. Experiments are also performed to show that the mechanical behavior of the realizations of the stochastic model is sensitive to changes in the parameters that control the morphological characteristics of the Si component.
    Archive of Applied Mechanics 01/2015; DOI:10.1007/s00419-014-0956-5 · 1.44 Impact Factor
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    ABSTRACT: We carry out Monte Carlo experiments to study the scaling behavior of shortest path lengths in continuum percolation. These studies suggest that the critical exponent governing this scaling is the same for both continuum and lattice percolation. We use splitting, a technique that has not yet been fully exploited in the physics literature, to increase the speed of our simulations. This technique can also be applied to other models where clusters are grown sequentially.
    Journal of Physics A Mathematical and Theoretical 12/2014; 47(50):505003. DOI:10.1088/1751-8113/47/50/505003 · 1.77 Impact Factor
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    Lothar Heinrich, Sebastian Lück, Volker Schmidt
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    ABSTRACT: We consider spatially homogeneous marked point patterns in an unboundedly expanding convex sampling window. Our main objective is to identify the distribution of the typical mark by constructing an asymptotic $\chi^2$-goodness-of-fit test. The corresponding test statistic is based on a natural empirical version of the Palm mark distribution and a smoothed covariance estimator which turns out to be mean square consistent. Our approach does not require independent marks and allows dependences between the mark field and the point pattern. Instead we impose a suitable $\beta$-mixing condition on the underlying stationary marked point process which can be checked for a number of Poisson-based models and, in particular, in the case of geostatistical marking. In order to study test performance, our test approach is applied to detect anisotropy of specific Boolean models.
    Bernoulli 10/2014; 20(4). DOI:10.3150/13-BEJ523 · 1.30 Impact Factor
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    ABSTRACT: Focused ion beam tomography has proven to be capable of imaging porous structures on a nano-scale. However, due to shine-through artefacts, common segmentation algorithms often lead to severe dislocation of individual structures in z-direction. Recently, a number of approaches have been developed, which take into account the specific nature of focused ion beam-scanning electron microscope images for porous media. In the present study, we analyse three of these approaches by comparing their performance based on simulated focused ion beam-scanning electron microscope images. Performance is measured by determining the amount of misclassified voxels as well as the fidelity of structural characteristics. Based on this analysis we conclude that each algorithm has certain strengths and weaknesses and we determine the scenarios for which each approach might be the best choice.
    Journal of Microscopy 09/2014; 257(1). DOI:10.1111/jmi.12182 · 1.63 Impact Factor
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    ABSTRACT: We consider a spatial stochastic model for the simulation of tropical cyclone tracks, which has recently been introduced. Cyclone tracks are represented as labeled polygonal lines, which are described by the movement directions, translational speeds, and wind speeds of the cyclones in regular 6-h intervals. In the present paper, we compare return levels for wind speeds of historically observed cyclone tracks with those generated by the simulator, where a mismatch is shown for most of the considered coastal regions. To adjust this discrepancy, we develop a stochastic algorithm for acceptance and rejection of simulated cyclone tracks with landfall. It is based on the fact that the locations, translational speeds, and wind speeds of cyclones at landfall constitute three-dimensional Poisson point processes, which are a basic model type in stochastic geometry. Due to that, a well-known thinning property of Poisson processes can be applied. This means that to each simulated cyclone, an acceptance probability is assigned, which is higher for cyclones with suitable landfall characteristics and lower for implausible ones. More intuitively, the algorithm comprises the simulation of a more comprehensive cyclone event set than needed and the random selection of those tracks that best match historical observations at landfall. A particular advantage of our algorithm is its applicability to multiple landfalls, i.e., to cyclones that successively make landfall at two geographically distinct coastlines, which is the most relevant case in applications. It turns out that the extended simulator provides a much better accordance between landfall characteristics of historical and simulated cyclone tracks.
    Natural Hazards 09/2014; 73(2). DOI:10.1007/s11069-014-1075-x · 1.96 Impact Factor
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    ABSTRACT: A new algorithmic approach to segmentation of highly porous three dimensional image data gained by focused ion beam tomography is described which extends the key-principle of local threshold backpropagation described in [1]. The technique of focused ion beam tomography has shown to be capable of imaging the microstructure of functional materials. In order to perform a quantitative analysis on the corresponding microstructure a segmentation task needs to be performed. However, algorithmic segmentation of images obtained with focused ion beam tomography is a challenging problem for highly porous materials if filling the pore phase, e.g. with epoxy resin, is difficult. The grey intensities of individual voxels are not sufficient to determine the phase represented by them and usual thresholding methods are not applicable. We thus propose a new approach to segmentation, that pays respect to the specifics of the imaging process of focused ion beam tomography. As an application of our approach, the segmentation of three dimensional images for a cathode material used in polymer electrolyte membrane fuel cells is discussed. We show that our approach preserves significantly more of the original nanostructure than an thresholding approach.
    Materials Characterization 09/2014; 95. DOI:10.1016/j.matchar.2014.05.014 · 1.93 Impact Factor
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    ABSTRACT: A set of computationally generated granular packings of frictionless grains is statistically analyzed using tools from stochastic geometry. We consider both the graph of the solid phase (formed using the particle mid-points) and the pore-phase. Structural characteristics rooted in the analysis of random point processes are seen to yield valuable insights into the underlying structure of granular systems. The graph of the solid phase is analyzed using traditional measures such as edge length and coordination number, as well as more instructive measures of the overall transport properties such as geometric tortuosity, where significant differences are observed in the windedness of paths through the different particle graphs considered. In contrast, the distributions of pore-phase characteristics have a similar shape for all considered granular packings. Interestingly, it is found that prolate and oblate ellipsoid packings show a striking similarity between their solid-phase graphs as well as between their pore-phase graphs.
    Granular Matter 08/2014; 16(4). DOI:10.1007/s10035-014-0486-4 · 1.70 Impact Factor
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    ABSTRACT: Distributional properties and a simulation algorithm for the Palm version of stationary iterated tessellations are considered. In particular, we study the limit behaviour of functionals related to Cox–Voronoi cells (such as typical shortest-path lengths) if either the intensity γ0 of the initial tessellation or the intensity γ1 of the component tessellation converges to 0. We develop an explicit description of the Palm version of Poisson–Delaunay tessellations (PDT), which provides a new direct simulation algorithm for the typical Cox–Voronoi cell based on PDT. It allows us to simulate the Palm version of stationary iterated tessellations, where either the initial or component tessellation is a PDT and can furthermore be used in order to show numerically that the qualitative and quantitative behaviour of certain functionals related to Cox–Voronoi cells strongly depends on the type of the underlying iterated tessellation.
    Journal of Statistical Computation and Simulation 07/2014; 84(7). DOI:10.1080/00949655.2012.749877 · 0.71 Impact Factor
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    ABSTRACT: A novel parametrized model that describes the 3D microstructure of compressed fiber-based materials is introduced. It allows to virtually generate the microstructure of realistically compressed gas-diffusion layers (GDL). Given the input of a 3D microstructure of some fiber-based material, the model compresses the system of fibers in a uniaxial direction for arbitrary compression rates. The basic idea is to translate the fibers in the direction of compression according to a vector field which depends on the rate of compression and on the locations of fibers within the material. In order to apply the model to experimental 3D image data of fiber-based materials given for several compression states, an optimal vector field is estimated by simulated annealing. The model is applied to 3D image data of non-woven GDL in PEMFC gained by synchrotron tomography for different compression rates. The compression model is validated by comparing structural characteristics computed for experimentally compressed and virtually compressed microstructures, where two kinds of compression – using a flat stamp and a stamp with a flow-field profile – are applied. For both stamps types, a good agreement is found. Furthermore, the compression model is combined with a stochastic 3D microstructure model for uncompressed fiber-based materials. This allows to efficiently generate compressed fiber-based microstructures in arbitrary volumes.
    Journal of Power Sources 07/2014; DOI:10.1016/j.jpowsour.2014.01.095 · 5.21 Impact Factor
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    ABSTRACT: A general framework is proposed for the study of the charge transport properties of materials via Random Walks in Random Environments (RWRE). The material of interest is modelled by a random environment and the charge carrier is modelled by a random walker. The framework combines a model for the fast generation of random environments that realistically mimic materials morphology with an algorithm for efficient estimation of key properties of the resulting random walk. The model of the environment makes use of tools from spatial statistics and the theory of random geometric graphs. More precisely, the disordered medium is represented by a random spatial graph with directed edge weights, where the edge weights represent the transition rates of a Markov Jump Process (MJP) modelling the motion of the random walker. This MJP is a multiscale stochastic process. In the long term, it explores all vertices of the random graph model. In the short term, however, it becomes trapped in small subsets of the state space and makes many transitions in these small regions. This behaviour makes efficient estimation of velocity by Monte Carlo simulations a challenging task. Therefore, we use Aggregate Monte Carlo (AMC), introduced in [5], for estimating the velocity of a random walker as it passes through a realisation of the random environment. In this paper, we prove the strong consistency of the AMC velocity estimator and use this result to conduct a detailed case study, in which we describe the motion of holes in an amorphous mesophase of an organic semiconductor, dicyanovinyl-substituted oligothiophene (DCV4T). In particular, we analyse the effect of system size (i.e. number of molecules) on the velocity of single charge carriers.
    SIAM Journal on Multiscale Modeling and Simulation 07/2014; 12(3):1108-1134. DOI:10.1137/130942504 · 1.80 Impact Factor
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    ABSTRACT: The relationship between the 3D morphology of gas-diffusion layers (GDL) of HT-PEFCs and their functionality is analyzed. A stochastic model describing the microstructure of paper-type GDL is combined with the Lattice-Boltzmann method (LBM) to simulate gas transport within the GDL microstructure. Virtual 3D microstructures representing paper-type GDL are generated by a stochastic model, where the binder morphology is systematically modified. On these structures, single phase single component gas flow is computed by the LBM. Quality criteria evaluating the spatial homogeneity of gas supply are introduced and related to the binder morphology. The spatial homogeneity of the gas supply is analyzed by a parametrized stochastic model describing the gas flow at the exit of the GDL. This approach gives insight into the spatial structure of the gas flow at the GDL exit. The quality of gas supply is quantified by characterizing size and arrangement of regions with high gas supply. This stochastic gas flow model predicts the quality of gas supply for further binder morphologies. Analyzing the quality criteria and the stochastic evaluation of the spatial structure of the gas flow field at the GDL exit, it is found that the binder morphology has an essential influence on the gas supply.
    Transport in Porous Media 07/2014; 103(3). DOI:10.1007/s11242-014-0312-9 · 1.55 Impact Factor
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    ABSTRACT: Microstructure has an important influence on the performance of SOFC electrodes. In recent years considerable progress has been achieved in describing microstructure parameters (e.g. TPB, tortuosity, particle size distributions) on a quantitative level based on high-resolution tomography. However, the performance of fuel cell electrodes is based on a complex interplay of various transport and electrochemical processes. Hence, in order to unravel the influence of microstructure (and microstructure degradation) on the electrode performance, it is not sufficient to just quantify the critical microstructure parameters, but also to incorporate these parameters into models that allow simulation of electrode reaction mechanism including the complex interplay of various physico-chemical processes. In this study we first present the recent progress in the elaboration of the relationship between effective transport properties with the transport relevant parameters (i.e. percolating phase volume fraction, tortuosity, constrictivity, size distributions of particle bulges and bottlenecks). Furthermore a model was developed to simulate the complex reaction mechanism of Ni-YSZ anodes. This model is capable to incorporate all relevant microstructure parameters that influence charge transport (ionic, electric) and charge transfer (fuel oxidation). The model allows distinguishing between different components of the ASR, which are related either to limitations of charge transport (ionic, electric) or charge transfer (electrochemistry) within the anode. In literature the influence of active reaction sites (i.e. TPB) is strongly emphasized. In the present paper we also focus on limitations in charge transport due to microstructure effects. Examples are presented which highlight the effects of grain size on the effective electric and ionic conductivity and corresponding anode performance. The data are compared with experimental data from EIS. The presented methodology gives new insight on the effects of microstructure variation, because it links critical microstructure parameters with anode performance and with the associated ASR components from different rate limiting processes.
    11th European SOFC Forum, Lucerne, Switzerland; 07/2014
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    ABSTRACT: Simulations of organic semiconducting devices using drift-diffusion equations are vital for the understanding of their functionality as well as for the optimization of their performance. Input parameters for these equations are usually determined from experiments and do not provide a direct link to the chemical structures and material morphology. Here we demonstrate how such a parametrization can be performed by using atomic-scale (microscopic) simulations. To do this, a stochastic network model, parametrized on atomistic simulations, is used to tabulate charge mobility in a wide density range. After accounting for finite-size effects at small charge densities, the data is fitted to the uncorrelated and correlated extended Gaussian disorder models. Surprisingly, the uncorrelated model reproduces the results of microscopic simulations better than the correlated one, compensating for spatial correlations present in a microscopic system by a large lattice constant. The proposed method retains the link to the material morphology and the underlying chemistry and can be used to formulate structure–property relationships or optimize devices prior to compound synthesis.
    Journal of Chemical Theory and Computation 06/2014; 10(6-6):2508-2513. DOI:10.1021/ct500269r · 5.31 Impact Factor
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    ABSTRACT: A methodology is proposed that is suitable for efficient simulation of continuous-time Markov chains that are nearly-completely decomposable. For such Markov chains the effort to adequately explore the state space via Crude Monte Carlo (CMC) simulation can be extremely large. The purpose of this paper is to provide a fast alternative to the standard CMC algorithm, which we call Aggregate Monte Carlo (AMC). The idea of the AMC algorithm is to reduce the jumping back and forth of the Markov chain in small subregions of the state space. We accomplish this by aggregating such problem regions into single states. We discuss two methods to identify collections of states where the Markov chain may become ‘trapped’: the stochastic watershed segmentation from image analysis, and a graph-theoretic decomposition method. As a motivating application, we consider the problem of estimating the charge carrier mobility of disordered organic semiconductors, which contain low-energy regions in which the charge carrier can quickly become stuck. It is shown that the AMC estimator for the charge carrier mobility reduces computational costs by several orders of magnitude compared to the CMC estimator.
    Methodology And Computing In Applied Probability 06/2014; 16:465. DOI:10.1007/s11009-013-9327-x · 0.78 Impact Factor
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    ABSTRACT: The microstructure influence on conductive transport processes is described in terms of volume fraction ε, tortuosity τ, and constrictivity β. Virtual microstructures with different parameter constellations are produced using methods from stochastic geometry. Effective conductivities σeff are obtained from solving the diffusion equation in a finite element model. In this way a large database is generated, which is used to test expressions describing different micro-macro relationships such as Archie's law, tortuosity and constrictivity equations. It turns out that the constrictivity equation has the highest accuracy indicating that all three parameters (ε, τ, β) are necessary to capture the microstructure influence correctly. The predictive capability of the constrictivity equation is improved by introducing modifications of it and using error-minimization, which leads to the following expression: σeff = σ0 2.03 ε1.57β0.72/τ2 with intrinsic conductivity σ0. The equation is important for future studies in e.g. batteries, fuel cells and for transport processes in porous materials. © 2014 American Institute of Chemical Engineers AIChE J, 2014
    AIChE Journal 06/2014; 60(6). DOI:10.1002/aic.14416 · 2.58 Impact Factor
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    ABSTRACT: We present a synchrotron X-ray tomographic study on the morphology of carbon fiber-based gas diffusion layer (GDL) material under compression. A dedicated compression device is used to provide well-defined compression conditions. A flat compression punch is employed to study the fiber geometry at different degrees of compression. Transport relevant geometrical parameters such as porosity, pore size and tortuosity distributions are calculated. The geometric properties notably change upon compression which has direct impact on transport conditions for gas and fluid flow. The availability of broad 3D paths, which are most important for the transport of liquid water from the catalyst layer through the GDL, is markedly reduced after compression. In a second experiment, we study the influence of the channel-land-pattern of the flow-field on shape and microstructure of the GDL. A flow-field compression punch is employed to reproduce the inhomogeneous compression conditions found during fuel cell assembly. While homogenously compressed underneath the land the GDL is much less and inhomogeneously compressed under the channel. The GDL material extends far into the channel volume where it can considerably influence gas and fluid flow. Loose fiber endings penetrate deeply into the channel and form obstacles for the discharge of liquid water droplets.
    Journal of Power Sources 05/2014; 253:123–131. DOI:10.1016/j.jpowsour.2013.12.062 · 5.21 Impact Factor
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    ABSTRACT: Dialectometric intensity estimation as introduced in Rumpf etal. (2009) and Pickl and Rumpf (2011, 2012) is a method for the unsupervised generation of maps visualizing geolinguistic data on the level of linguistic variables. It also extracts spatial information for subsequent statistical analysis. However, as intensity estimation involves geographically conditioned smoothing, this method can lead to undesirable results. Geolinguistically relevant structures such as rivers, political borders or enclaves, for instance, are not taken into account and thus their manifestations in the distributions of linguistic variants are blurred. A possible solution to this problem, as suggested and put to the test in this paper, is to use linguistic distances rather than geographical (Euclidean) distances in the estimation. This methodological adjustment leads to maps which render geolinguistic distributions more faithfully, especially in areas that are deemed critical for the interpretation of the resulting maps and for subsequent statistical analyses of the results.
    03/2014; 2(01):25-40. DOI:10.1017/jlg.2014.3

Publication Stats

1k Citations
301.89 Total Impact Points

Institutions

  • 1996–2015
    • Universität Ulm
      • Institute of Stochastics
      Ulm, Baden-Württemberg, Germany
  • 2009
    • Orange Labs
      Rhône-Alpes, France
    • Technische Universiteit Eindhoven
      • Department of Chemical Engineering and Chemistry
      Eindhoven, North Brabant, Netherlands
  • 2004–2005
    • Universität Augsburg
      • Institute of Mathematics
      Augsberg, Bavaria, Germany