Volker Schmidt

Universität Ulm, Ulm, Baden-Württemberg, Germany

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Publications (184)356.37 Total impact

  • [Show abstract] [Hide abstract]
    ABSTRACT: The performance and durability of lithium-ion batteries are highly dependent on the microstructures of their components. Recently, methods have been developed that make possible the simulation of electrochemical processes on 3D representations of lithium-ion batteries. However, it is difficult to obtain realistic microstructures on which these simulations can be carried out. In this paper, we develop a stochastic model that is able to produce realistic microstructures of lithium-ion battery anodes, which can serve as input for the simulations. We introduce the use of Gaussian random fields on the sphere as models for the particles that form the anodes. Using this new approach, we are able to model realistic particle geometries. The stochastic model also uses a number of techniques from stochastic geometry and spatial statistics. We carry out validation of our model, in order to demonstrate that it realistically describes the key features of the anode’s microstructure.
    Computational Materials Science 11/2015; 109:137 - 146. DOI:10.1016/j.commatsci.2015.06.025 · 2.13 Impact Factor
  • A Spettl · R Wimmer · T Werz · M Heinze · S Odenbach · C E Krill · V Schmidt
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    ABSTRACT: We present a (dynamic) stochastic simulation model for 3D grain morphologies undergoing a grain coarsening phenomenon known as Ostwald ripening. For low volume fractions of the coarsening phase, the classical LSW theory predicts a power-law evolution of the mean particle size and convergence toward self-similarity of the particle size distribution; experiments suggest that this behavior holds also for high volume fractions. In the present work, we have analyzed 3D images that were recorded in situ over time in semisolid Al–Cu alloys manifesting ultra-high volume fractions of the coarsening (solid) phase. Using this information we developed a stochastic simulation model for the 3D morphology of the coarsening grains at arbitrary time steps. Our stochastic model is based on random Laguerre tessellations and is by definition self-similar—i.e. it depends only on the mean particle diameter, which in turn can be estimated at each point in time. For a given mean diameter, the stochastic model requires only three additional scalar parameters, which influence the distribution of particle sizes and their shapes. An evaluation shows that even with this minimal information the stochastic model yields an excellent representation of the statistical properties of the experimental data.
    Modelling and Simulation in Materials Science and Engineering 09/2015; 23(6). DOI:10.1088/0965-0393/23/6/065001 · 1.49 Impact Factor
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    ABSTRACT: Many important properties of particulate materials are heavily influenced by the size and shape of the constituent particles. Thus, in order to control and improve product quality, it is important to develop a good understanding of the shape and size of the particles that make up a given particulate material. In this paper, we show how the spherical harmonics expansion can be used to approximate particles obtained from tomographic 3D images. This yields an analytic representation of the particles which can be used to calculate structural characteristics. We present an estimation method for the optimal length of expansion depending on individual particle shapes, based on statistical hypothesis testing. A suitable choice of this parameter leads to a smooth approximation that preserves the main shape features of the original particle. To show the wide applicability of this procedure, we use it to approximate particles obtained from two different tomographic 3D datasets of particulate materials. The first one describes an anode material from lithium-ion cells that consists of sphere-like particles with different sizes. The second dataset describes a powder of highly non-spherical titanium dioxide particles.
    Materials Characterization 08/2015; 106. DOI:10.1016/j.matchar.2015.05.023 · 1.93 Impact Factor
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    ABSTRACT: The analysis of polycrystalline materials benefits greatly from accurate quantitative descriptions of their grain structures. Laguerre tessellations approximate such grain structures very well. However, it is a quite challenging problem to fit a Laguerre tessellation to tomographic data, as a high-dimensional optimization problem with many local minima must be solved. In this paper, we formulate a version of this optimization problem that can be solved quickly using the cross-entropy method, a robust stochastic optimization technique that can avoid becoming trapped in local minima. We demonstrate the effectiveness of our approach by applying it to both artificially generated and experimentally produced tomographic data.
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    ABSTRACT: Keywords: cermet; degradation; microstructure; tomography; conductivity; solid oxide fuel cells; Ni-YSZ; redox cycling This study investigates the influence of microstructure on the effective ionic and electrical conductivities of Ni-YSZ (yttria-stabilized zirconia) anodes. Fine, medium, and coarse microstructures are exposed to redox cycling at 950 °C. FIB (focused ion beam)-tomography and image analysis are used to quantify the effective (connected) volume fraction (Φeff), constriction factor (β), and tortuosity (τ). The effective conductivity (σeff) is described as the product of intrinsic conductivity (σ0) and the so-called microstructure-factor (M): σeff = σ0 × M. Two different methods are used to evaluate the M-factor: (1) by prediction using a recently established relationship, Mpred = εβ0.36/τ5.17, and (2) by numerical simulation that provides conductivity, from which the simulated M-factor can be deduced (Msim). Both methods give complementary and consistent information about the effective transport properties and the redox degradation mechanism. The initial microstructure has a strong influence on effective conductivities and their degradation. Finer anodes have higher initial conductivities but undergo more intensive Ni coarsening. Coarser anodes have a more stable Ni phase but exhibit lower YSZ stability due to lower sintering activity. Consequently, in order to improve redox stability, it is proposed to use mixtures of fine and coarse powders in different proportions for functional anode and current collector layers.
    Materials 08/2015; 8(9):5554. DOI:10.3390/ma8095265 · 1.88 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 08/2015; 85(8). DOI:10.1007/s00419-014-0956-5 · 1.44 Impact Factor
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    ABSTRACT: Lithium/sulphur batteries are promising candidates for future energy storage systems, mainly due to their high potential capacity. However low sulphur utilization and capacity fading hinder practical realizations. In order to improve understanding of the system, we investigate Li/S electrode morphology changes for different ageing steps, using X-ray phase contrast tomography. Thereby we find a strong decrease of sulphur loading after the first cycle, and a constant loading of about 15% of the initial loading afterwards. While cycling, the mean sulphur particle diameters decrease in a qualitatively similar fashion as the discharge capacity fades. The particles spread, migrate into the current collector and accumulate in the upper part again. Simultaneously sulphur particles lose contact area with the conducting network but regain it after ten cycles because their decreasing size results in higher surface areas. Since the capacity still decreases, this regain could be associated with effects such as surf
    Scientific Reports 06/2015; 5. DOI:10.1038/srep10921 · 5.58 Impact Factor
  • C. Hirsch · D. Neuhäuser · C. Gloaguen · V. Schmidt
    Advances in Applied Probability 06/2015; 47(2):328-354. DOI:10.1239/aap/1435236978 · 0.83 Impact Factor
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    ABSTRACT: A parametric stochastic model of the morphology of thin polymer:fullerene films is developed. This model uses a number of tools from stochastic geometry and spatial statistics. The fullerene-rich phase is represented by random closed sets and the polymer-rich phase is given by their complement. The model has three stages. First, a point pattern is used to model the locations of fullerene-rich domains. Second, domains are formed at these points. Third, the domains are rearranged to ensure a realistic configuration. The model is fitted to polymer:fullerene films produced using seven different spin coating velocities and validated using a variety of morphological characteristics. The model is then used to simulate morphologies corresponding to spin velocities for which no empirical data exists. The viability of this approach is demonstrated using cross-validation.
    Modelling and Simulation in Materials Science and Engineering 06/2015; 23(4):045003. DOI:10.1088/0965-0393/23/4/045003 · 1.49 Impact Factor
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    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.
    05/2015; 12. DOI:10.1016/j.spasta.2015.01.002
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    ABSTRACT: The internal microstructure of agglomerates has a great influence on their stability and breakage characteristics. Therefore, to optimize production processes and to improve characteristics of the final product, it is very important to understand dependencies between structural and mechanical properties of agglomerates. In this paper, we discuss usage of the discrete element method (DEM) for understanding the breakage behavior of spherical agglomerates under uniaxial compression depending on their microstructure. A flexible stochastic model has been developed to generate agglomerates with various types of microstructures. As an example, we investigate the effect of the primary particle size distribution on agglomerate strength and breakage behavior. In particular, the size distribution of primary particles is specified by a mixing of two fixed particle sizes. The model construction ensures that the size and mass of agglomerates as well as primary particles and binder content remain constant in all experiments. From the obtained results it can be seen that the breakage behavior of agglomerates is influenced in different ways. Breakage energy and the maximum force applied before the primary break depend on the mixing ratio and the variability inside the microstructure. On the other hand, the size of fragments is very similar for all mixing ratios.
    Advanced Powder Technology 04/2015; 26(3). DOI:10.1016/j.apt.2015.04.011 · 1.64 Impact Factor
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    ABSTRACT: We provide a parametric modeling approach suitable for various kinds of hierarchical networks based on random geometric graphs. In these networks, we have two kinds of components, so-called high-level components (HLC) and low-level components (LLC). Each HLC is associated with a serving zone and all LLC within this area are connected to the corresponding HLC. So-called sparse LLC networks, where only a few LLC occur in the typical serving zone, are a non-negligible subdomain when investigating hierarchical networks. Therefore, we supply distributional results for structural characteristics where two LLC are independently and uniformly distributed along the segment system of the typical serving zone. In particular, we are interested in the joint distribution of three quantities, namely the length of the joint part of the shortest paths from the LLC to the HLC as well as the lengths of the corresponding disjoint remaining parts. In order to provide a parametric, three-dimensional distribution function for these random variables, we utilize a pseudo-maximum likelihood approach. More precisely, we fit parametric approximation formulas to the marginal density functions as well as parametric copula functions that match with the observed correlation structure. We also provide an asymptotic result for the joint distribution of the connection lengths as the size of the typical cell increases unboundedly. This general modeling approach is explicitly explained for the case that the random geometric graph is formed by the edges of random tessellations.
    Stochastic Models 04/2015; 31(2). DOI:10.1080/15326349.2014.999285 · 0.50 Impact Factor
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    ABSTRACT: We present an experimental approach to study the three-dimensional microstructure of gas diffusion layer (GDL) materials under realistic compression conditions. A dedicated compression device was designed that allows for synchrotron-tomographic investigation of circular samples under well-defined compression conditions. The tomographic data provide the experimental basis for stochastic modeling of nonwoven GDL materials. A plain compression tool is used to study the fiber courses in the material at different compression stages. Transport relevant geometrical parameters, such as porosity, pore size, and tortuosity distributions, are exemplarily evaluated for a GDL sample in the uncompressed state and for a compression of 30 vol.%. To mimic the geometry of the flow-field, we employed a compression punch with an integrated channel-rib-profile. It turned out that the GDL material is homogeneously compressed under the ribs, however, much less compressed underneath the channel. GDL fibers extend far into the channel volume where they might interfere with the convective gas transport and the removal of liquid water from the cell.
    The Review of scientific instruments 04/2015; 86(4):043702. DOI:10.1063/1.4918291 · 1.58 Impact Factor
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    ABSTRACT: A novel approach for the marking of deposited lithium on graphite anodes from large automotive lithium-ion cells (≥6 Ah) is presented. Graphite anode samples were extracted from two different formats (cylindrical and pouch cells) of pristine and differently aged lithium-ion cells. The samples present a variety of anodes with various states of lithium deposition (also known as plating). A chemical modification was performed to metallic lithium deposited on the anode surface due to previous plating with isopropanol (IPA). After this procedure an oxygenated species was detected by scanning electron microscopy (SEM), which later was confirmed as Li2 CO3 by Fourier transform infrared spectroscopy (FTIR) and X-ray powder diffraction (XRPD). A valuation of the covered area by Li2 CO3 was carried out with an image analysis using energy-dispersive X-ray spectroscopy (EDX) and quantitative Rietveld refinement. © 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
    Chemistry - A European Journal 03/2015; 21(16). DOI:10.1002/chem.201406606 · 5.70 Impact Factor
  • 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 · 0.42 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 · 11.81 Impact Factor
  • Tim Brereton · Christian Hirsch · Dirk P. Kroese · Volker Schmidt
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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 · 1.69 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 · 2.15 Impact Factor
  • Björn Kriesche · Helga Weindl · Anselm Smolka · Volker Schmidt
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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

Publication Stats

2k Citations
356.37 Total Impact Points


  • 1996–2015
    • Universität Ulm
      • Institute of Stochastics
      Ulm, Baden-Württemberg, Germany
  • 2009
    • Orange Labs
      Rhône-Alpes, France
  • 2005
    • Universität Augsburg
      Augsberg, Bavaria, Germany