Volker Schmidt

Universität Ulm, Ulm, Baden-Württemberg, Germany

Are you Volker Schmidt?

Claim your profile

Publications (196)382.1 Total impact

  • [Show abstract] [Hide abstract]
    ABSTRACT: Negative electrodes of lithium-ion batteries generally consist of graphite-based active materials. In order to realize batteries with a high current density and therefore accelerated charging processes, the intercalation of lithium and the diffusion processes of these carbonaceous materials must be understood. In this paper, we visualized the electrochemical active surface area for three different anode materials using a novel OsO4 staining method in combination with scanning electron microscopy techniques. The diffusion behavior of these three anode materials is investigated by potentiostatic intermittent titration technique measurements. From those we determine the diffusion coefficient with and without consideration of the electrochemical active surface area.
    No preview · Article · Mar 2016
  • Source
    [Show abstract] [Hide abstract]
    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.
    Full-text · Article · Jan 2016 · Philosophical Magazine
  • [Show abstract] [Hide abstract]
    ABSTRACT: Empirical relationships between effective conductivities in porous and composite materials and their geometric characteristics such as volume fraction ε, tortuosity τ and constrictivity β are established. For this purpose, 43 virtually generated 3D microstructures with varying geometric characteristics are considered. Effective conductivities σeff are determined by numerical transport simulations. Using error-minimization the following relationships have been established: and (simplified formula) with intrinsic conductivity σ0, geodesic tortuosity τgeod and relative prediction errors of 19% and 18%, respectively. We critically analyze the methodologies used to determine tortuosity and constrictivity. Comparing geometric tortuosity and geodesic tortuosity, our results indicate that geometric tortuosity has a tendency to overestimate the windedness of transport paths. Analyzing various definitions of constrictivity, we find that the established definition describes the effect of bottlenecks well. In summary, the established relationships are important for a purposeful optimization of materials with specific transport properties, such as porous electrodes in fuel cells and batteries. This article is protected by copyright. All rights reserved.
    No preview · Article · Jan 2016 · AIChE Journal
  • [Show abstract] [Hide abstract]
    ABSTRACT: We consider asymptotic properties of two functionals on Euclidean shortest-path trees appearing in random geometric graphs in R2 which can be used, for example, as models for fixed-access telecommunication networks. First, we determine the asymptotic bivariate distribution of the two backbone lengths inside a certain class of typical Cox-Voronoi cells as the size of this cell grows unboundedly. The corresponding Voronoi tessellation is generated by a stationary Cox process which is concentrated on the edges of the random geometric graph and whose intensity tends to 0. The limiting random vector can be represented as a simple geometric functional of a decomposition of a typical Poisson-Voronoi cell induced by an independent random sector. Using similar methods, we consider the asymptotic bivariate distribution of the total lengths of the two subtrees inside the Cox-Voronoi cell.
    No preview · Article · Dec 2015 · Statistics [?] Probability Letters
  • Tim Brereton · Christian Eckard · Volker Schmidt
    [Show abstract] [Hide abstract]
    ABSTRACT: We consider the problem of estimating hitting probabilities related to a class of interacting particle systems. These systems, in which two types of particles --- `electrons' and `holes' --- move on a graph, are simplified versions of models describing charge transport in disordered materials. The probability of interest is the probability that an electron reaches a certain region of the graph before colliding with a hole. We provide a detailed description of our model and explain how it can be simulated. Next, we give a brief introduction to importance sampling, which we use to improve the efficiency of our estimators. To our knowledge, importance sampling has not yet been used to estimate probabilities related to interacting particle systems. We describe how importance sampling can be used to improve the efficiency of estimators of hitting time probabilities involving discrete time Markov chains. We then use importance sampling to estimate the probability that we are interested in. In doing so, we observe that there are a number of complexities that arise when working with interacting particle systems. We describe some simple heuristics for implementing importance sampling. These heuristics make minimal changes to the probability measure under which the original system evolves. We consider a specific example of our problem and investigate the effectiveness of the importance sampling approach. We show that our estimators outperform standard Monte Carlo estimators. Finally, we describe possible future work, which includes a more sophisticated importance sampling approach that uses `locally optimal' changes of measure.
    No preview · Conference Paper · Nov 2015
  • [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.
    No preview · Article · Nov 2015 · Computational Materials Science
  • [Show abstract] [Hide abstract]
    ABSTRACT: A strategy to mitigate typical reconstruction artefacts in missing wedge computed tomography is presented. These artefacts appear as elongations of reconstructed details along the mean direction (i.e. the symmetry centre of the projections). Although absent in standard computed tomography applications, they are most prominent in advanced electron tomography and also in special topics of X-ray and neutron tomography under restricted geometric boundary conditions. We investigate the performance of the DIRECTT (Direct Iterative Reconstruction of Computed Tomography Trajectories) algorithm to reduce the directional artefacts in standard procedures. In order to be sensitive to the anisotropic nature of missing wedge artefacts, we investigate isotropic substructures of metal foam as well as circular disc models. Comparison is drawn to filtered backprojection and algebraic techniques. Reference is made to reconstructions of complete data sets. For the purpose of assessing the reconstruction quality, Fourier transforms are employed to visualize the missing wedge directly. Deficient reconstructions of disc models are evaluated by a length-weighted kernel density estimation, which yields the probabilities of boundary orientations. The DIRECTT results are assessed at different signal-to-noise ratios by means of local and integral evaluation parameters.
    No preview · Article · Sep 2015 · Journal of Microscopy
  • Source

    Full-text · Dataset · Sep 2015
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: As the Cordilleran and Laurentide Ice Sheets retreated, North America was colonized by human populations; however, the spatial patterns of subsequent population growth are unclear. Temporal frequency distributions of aggregated radiocarbon ((14)C) dates are used as a proxy of population size and can be used to track this expansion. The Canadian Archaeological Radiocarbon Database contains more than 35,000 (14)C dates and is used in this study to map the spatiotemporal demographic changes of Holocene populations in North America at a continental scale for the past 13,000 y. We use the kernel method, which converts the spatial distribution of (14)C dates into estimates of population density at 500-y intervals. The resulting maps reveal temporally distinct, dynamic patterns associated with paleodemographic trends that correspond well to genetic, archaeological, and ethnohistoric evidence of human occupation. These results have implications for hypothesizing and testing migration routes into and across North America as well as the relative influence of North American populations on the evolution of the North American ecosystem.
    Full-text · Article · Sep 2015 · Proceedings of the National Academy of Sciences
  • A Spettl · R Wimmer · T Werz · M Heinze · S Odenbach · C E Krill · V Schmidt
    [Show abstract] [Hide abstract]
    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.
    No preview · Article · Sep 2015 · Modelling and Simulation in Materials Science and Engineering
  • [Show abstract] [Hide abstract]
    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.
    No preview · Article · Aug 2015 · Materials Characterization
  • Source
    [Show abstract] [Hide abstract]
    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.
    Full-text · Article · Aug 2015 · Materials
  • [Show abstract] [Hide abstract]
    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.
    No preview · Article · Aug 2015 · Archive of Applied Mechanics
  • Christian Hirsch · Gary Delaney · Volker Schmidt
    [Show abstract] [Hide abstract]
    ABSTRACT: The notion of stationary Apollonian packings in the d-dimensional Euclidean space is introduced as a mathematical formalization of so-called random Apollonian packings and rotational random Apollonian packings, which constitute popular grain packing models in physics. Apart from dealing with issues of existence and uniqueness in the entire Euclidean space, asymptotic results are provided for the growth durations and it is shown that the packing is space-filling with probability 1, in the sense that the Lebesgue measure of its complement is zero. Finally, the phenomenon is studied that grains arrange in clusters and properties related to percolation are investigated.
    No preview · Article · Jul 2015 · Journal of Statistical Physics
  • J.G. Pharoah · L. Handl · V. Schmidt
    [Show abstract] [Hide abstract]
    ABSTRACT: Three different electrode morphologies are generated from three different starting powders, spheres representing non-aggregated powders, agglomerates of spheres and high aspect ratio cylinders modelling splats formed in plasma sprays. Electrodes from each morphology are analysed using finite volumes to predict the effective transport coefficients, the triple phase boundary length and the performance of the electrode. The same structures are also analysed using morphological characterization which can be much more efficient. It was found that high aspect ratio base particles are favourable, and that constrictivity correlates best with the finite volume transport calculations.
    No preview · Article · Jul 2015 · ECS Transactions
  • [Show abstract] [Hide abstract]
    ABSTRACT: We provide a stochastic modelling approach for multi-hierarchical fixed-access telecommunication networks where cables are installed along the underlying road system. It constitutes an extension of network models consisting of only two hierarchy levels. We consider the effects of the introduction of an additional level of hierarchy on two functionals relevant in telecommunication networks, namely typical shortest-path lengths and total fibre lengths. Intuitively speaking, in the extended scenario, the typical shortest-path length gets longer whereas the total fibre length decreases. Both theoretical and numerical results are provided. The underlying infrastructure is assumed to be represented by a STIT tessellation which is particularly suitable for stochastic modelling of multi-hierarchical fixed-access telecommunication networks. In this context, we present a description of the Palm version of a planar STIT tessellation and give an appropriate simulation algorithm.
    No preview · Article · Jun 2015 · Methodology And Computing In Applied Probability
  • Source
    [Show abstract] [Hide abstract]
    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
    Full-text · Article · Jun 2015 · Scientific Reports
  • C. Hirsch · D. Neuhäuser · C. Gloaguen · V. Schmidt
    [Show abstract] [Hide abstract]
    ABSTRACT: We consider Euclidean first passage percolation on a large family of connected random geometric graphs in the d-dimensional Euclidean space encompassing various well-known models from stochastic geometry. In particular, we establish a strong linear growth property for shortest-path lengths on random geometric graphs which are generated by point processes. We consider the event that the growth of shortest-path lengths between two (end) points of the path does not admit a linear upper bound. Our linear growth property implies that the probability of this event tends to zero sub-exponentially fast if the direct (Euclidean) distance between the endpoints tends to infinity. Besides, for a wide class of stationary and isotropic random geometric graphs, our linear growth property implies a shape theorem for the Euclidean first passage model defined by such random geometric graphs. Finally, this shape theorem can be used to investigate a problem which is considered in structural analysis of fixed-access telecommunication networks, where we determine the limiting distribution of the length of the longest branch in the shortest-path tree extracted from a typical segment system if the intensity of network stations converges to 0.
    No preview · Article · Jun 2015 · Advances in Applied Probability
  • [Show abstract] [Hide abstract]
    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.
    No preview · Article · Jun 2015 · Modelling and Simulation in Materials Science and Engineering
  • [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.
    No preview · Article · May 2015 · Spatial Statistics