Aaron Spettl

Stochastic 3D modeling of Ostwald ripening at ultra-high volume fractions of the coarsening phase

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.

Fitting Laguerre tessellation approximations to tomographic image data

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.

Inverting Laguerre tessellations

A Laguerre tessellation is a generalization of a Voronoi tessellation where the proximity between points is measured via a power distance rather than the Euclidean distance. Laguerre tessellations have found significant applications in materials science, providing improved modeling of (poly)crystalline microstructures and grain growth. There exist efficient algorithms to construct Laguerre tessellations from given sets of weighted generator points, similar to methods used for Voronoi tessellations. The purpose of this paper is to provide theory and methodology for the inverse construction; that is, to recover the weighted generator points from a given Laguerre tessellation. We show that, unlike the Voronoi case, the inverse problem is in general non-unique: different weighted generator points can create the same tessellation. To recover pertinent generator points, we formulate the inversion problem as a multimodal optimization problem and apply the cross-entropy method to solve it.

Quantitative comparison of segmentation algorithms for FIB-SEM images of porous media.

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

Copula-based approximation of particle breakage as link between DEM and PBM

Abstract In process engineering, the breakage behavior of particles is needed for the modeling and optimization of comminution processes. A popular tool to describe (dynamic) processes is population balance modeling (PBM), which captures the statistical distribution of particle properties and their evolution over time. It has been suggested previously to split up the description of breakage into a machine function (modeling of loading conditions) and a material function (modeling of particle response to mechanical stress). Based on this idea, we present a mathematical formulation of machine and material functions and a general approach to compute them. Both functions are modeled using multivariate probability distributions, where in particular so-called copulas are helpful. These can be fitted to data obtained by the discrete element method (DEM). In this paper, we describe the proposed copula-based breakage model, and we construct such a model for an artificial dataset that allows to evaluate the prediction quality.

8. Neue Dialektometrie mit Methoden der stochastischen Bildanalyse

Vorrangiger Zweck ist die Entwicklung neuer Methoden zur quantitativen sowie qualitativen Auswertung großer Korpora areallinguistischer Daten. Zielpunkt ist die Bereitstellung der im Projekt entwickelten und erprobten Methoden in einem kompakten und anwenderfreundlichen Softwarepaket namens GeoLing, das es anderen Nutzern ermöglicht, mit ihren eigenen Daten entsprechende Analysen eigenständig durchzuführen. Die Software ist komplett in Java geschrieben und nicht nur plattformübergreifend lauffähig, sondern vom Benutzer bei Bedarf auch individuell anpassbar. Ein erster Ausgangspunkt für die Arbeiten im Projekt war die „klassische“ Dialektometrie (Séguy 1971, 1973; Goebl 1982, 1984), die bislang in der Hauptsache mittels Aggregation versucht, der Variationsvielfalt in Sprachatlanten Herr zu werden. Während diese aggregativen Vorgehensweisen (die weiterhin die Basis vieler quantitativer Zugänge zur Sprachgeographie sind, vgl. für einen Überblick etwa Heeringa 2004: 14–24; Nerbonne 2010; Nerbonne & Kretzschmar 2013) zweifelsohne die „dominanten“ (d.h. „möglichst hochrangige[n]“; Goebl 1986: 43) Strukturen der Variation gut abbilden können, werden schwächere oder weniger hochrangige Aspekte der Variation ausgeblendet. Einher geht damit oftmals auch eine starre Sicht auf „Areale“, die implizit als einheitliche Dialekträume konzeptualisiert werden, die sich scheinbar klar an Grenzen voneinander scheiden, statt fließend ineinander überzugehen. Darüber hinaus blieben (und bleiben bis heute) eventuell auftretende Mehrfachbelege an einem Ort in diesen Herangehensweisen unberücksichtigt. 2