ORCID Profile
0000-0002-1029-5960
Current Organisations
Azienda Ospedaliera di Perugia
,
Universität des Saarlandes
,
Heinrich-Heine-Universität Düsseldorf
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Publisher: American Physical Society (APS)
Date: 04-02-2015
Publisher: Wiley
Date: 26-05-2017
DOI: 10.1002/MP.12280
Abstract: Structure-property relations, which relate the shape of the microstructure to physical properties such as transport or mechanical properties, need sensitive measures of structure. What are suitable fabric tensors to quantify the shape of anisotropic heterogeneous materials? The mean intercept length is among the most commonly used characteristics of anisotropy in porous media, e.g., of trabecular bone in medical physics. Yet, in this series of two papers we demonstrate that it has conceptual shortcomings that limit the validity of its results. We test the validity of general assumptions regarding the properties of the mean-intercept length tensor using analytical formulas for the mean-intercept lengths in anisotropic Boolean models (derived in part I of this series), augmented by numerical simulations. We discuss in detail the functional form of the mean intercept length as a function of the test line orientations. As the most prominent result, we find that, at least for the ex le of overlapping grains modeling porous media, the polar plot of the mean intercept length is in general not an ellipse and hence not represented by a second-rank tensor. This is in stark contrast to the common understanding that for a large collection of grains the mean intercept length figure averages to an ellipse. The standard mean intercept length tensor defined by a least-square fit of an ellipse is based on a model mismatch, which causes an intrinsic lack of accuracy. Our analysis reveals several shortcomings of the mean intercept length tensor analysis that pose conceptual problems and limitations on the information content of this commonly used analysis method. We suggest the Minkowski tensors from integral geometry as alternative sensitive measures of anisotropy. The Minkowski tensors allow for a robust, comprehensive, and systematic approach to quantify various aspects of structural anisotropy. We show the Minkowski tensors to be more sensitive, in the sense, that they can quantify the remnant anisotropy of structures not captured by the mean intercept length analysis. If applied to porous tissue and microstructures, this improved structure characterization can yield new insights into the relationships between geometry and material properties.
Publisher: Wiley
Date: 26-05-2017
DOI: 10.1002/MP.12281
Abstract: Structure-property relations, which relate the shape of the microstructure to physical properties such as transport or mechanical properties, need sensitive measures of structure. What are suitable fabric tensors that quantify the shape of anisotropic heterogeneous materials? The mean intercept length is among the most commonly used characteristics of anisotropy in porous media, for ex le, of trabecular bone in medical physics. We analyze the orientation-biased Boolean model, a versatile stochastic model that represents microstructures as overlapping grains with an orientation bias towards a preferred direction. This model is an extension of the isotropic Boolean model, which has been shown to truthfully reproduce multi-functional properties of isotropic porous media. We explain the close relationship between the concept of intersections with test lines to the elaborate mathematical theory of queues, and how explicit results from the latter can be directly applied to characterize microstructures. In this series of two papers, we provide analytic formulas for the anisotropic Boolean model and demonstrate often overlooked conceptual shortcomings of this approach. Queuing theory is used to derive simple and illustrative formulas for the mean intercept length. It separates into an intensity-dependent and an orientation-dependent factor. The global average of the mean intercept length can be expressed by local characteristics of a single grain alone. We thus identify which shape information about the random process the mean intercept length contains. The connection between global and local quantities helps to interpret observations and provides insights into the possibilities and limitations of the analysis. In the second paper of this series, we discuss, based on the findings in this paper, short-comings of the mean intercept analysis for (bone-)microstructure characterization. We will suggest alternative and better defined sensitive anisotropy measures from integral geometry.
Publisher: AIP Publishing
Date: 21-12-2020
DOI: 10.1063/5.0029301
Abstract: The quantizer problem is a tessellation optimization problem where point configurations are identified such that the Voronoi cells minimize the second moment of the volume distribution. While the ground state (optimal state) in 3D is almost certainly the body-centered cubic lattice, disordered and effectively hyperuniform states with energies very close to the ground state exist that result as stable states in an evolution through the geometric Lloyd’s algorithm [M. A. Klatt et al. Nat. Commun. 10, 811 (2019)]. When considered as a statistical mechanics problem at finite temperature, the same system has been termed the “Voronoi liquid” by Ruscher, Baschnagel, and Farago [Europhys. Lett. 112, 66003 (2015)]. Here, we investigate the cooling behavior of the Voronoi liquid with a particular view to the stability of the effectively hyperuniform disordered state. As a confirmation of the results by Ruscher et al., we observe, by both molecular dynamics and Monte Carlo simulations, that upon slow quasi-static equilibrium cooling, the Voronoi liquid crystallizes from a disordered configuration into the body-centered cubic configuration. By contrast, upon sufficiently fast non-equilibrium cooling (and not just in the limit of a maximally fast quench), the Voronoi liquid adopts similar states as the effectively hyperuniform inherent structures identified by Klatt et al. and prevents the ordering transition into a body-centered cubic ordered structure. This result is in line with the geometric intuition that the geometric Lloyd’s algorithm corresponds to a type of fast quench.
Publisher: Springer International Publishing
Date: 2017
Publisher: Springer Science and Business Media LLC
Date: 18-02-2019
DOI: 10.1038/S41467-019-08360-5
Abstract: Partitioning space into cells with certain extreme geometrical properties is a central problem in many fields of science and technology. Here we investigate the Quantizer problem, defined as the optimisation of the moment of inertia of Voronoi cells, i.e., similarly-sized ‘sphere-like’ polyhedra that tile space are preferred. We employ Lloyd’s centroidal Voronoi diagram algorithm to solve this problem and find that it converges to disordered states associated with deep local minima. These states are universal in the sense that their structure factors are characterised by a complete independence of a wide class of initial conditions they evolved from. They moreover exhibit an anomalous suppression of long-wavelength density fluctuations and quickly become effectively hyperuniform. Our findings warrant the search for novel amorphous hyperuniform phases and cellular materials with unique physical properties.
Publisher: IOP Publishing
Date: 16-02-2017
Publisher: Authorea, Inc.
Date: 29-05-2021
DOI: 10.22541/AU.161918947.77588494/V2
Abstract: Background . This paper presents, for the first time, the Epidemic Volatility Index (EVI), a conceptually simple, early warning tool for emerging epidemic waves. Methods . EVI is based on the volatility of the newly reported cases per unit of time, ideally per day, and issues an early warning when the rate of the volatility change exceeds a threshold. Results . Results from the COVID-19 epidemic in Italy and New York are presented here, while daily updated predictions for all world countries and each of the United States are available online. Interpretation . EVI’s application to data from the current COVID-19 pandemic revealed a consistent and stable performance in terms of detecting oncoming waves. The application of EVI to other epidemics and syndromic surveillance tasks in combination with existing early warning systems will enhance our ability to act fast and optimize containment of outbreaks.
Publisher: American Physical Society (APS)
Date: 30-10-2015
Publisher: Wiley
Date: 16-06-2011
Abstract: Predicting physical properties of materials with spatially complex structures is one of the most challenging problems in material science. One key to a better understanding of such materials is the geometric characterization of their spatial structure. Minkowski tensors are tensorial shape indices that allow quantitative characterization of the anisotropy of complex materials and are particularly well suited for developing structure‐property relationships for tensor‐valued or orientation‐dependent physical properties. They are fundamental shape indices, in some sense being the simplest generalization of the concepts of volume, surface and integral curvatures to tensor‐valued quantities. Minkowski tensors are based on a solid mathematical foundation provided by integral and stochastic geometry, and are endowed with strong robustness and completeness theorems. The versatile definition of Minkowski tensors applies widely to different types of morphologies, including ordered and disordered structures. Fast linear‐time algorithms are available for their computation. This article provides a practical overview of the different uses of Minkowski tensors to extract quantitative physically‐relevant spatial structure information from experimental and simulated data, both in 2D and 3D. Applications are presented that quantify (a) alignment of co‐polymer films by an electric field imaged by surface force microscopy (b) local cell anisotropy of spherical bead pack models for granular matter and of closed‐cell liquid foam models (c) surface orientation in open‐cell solid foams studied by X‐ray tomography and (d) defect densities and locations in molecular dynamics simulations of crystalline copper.
Publisher: American Association for the Advancement of Science (AAAS)
Date: 07-04-2017
Abstract: High-resolution microscopy of hierarchically organized solid gyroid nanostructures sheds light on the underlying dynamic formation process.
No related grants have been discovered for Michael Andreas Klatt.