Minkowski tensors of anisotropic spatial structure

Schröder-Turk G, Mickel W, Kapfer S, Schaller F, Breidenbach B, Hug D, Mecke K (2013)

Publication Status: Published

Publication Type: Journal article

Publication year: 2013

Journal

New Journal of Physics Institute of Physics: Open Access Journals / Institute of Physics (IoP) and Deutsche Physikalische Gesellschaft

Publisher: IOP PUBLISHING LTD

Book Volume: 15

DOI: 10.1088/1367-2630/15/8/083028

Abstract

This paper describes the theoretical foundation of and explicit algorithms for a novel approach to morphology and anisotropy analysis of complex spatial structure using tensor-valued Minkowski functionals, the so-called Minkowski tensors. Minkowski tensors are generalizations of the well-known scalar Minkowski functionals and are explicitly sensitive to anisotropic aspects of morphology, relevant for example for elastic moduli or permeability of microstructured materials. Here we derive explicit linear-time algorithms to compute these tensorial measures for three-dimensional shapes. These apply to representations of any object that can be represented by a triangulation of its bounding surface; their application is illustrated for the polyhedral Voronoi cellular complexes of jammed sphere configurations and for triangulations of a biopolymer fibre network obtained by confocal microscopy. The paper further bridges the substantial notational and conceptual gap between the different but equivalent approaches to scalar or tensorial Minkowski functionals in mathematics and in physics, hence making the mathematical measure theoretic formalism more readily accessible for future application in the physical sciences.

Authors with CRIS profile

Gerd Schröder-Turk Professur für Theoretische Physik Sebastian Kapfer Lehrstuhl für Theoretische Physik Fabian Schaller Lehrstuhl für Theoretische Physik Klaus Mecke Lehrstuhl für Theoretische Physik

Involved external institutions

Karlsruhe Institute of Technology (KIT) DE Germany (DE)

How to cite

APA:

Schröder-Turk, G., Mickel, W., Kapfer, S., Schaller, F., Breidenbach, B., Hug, D., & Mecke, K. (2013). Minkowski tensors of anisotropic spatial structure. New Journal of Physics, 15. https://doi.org/10.1088/1367-2630/15/8/083028

MLA:

Schröder-Turk, Gerd, et al. "Minkowski tensors of anisotropic spatial structure." New Journal of Physics 15 (2013).

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