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Tensorial Minkowski functionals of triply periodic minimal surfaces

Mickel, W., Schröder-Turk, G.E. and Mecke, K. (2012) Tensorial Minkowski functionals of triply periodic minimal surfaces. Interface Focus, 2 (5). pp. 623-633.

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A fundamental understanding of the formation and properties of a complex spatial structure relies on robust quantitative tools to characterize morphology. A systematic approach to the characterization of average properties of anisotropic complex interfacial geometries is provided by integral geometry which furnishes a family of morphological descriptors known as tensorial Minkowski functionals. These functionals are curvature-weighted integrals of tensor products of position vectors and surface normal vectors over the interfacial surface. We here demonstrate their use by application to non-cubic triply periodic minimal surface model geometries, whose Weierstrass parametrizations allow for accurate numerical computation of the Minkowski tensors.

Item Type: Journal Article
Publisher: Royal Society Publishing
Copyright: © 2012 The Royal Society
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