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CeNS Colloquium

Place: Kleiner Physik-Hörsaal, Geschwister-Scholl-Platz
Date: 08.05.09, Time: 15:30 h

Tensor valuations: linking physics and geometry of materials

Prof. Klaus Mecke
Universität Erlangen


Spatially structured matter such as foams, gels or biomaterials are of increasing technological importance due to their shape-dependent material properties. But the shape of disordered structures is a remarkably incoherent concept and cannot be captured by correlation functions alone. Integral geometry furnishes a suitable family of morphological descriptors, so-called tensorial valuations, which are related to curvature integrals and do not only characterize shape but also anisotropy of disordered structures. These measures can be related to the spectrum of the Laplace operator and to thermodynamic potentials of confined systems, so that structure-property relations can be derived for complex materials.


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P.-M. Koenig et al.: "Morphological thermodynamics of fluids: shape dependence of free energies"
PRL 93, 160601 (2004).

H. Hansen-Goos et al.: "Solvation of proteins: linking thermodynamics to geometry"
PRL 99, 128101 (2007).

H. Hansen-Goos et al.: "Fundamental measure theory for inhomogeneous fluids of non-spherical hard particles"
PRL 102, 018302 (2009).