Colloquium on April 26, 2010

Klaus Mecke
Universität Erlangen-Nürnberg

Minkowski Tensors: linking physics and geometry of materials

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 Minkowski functionals, which are related to curvature integrals and do not only characterize shape but also  anisotropy and even topology 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.