11/16/04, 4:00 p.m. – 5:30 p.m.
||Herr Mecke, Max-Planck-Institut Stuttgart
||Pfaffenwaldring 61, Raum U1.003 (MML), Universität Stuttgart
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The structure of a disordered material - an oil bearing rock, a piece ofpaper, a polymer composite - is a remarkably incoherent concept. Despitethis, scientists and engineers are asked to relate its properties to thestructure of its constituent components.For instance, the fluid flow in sandstones depend crucially on the shape and distributiuon of the pores. Integral geometryfurnishes a suitable family of morphological descriptors, known asMinkowski functionals, which are related to curvatureintegrals and do not only characterize connectivity (topology) but alsosize and shape (geometry) of spatial structures.Applying the Minkowski functionals to parallelsurfaces of distance (r) to a structure one can definea family of morphological functions to characterize and reconstruct complex materials at porosity.Based on the morphological functions one can derive accurate expressions forpercolation thresholds, transport properties and phase equilibria inporous media.We illustrate this for the conductivity and elasticity ofcomplex model systems and experimental sandstone samples.In particular, for Boolean models the morphological functions areuniquely determined by its value at r=0 at any porosity. Thusa single image of a porous mediais sufficient to estimate and to predict physicalproperties such as permeabilities andelastic moduli.
C. H. Arns, M. A. Knackstedt, and K. Mecke,Reconstructing complex materials via effective grain shapes,Phys. Rev. Lett. 91, 215506 (2003).
Mecke, K. R. and D. Stoyan, Morphology of Condensed Matter - Physics andGeometry of Spatially Complex Systems,Lecture Notes in Physics, Vol. 600, Springer 2002.