Dresden 2003 – scientific programme

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DY: Dynamik und Statistische Physik

DY 53: Statistical physics (general) II

DY 53.2: Talk

Friday, March 28, 2003, 11:45–12:00, G\"OR/229

Continuous real-space renormalization group for morphological measures — •Boris Breidenbach and Klaus Mecke — Max-Planck-Institut für Metallforschung, Heisenbergstr. 1, 70569 Stuttgart

Since many physical phenomena depend essentially on the geometry of spatial structures it is important to study geometry-based energies, e.g., Hamiltonians depending on curvatures of configurations. We study a morphological fluid model of overlapping spheres with an Hamiltonian linear in the Minkowski functionals, namely the covered volume, surface area, integral mean curvature, and Euler characteristic, known from integral geometry to be suitable descriptors of spatial patterns. This model naturally extends the well-known Widom-Rowlinson model and can be applied to complex fluids such as colloidal suspensions or microemulsion where curvatures play a major role. We present a novel real-space renormalization group technique in continuous space - in contrast to lattice models. Integrating partially over the positions of spheres one can rewrite the Hamiltonian in terms of a scaled particle yielding coupled differential equations for the renormalized Minkowski functionals. Results will be presented from both a mean-field theory approach and from renormalization group calculations. The phase diagram of the model shows a rich behavior of fluid structures and the scaling of bending rigidities are studied in different phases. Structure functions can be calculated and compared to results from scattering experiments.