Berlin 2008 – scientific programme

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CPP: Fachverband Chemische Physik und Polymerphysik

CPP 21: POSTERS Colloids, Nanoparticles and Aggregates

CPP 21.29: Poster

Wednesday, February 27, 2008, 16:00–18:30, Poster A

Geometric Order Parameters for Point Patterns — •Sebastian Bittner and Klaus Mecke — Institut für Theoretische Physik Universität Erlangen-Nürnberg, Staudtstrasse 7, 91058 Erlangen, Germany

Higher correlations are important to characterise hexatic phases in colloidal systems or non-Gaussian fluctuations in fluids beyond the two-point structure function. A hybrid technique of two-point correlation functions and Minkowski functions of point patterns offer the possibility to measure higher correlations in a statistically robust way.

The geometrical idea of the morphological technique is simple: a ring of outer radius R and inner radius r<R is attached at each point of the pattern, which will overlap mutually. The morphology of the coverage is then analysed geometrically for all reasonable values of r and R by measuring its area, boundary length and Euler characteristic. For r=0 one recovers the standard Minkowski functions of point patterns whereas for r→ R the measures reduce to the two-point characteristics.

We present an algorithm for computing the morphological functions of the coverage and snapshots from visualisations of the rings. Finally, we apply this hybrid method on various point patterns in physics and biology, e.g. on colloidal configurations.