Cavity averages for hard spheres in the presence of polydispersity and incomplete data

We develop a cavity-based method which allows to extract thermodynamic properties from position information in hard-sphere/disk systems. So far, there are 'available-volume' and 'free-volume' methods. We add a third one, which we call 'available-volume-after-takeout', and which is shown to be mathematically equivalent to the others. In applications, where data sets are finite, all three methods show limitations, and they do this in different parameter ranges. We illustrate the principal equivalence and the limitations on data from molecular dynamics -- In particular, we test robustness against missing data. We have in mind experimental limitations where there is a small polydispersity, say 4% in the particle radii, but individual radii cannot be determined. We observe that, depending on the used method, the errors in such a situation are easily 100% for the pressure and 10kT for the chemical potentials. Our work is meant as guideline to the experimentalist for choosing the right one of the three methods, in order to keep the outcome of experimental data analysis meaningful.Comment: 13 pages, 6 figures. The final publication is available at Springer via http://dx.doi.org/10.1140/epje/i2015-15097-

The range and nature of effective interactions in hard-sphere solids

Colloidal systems observed in video microscopy are often analysed using the displacements correlation matrix of particle positions. In non-thermal systems, the inverse of this matrix can be interpreted as a pair-interaction potential between particles. If the system is thermally agitated, however, only an effective interaction is accessible from the correlation matrix. We show how this effective interaction differs from the non-thermal case by comparing with high-statistics numerical data from hard-sphere crystals.Comment: 12 pages, 10 figures, Soft Matter 201

Texte schreiben

Der vorliegende Sammelband dokumentiert die Arbeit in der Sektion „Texte schreiben“ des 16. Symposions Deutschdidaktik 2006 in Weingarten. Innerhalb des Rahmenthemas „Kompetenzen im Deutschunterricht“ lag der Schwerpunkt der Sektionsarbeit auf der Schreibkompetenz, d.h. der Fähigkeit, selbstständig und kooperativ Texte für unterschiedliche Zwecke zu produzieren. Gefragt wurde, was das Besondere der Schreibkompetenz ausmacht, wie sie sich entwickelt und welche Anforderungen an sie aus unterschiedlichen Aufgabenbereichen gestellt werden. Die Beiträge dieses Sammelbandes beleuchten diese Thematik aus verschiedenen Perspektiven und mit unterschiedlichen Schwerpunktsetzungen