Kinetic and Dynamic Delaunay tetrahedralizations in three dimensions

We describe the implementation of algorithms to construct and maintain three-dimensional dynamic Delaunay triangulations with kinetic vertices using a three-simplex data structure. The code is capable of constructing the geometric dual, the Voronoi or Dirichlet tessellation. Initially, a given list of points is triangulated. Time evolution of the triangulation is not only governed by kinetic vertices but also by a changing number of vertices. We use three-dimensional simplex flip algorithms, a stochastic visibility walk algorithm for point location and in addition, we propose a new simple method of deleting vertices from an existing three-dimensional Delaunay triangulation while maintaining the Delaunay property. The dual Dirichlet tessellation can be used to solve differential equations on an irregular grid, to define partitions in cell tissue simulations, for collision detection etc.Comment: 29 pg (preprint), 12 figures, 1 table Title changed (mainly nomenclature), referee suggestions included, typos corrected, bibliography update

Kinetics of Fluid Demixing in Complex Plasmas: Domain Growth Analysis using Minkowski Tensors

A molecular dynamics simulation of the demixing process of a binary complex plasma is analysed and the role of distinct interaction potentials is discussed by using morphological Minkowski tensor analysis of the minority phase domain growth in a demixing simulated binary complex plasma. These Minkowski tensor methods are compared with previous results that utilized a power spectrum method based on the time-dependent average structure factor. It is shown that the Minkowski tensor methods are superior to the previously used power spectrum method in the sense of higher sensitivity to changes in domain size. By analysis of the slope of the temporal evolution of Minkowski tensor measures qualitative differences between the case of particle interaction with a single length scale compared to particle interactions with two different length scales (dominating long range interaction) are revealed. After proper scaling the graphs for the two length scale scenario coincide, pointing towards universal behaviour. The qualitative difference in demixing scenarios is evidenced by distinct demixing behaviour: In the long range dominated cases demixing occurs in two stages. At first neighbouring particles agglomerate then domains start to merge in cascades. However in the case of only one interaction length scale only agglomeration but no merging of domains can be observed. Thus, Minkowski Tensor analysis are likely to become a useful tool for further investigation of this (and other) demixing processes. It is capable to reveal (nonlinear) local topological properties, probing deeper than (linear) global power spectrum analysis, however still providing easily interpretable results founded on a solid mathematical framework.Comment: 12 pages, 10 figures, Phys. Rev. E, accepted for publication, http://journals.aps.org/pr