Pomelo, a tool for computing Generic Set Voronoi Diagrams of Aspherical Particles of Arbitrary Shape

We describe the development of a new software tool, called "Pomelo", for the calculation of Set Voronoi diagrams. Voronoi diagrams are a spatial partition of the space around the particles into separate Voronoi cells, e.g. applicable to granular materials. A generalization of the conventional Voronoi diagram for points or monodisperse spheres is the Set Voronoi diagram, also known as navigational map or tessellation by zone of influence. In this construction, a Set Voronoi cell contains the volume that is closer to the surface of one particle than to the surface of any other particle. This is required for aspherical or polydisperse systems. Pomelo is designed to be easy to use and as generic as possible. It directly supports common particle shapes and offers a generic mode, which allows to deal with any type of particles that can be described mathematically. Pomelo can create output in different standard formats, which allows direct visualization and further processing. Finally, we describe three applications of the Set Voronoi code in granular and soft matter physics, namely the problem of packings of ellipsoidal particles with varying degrees of particle-particle friction, mechanical stable packings of tetrahedra and a model for liquid crystal systems of particles with shapes reminiscent of pearsComment: 4 pages, 9 figures, Submitted to Powders and Grains 201

Non-universal Voronoi cell shapes in amorphous ellipsoid packings

In particulate systems with short-range interactions, such as granular matter or simple fluids, local structure plays a pivotal role in determining the macroscopic physical properties. Here, we analyse local structure metrics derived from the Voronoi diagram of configurations of oblate ellipsoids, for various aspect ratios $\alpha$ and global volume fractions $\phi_g$. We focus on jammed static configurations of frictional ellipsoids, obtained by tomographic imaging and by discrete element method simulations. In particular, we consider the local packing fraction $\phi_l$, defined as the particle's volume divided by its Voronoi cell volume. We find that the probability $P(\phi_l)$ for a Voronoi cell to have a given local packing fraction shows the same scaling behaviour as function of $\phi_g$ as observed for random sphere packs. Surprisingly, this scaling behaviour is further found to be independent of the particle aspect ratio. By contrast, the typical Voronoi cell shape, quantified by the Minkowski tensor anisotropy index $\beta=\beta_0^{2,0}$, points towards a significant difference between random packings of spheres and those of oblate ellipsoids. While the average cell shape $\beta$ of all cells with a given value of $\phi_l$ is very similar in dense and loose jammed sphere packings, the structure of dense and loose ellipsoid packings differs substantially such that this does not hold true. This non-universality has implications for our understanding of jamming of aspherical particles.Comment: 6 pages, 5 figure

Tomographic analysis of jammed ellipsoid packings

Disordered packings of ellipsoidal particles are an important model for disordered granular matter. Here we report a way to determine the average contact number of ellipsoid packings from tomographic analysis. Tomographic images of jammed ellipsoid packings prepared by vertical shaking of loose configurations are recorded and the positions and orientations of the ellipsoids are reconstructed. The average contact number can be extracted from a contact number scaling (CNS) function. The size of the particles, that may vary due to production inaccuracies, can also be determined by this method

The microscopic structure of mono-disperse granular heaps and sediments of particles on inclined surfaces

Granular heaps of particles created by deposition of mono-disperse particles raining from an extended source of finite size are characterized by a non-homogeneous field of density. It was speculated that this inhomogeneity is due to the transient shape of the sediment during the process of construction of the heap, thus reflecting the history of the creation of the heap. By comparison of structural characteristics of the heap with sediments created on top of inclined planes exploiting the method of Minkowski tensors, we provide further evidence to support this hypothesis. Moreover, for the case of sediments generated by homogeneous rain on surfaces, we provide relationships between the inclination of the surface and the Minkowski measures characterizing the isotropy of local particle environments

Keck Spectroscopy of Candidate Proto-globular Clusters in NGC 1275

Keck spectroscopy of 5 proto-globular cluster candidates in NGC 1275 has been combined with HST WFPC2 photometry to explore the nature and origin of these objects and discriminate between merger and cooling flow scenarios for globular cluster formation. The objects we have studied are not HII regions, but rather star clusters, yet their integrated spectral properties do not resemble young or intermediate age Magellanic Cloud clusters or Milky Way open clusters. The clusters' Balmer absorption appears to be too strong to be consistent with any of the standard Bruzual & Charlot evolutionary models at any metallicity. If these models are adopted, an IMF which is skewed to high masses provides a better fit to the data. A truncated IMF with a mass range of 2-3 Mo reproduces the observed Balmer equivalent widths and colors at about 450 Myr. Formation in a continuous cooling flow appears to be ruled out since the age of the clusters is much larger than the cooling time, the spatial scale of the clusters is much smaller than the cooling flow radius, and the deduced star formation rate in the cooling flow favors a steep rather than a flat IMF. A merger would have to produce clusters only in the central few kpc, presumably from gas in the merging galaxies which was channeled rapidly to the center. Widespread shocks in merging galaxies cannot have produced these clusters. If these objects are confirmed to have a relatively flat, or truncated, IMF it is unclear whether or not they will evolve into objects we would regard as bona fide globular clusters.Comment: 30 pages (AAS two column style, including 9 tables and 7 figures) to appear in the AJ (August issue), also available at http://www.ucolick.org/~mkissler/Sages/sages.html (with a full resolution Fig.1) Revised Version: previous posted version was an uncorrect ealier iteration, parts of the text, tables and figures changed. The overall conclusions remain unchange

Multiwavelength study of the starburst galaxy NGC7714. I: Ultraviolet-Optical spectroscopy

We have studied the physical conditions in the central 300 pc of the proto-typical starburst galaxy NGC 7714. Our analysis is based on ultraviolet spectroscopy with the HST+GHRS and ground-based optical observations.The data are interpreted using evolutionary models optimized for young starburst regions. The massive stellar population is derived in a self-consistent way using the continuum and stellar absorption lines in the ultraviolet and the nebular emission line optical spectrum. The central starburst has an age of about 4.5 Myr, with little evidence for an age spread. Wolf-Rayet features at the ultraviolet indicates a stellar population of $\sim$ 2000 Wolf-Rayet stars. The overall properties of the newly formed stars are quite similar to those derived, e.g., in 30 Doradus. A standard Salpeter IMF is consistent with all observational constraints. We find evidence for spatial structure within the central 300 pc sampled. Therefore it is unlikely that the nucleus of NGC 7714 hosts a single star cluster exceeding the properties of other known clusters. Contrary to previous suggestions, we find no evidence for a nuclear supernova rate that would significantly exceed the total disk-integrated rate. About one supernova event per century is predicted.Comment: 19 pages, 9 figures in a tar file. Accepted for publication in ApJ, 1999, March, issue 51

Universal hidden order in amorphous cellular geometries

Partitioning space into cells with certain extreme geometrical properties is a central problem in many fields of science and technology. Here we investigate the Quantizer problem, defined as the optimisation of the moment of inertia of Voronoi cells, i.e., similarly-sized ‘sphere-like’ polyhedra that tile space are preferred. We employ Lloyd’s centroidal Voronoi diagram algorithm to solve this problem and find that it converges to disordered states associated with deep local minima. These states are universal in the sense that their structure factors are characterised by a complete independence of a wide class of initial conditions they evolved from. They moreover exhibit an anomalous suppression of long-wavelength density fluctuations and quickly become effectively hyperuniform. Our findings warrant the search for novel amorphous hyperuniform phases and cellular materials with unique physical properties

Universal hidden order in amorphous cellular geometries

Partitioning space into cells with certain extreme geometrical properties is a central problem in many fields of science and technology. Here we investigate the Quantizer problem, defined as the optimisation of the moment of inertia of Voronoi cells, i.e., similarly-sized ‘sphere-like’ polyhedra that tile space are preferred. We employ Lloyd’s centroidal Voronoi diagram algorithm to solve this problem and find that it converges to disordered states associated with deep local minima. These states are universal in the sense that their structure factors are characterised by a complete independence of a wide class of initial conditions they evolved from. They moreover exhibit an anomalous suppression of long-wavelength density fluctuations and quickly become effectively hyperuniform. Our findings warrant the search for novel amorphous hyperuniform phases and cellular materials with unique physical properties