On Colorful Bin Packing Games

We consider colorful bin packing games in which selfish players control a set of items which are to be packed into a minimum number of unit capacity bins. Each item has one of $m\geq 2$ colors and cannot be packed next to an item of the same color. All bins have the same unitary cost which is shared among the items it contains, so that players are interested in selecting a bin of minimum shared cost. We adopt two standard cost sharing functions: the egalitarian cost function which equally shares the cost of a bin among the items it contains, and the proportional cost function which shares the cost of a bin among the items it contains proportionally to their sizes. Although, under both cost functions, colorful bin packing games do not converge in general to a (pure) Nash equilibrium, we show that Nash equilibria are guaranteed to exist and we design an algorithm for computing a Nash equilibrium whose running time is polynomial under the egalitarian cost function and pseudo-polynomial for a constant number of colors under the proportional one. We also provide a complete characterization of the efficiency of Nash equilibria under both cost functions for general games, by showing that the prices of anarchy and stability are unbounded when $m\geq 3$ while they are equal to 3 for black and white games, where $m=2$. We finally focus on games with uniform sizes (i.e., all items have the same size) for which the two cost functions coincide. We show again a tight characterization of the efficiency of Nash equilibria and design an algorithm which returns Nash equilibria with best achievable performance

Small-scale swirl events in the quiet Sun chromosphere

Recent progress in instrumentation enables solar observations with high resolution simultaneously in the spatial, temporal, and spectral domains. We use such high-resolution observations to study small-scale structures and dynamics in the chromosphere of the quiet Sun. We analyze time series of spectral scans through the Ca II 854.2nm spectral line obtained with the CRISP instrument at the Swedish 1-m Solar Telescope. The targets are quiet Sun regions inside coronal holes close to disc-centre. The line core maps exhibit relatively few fibrils compared to what is normally observed in quiet Sun regions outside coronal holes. The time series show a chaotic and dynamic scene that includes spatially confined "swirl" events. These events feature dark and bright rotating patches, which can consist of arcs, spiral arms, rings or ring fragments. The width of the fragments typically appears to be on the order of only 0.2", which is close to the effective spatial resolution. They exhibit Doppler shifts of -2 to -4 km/s but sometimes up to -7 km/s, indicating fast upflows. The diameter of a swirl is usually of the order of 2". At the location of these swirls, the line wing and wide-band maps show close groups of photospheric bright points that move with respect to each other. A likely explanation is that the relative motion of the bright points twists the associated magnetic field in the chromosphere above. Plasma or propagating waves may then spiral upwards guided by the magnetic flux structure, thereby producing the observed intensity signature of Doppler-shifted ring fragments.Comment: 4 pages, 3 figures, A&A Letter, accepted (final version

Ram pressure and dusty red galaxies - key factors in the evolution of the multiple cluster system Abell 901/902

We present spectroscopic observations of 182 disk galaxies (96 in the cluster and 86 in the field environment) in the region of the Abell 901/902 multiple cluster system, which is located at a redshift of $z\sim 0.165$. The presence of substructures and non-Gaussian redshift distributions indicate that the cluster system is dynamically young and not in a virialized state. We find evidence for two important galaxy populations. \textit{Morphologically distorted galaxies} are probably subject to increased tidal interactions. They show pronounced rotation curve asymmetries at intermediate cluster-centric radii and low rest-frame peculiar velocities. \textit{Morphologically undistorted galaxies} show the strongest rotation curve asymmetries at high rest-frame velocities and low cluster-centric radii. Supposedly, this group is strongly affected by ram-pressure stripping due to interaction with the intra-cluster medium. Among the morphologically undistorted galaxies, dusty red galaxies have particularly strong rotation curve asymmetries, suggesting ram pressure is an important factor in these galaxies. Furthermore, dusty red galaxies on average have a bulge-to-total ratio higher by a factor of two than cluster blue cloud and field galaxies. The fraction of kinematically distorted galaxies is 75% higher in the cluster than in the field environment. This difference mainly stems from morphological undistorted galaxies, indicating a cluster-specific interaction process that only affects the gas kinematics but not the stellar morphology. Also the ratio between gas and stellar scale length is reduced for cluster galaxies compared to the field sample. Both findings could be best explained by ram-pressure effects.Comment: Electronic version published in Astronomy and Astrophysics Volume 549, Page 0; 19 pages, 21 figure

The impact of draping effects on the stiffness and failure behavior of unidirectional non-crimp fabric fiber reinforced composites

Unidirectional non-crimp fabrics (UD-NCF) are often used to exploit the lightweight potential of continuous fiber reinforced plastics (CoFRP). During the draping process, the UD-NCF fabric can undergo large deformations that alter the local fiber orientation, the local fiber volume content (FVC) and create local fiber waviness. Especially the FVC is affected and has a large impact on the mechanical properties. This impact, resulting from different deformation modes during draping, is in general not considered in composite design processes. To analyze the impact of different draping effects on the mechanical properties and the failure behavior of UD-NCF composites, experimental results of reference laminates are compared to the results of laminates with specifically induced draping effects, such as non-constant FVC and fiber waviness. Furthermore, an analytical model to predict the failure strengths of UD laminates with in-plane waviness is introduced. The resulting stiffness and strength values for different FVC or amplitude to wavelength configurations are presented and discussed. In addition, failure envelopes based on the PUCK failure criterion for each draping effect are derived, which show a clear specific impact on the mechanical properties. The findings suggest that each draping effect leads to a “new fabric” type. Additionally, analytical models are introduced and the experimental results are compared to the predictions. Results indicate that the models provide reliable predictions for each draping effect. Recommendations regarding necessary tests to consider each draping effect are presented. As a further prospect the resulting stiffness and strength values for each draping effect can be used for a more accurate prediction of the structural performance of CoFRP parts