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The statistical mechanical investigation of Violent Relaxation of phase space elements of different densities first derived by Lynden-Bell (1967) is re-examined. It is found that the mass independence of the equations of motion of Violent Relaxation calls for a constraint on the volume of the phase space elements used to formulate the statistical mechanical description of Violent Relaxation. In agreement with observations of astrophysical objects believed to have been subject to Violent Relaxation (e.g. clusters of galaxies), the coarse grained phase space distributionf of the final state in the non-degenerate limit turns into a superposition of Maxwellians of a common velocity dispersion. Thus, the velocity dispersion problem present in the investigation of Lynden-Bell (1967) is removed.

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Figure 1: Visualizing time-varying frequencies of eye gaze fixations and transitions with AOI Rivers. AbstractIt is difficult to explore and analyze eye gaze trajectories for commonly applied visual task solution strategies because such data shows complex spatio-temporal structure. In particular, the traditional eye gaze plots of scan paths fail for a large number of study participants since these plots lead to much visual clutter. To address this problem we introduce the AOI Rivers technique as a novel interactive visualization method for investigating timevarying fixation frequencies, transitions between areas of interest (AOIs), and the sequential order of gaze visits to AOIs in a visual stimulus of an eye tracking experiment. To this end, we extend the ThemeRiver technique by influents, effluents, and transitions similar to the concept of Sankey diagrams. The AOI Rivers visualization is complemented by linked spatial views of the data in the form of heatmaps, gaze plots, or display of the visual stimulus. The usefulness of our technique is demonstrated for gaze trajectory data recorded in a previously conducted eye tracking experiment.

An analytic collapse model for the formation and density distribution of virialized cold dark matter halos is proposed. Hierarchical structure formation is taken into account explicitly. Monte Carlo methods are used to generate samples of mass histories of virialized halos. The mean density distribution found from the collapse model is in good agreement with numerical results in the mass range from 10 11 M ⊙ to 10 15 M ⊙ and in the radial range form 0.05r 200 to r 200 .