Flattening

Abstract: This paper summarizes our knowledge at the beginning of 2003 about splat formation. First, the analytical and numerical models related to the impact and flattening of single particles on smooth or rough substrates with different tilting are recalled. Then, the different diagnostic methods, including imaging, are briefly described. The last part of the paper is devoted to the results and their discussion. Studies are related to the effect of various parameters on particle flattening. They include the characteristics of particles prior to impact: normal impact velocity, temperature, molten state, oxidation state, etc.; the parameters related to the substrate: tilting angle, roughness, oxide layer composition, thickness and crystallinity, desorption of adsorbates and condensates, wetting properties between impacting particle and substrate, etc.; and, finally, the parameters related to the heat exchange between the flattening particle and the substrate. They depend on previous parameters and control the propagation of the solidification front within the flattening particle, eventually modifying its liquid flow. It is obvious from this review that, if our understanding of the involved phenomena has been drastically improved during the last years, many points have still to be clarified. This is of primary importance because all the coating properties are linked to the particle flattening, splat formation, and layering.

Abstract: The narrow GD-1 stream of stars, spanning 60 deg on the sky at a distance of ~10 kpc from the Sun and ~15 kpc from the Galactic center, is presumed to be debris from a tidally disrupted star cluster that traces out a test-particle orbit in the Milky Way halo. We combine SDSS photometry, USNO-B astrometry, and SDSS and Calar Alto spectroscopy to construct a complete, empirical 6-dimensional phase-space map of the stream. We find that an eccentric orbit in a flattened isothermal potential describes this phase-space map well. Even after marginalizing over the stream orbital parameters and the distance from the Sun to the Galactic center, the orbital fit to GD-1 places strong constraints on the circular velocity at the Sun's radius V_c=224 \pm 13 km/s and total potential flattening q_\Phi=0.87^{+0.07}_{-0.04}. When we drop any informative priors on V_c the GD-1 constraint becomes V_c=221 \pm 18 km/s. Our 6-D map of GD-1 therefore yields the best current constraint on V_c and the only strong constraint on q_\Phi at Galactocentric radii near R~15 kpc. Much, if not all, of the total potential flattening may be attributed to the mass in the stellar disk, so the GD-1 constraints on the flattening of the halo itself are weak: q_{\Phi,halo}>0.89 at 90% confidence. The greatest uncertainty in the 6-D map and the orbital analysis stems from the photometric distances, which will be obviated by Gaia.

Abstract: We propose a new method to compute planar triangulations of faceted surfaces for surface parameterization. In contrast to previous approaches that define the flattening problem as a mapping of the three-dimensional node locations to the plane, our method defines the flattening problem as a constrained optimization problem in terms of angles (only). After applying a scaling that derives from the ‘curvature’ at a node, we minimize the relative deformation of the angles in the plane with respect to their counterparts in the three-dimensional surface. This approach makes the method more stable and robust than previous approaches, which used node locations in their formulations. The new method can handle any manifold surface for which a connected, valid, two-dimensional parameterization exists, including surfaces with large curvature gradients. It does not require the boundary of the flat two-dimensional domain to be prede-fined or convex. We use only the necessary and sufficient constraints for a valid two-dimensional triangulation. As a result, the existence of a theoretical solution to the minimization procedure is guaranteed.