Coplanar constant mean curvature surfaces

We consider constant mean curvature surfaces of finite topology, properly embedded in three-space in the sense of Alexandrov. Such surfaces with three ends and genus zero were constructed and completely classified by the authors in arXiv:math.DG/0102183. Here we extend the arguments to the case of an arbitrary number of ends, under the assumption that the asymptotic axes of the ends lie in a common plane: we construct and classify the entire family of these genus-zero coplanar constant mean curvature surfaces.Comment: 35 pages, 10 figures; minor revisions including one new figure; to appear in Comm. Anal. Geo

New Results on LEPP-delaunay Algorithm for Quality Triangulations

AbstractIn this paper, we provide proofs of termination and size-optimality of the LEPP-Delaunay algorithm, for the quality generation of triangulations. We first prove that the algorithm cannot insert points arbitrarily close to each other. We also show that the algorithm terminates, producing well-graded triangulations with internal angles greater than 25.66 degrees for geometries with input constrained angles of at least 30 degrees

There are simple and robust refinements (almost) as good as Delaunay

A new edge-based partition for triangle meshes is presented, the Seven Triangle Quasi-Delaunay partition (7T-QD). The proposed partition joins together ideas of the Seven Triangle Longest-Edge partition (7T-LE), and the classical criteria for constructing Delaunay meshes. The new partition performs similarly compared to the Delaunay triangulation (7T-D) with the benefit of being more robust and with a cheaper cost in computation. It will be proved that in most of the cases the 7T-QD is equal to the 7T-D. In addition, numerical tests will show that the difference on the minimum angle obtained by the 7T-QD and by the 7T-D is negligible

Laboratory photo-chemistry of pyrene clusters: an efficient way to form large PAHs

In this work, we study the photodissociation processes of small PAH clusters (e.g., pyrene clusters). The experiments are carried out using a quadrupole ion trap in combination with time-of-flight (QIT-TOF) mass spectrometry. The results show that pyrene clusters are converted into larger PAHs under the influence of a strong radiation field. Specifically, pyrene dimer cations (e.g., [C$_{16}$H$_{10}$$-$C$_{16}$H$_{9}$]$^+$ or C$_{32}$H$_{19}$$^+$), will photo-dehydrogenate and photo-isomerize to fully aromatic cations (PAHs) (e.g., C$_{32}$H$_{16}$$^+$) with laser irradiation. The structure of new formed PAHs and the dissociation energy for these reaction pathways are investigated with quantum chemical calculations. These studies provide a novel efficient evolution routes for the formation of large PAHs in the interstellar medium (ISM) in a bottom-up process that will counteract the top-down conversion of large PAHs into rings and chains, and provide a reservoir of large PAHs that can be converted into C$_{60}$ and other fullerenes and large carbon cages