14,084 research outputs found
Flipping Cubical Meshes
We define and examine flip operations for quadrilateral and hexahedral
meshes, similar to the flipping transformations previously used in triangular
and tetrahedral mesh generation.Comment: 20 pages, 24 figures. Expanded journal version of paper from 10th
International Meshing Roundtable. This version removes some unwanted
paragraph breaks from the previous version; the text is unchange
Outerplanar crossing numbers of 3-row meshes, Halin graphs and complete p-partite graphs
An outerplanar (also called circular, convex, one-page) drawing
of an n-vertex graph G is a drawing in which the vertices are placed
on a circle and each edge is drawn using one straight-line segment. We
derive exact results for the minimal number of crossings in any outerplanar
drawings of the following classes of graphs: 3-row meshes, Halin
graphs and complete pâpartite graphs with equal size partite sets
Experimental Evaluation of Book Drawing Algorithms
A -page book drawing of a graph consists of a linear ordering of
its vertices along a spine and an assignment of each edge to one of the
pages, which are half-planes bounded by the spine. In a book drawing, two edges
cross if and only if they are assigned to the same page and their vertices
alternate along the spine. Crossing minimization in a -page book drawing is
NP-hard, yet book drawings have multiple applications in visualization and
beyond. Therefore several heuristic book drawing algorithms exist, but there is
no broader comparative study on their relative performance. In this paper, we
propose a comprehensive benchmark set of challenging graph classes for book
drawing algorithms and provide an extensive experimental study of the
performance of existing book drawing algorithms.Comment: Appears in the Proceedings of the 25th International Symposium on
Graph Drawing and Network Visualization (GD 2017
Finite-Difference Calculations for Atoms and Diatomic Molecules in Strong Magnetic and Static Electric Fields
Fully numerical mesh solutions of 2D quantum equations of Schroedinger and
Hartree-Fock type allow us to work with wavefunctions which possess a very
flexible geometry. This flexibility is especially important for calculations of
atoms and molecules in strong external fields where neither the external field
nor the internal interactions can be considered as a perturbation. The
applications of the present approach include calculations of atoms and diatomic
molecules in strong static electric and magnetic fields. For the latter we have
carried out Hartree-Fock calculations for He, Li, C and several other atoms.
This yields in particular the first comprehensive investigation of the ground
state configurations of the Li and C atoms in the whole range of magnetic
fields (0<B<10000 a.u.) and a study of the ground state electronic
configurations of all the atoms with 1<Z<11 and their ions A^+ in the
high-field fully spin-polarised regime. The results in a case of a strong
electric field relate to single-electron systems including the correct solution
of the Schroedinger equation for the H_2^+ ion (energies and decay rates) and
the hydrogen atom in strong parallel electric and magnetic fields.Comment: 20 pages, 7 figure
Geometrical approach to SU(2) navigation with Fibonacci anyons
Topological quantum computation with Fibonacci anyons relies on the
possibility of efficiently generating unitary transformations upon
pseudoparticles braiding. The crucial fact that such set of braids has a dense
image in the unitary operations space is well known; in addition, the
Solovay-Kitaev algorithm allows to approach a given unitary operation to any
desired accuracy. In this paper, the latter task is fulfilled with an
alternative method, in the SU(2) case, based on a generalization of the
geodesic dome construction to higher dimension.Comment: 12 pages, 5 figure
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