2,513 research outputs found
Duo: a general program for calculating spectra of diatomic molecules
Duo is a general, user-friendly program for computing rotational,
rovibrational and rovibronic spectra of diatomic molecules. Duo solves the
Schr\"{o}dinger equation for the motion of the nuclei not only for the simple
case of uncoupled, isolated electronic states (typical for the ground state of
closed-shell diatomics) but also for the general case of an arbitrary number
and type of couplings between electronic states (typical for open-shell
diatomics and excited states). Possible couplings include spin-orbit, angular
momenta, spin-rotational and spin-spin. Corrections due to non-adiabatic
effects can be accounted for by introducing the relevant couplings using
so-called Born-Oppenheimer breakdown curves.
Duo requires user-specified potential energy curves and, if relevant, dipole
moment, coupling and correction curves. From these it computes energy levels,
line positions and line intensities. Several analytic forms plus interpolation
and extrapolation options are available for representation of the curves. Duo
can refine potential energy and coupling curves to best reproduce reference
data such as experimental energy levels or line positions. Duo is provided as a
Fortran 2003 program and has been tested under a variety of operating systems
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Lie-group interpolation and variational recovery for internal variables
We propose a variational procedure for the recovery of internal variables, in effect extending them from integration points to the entire domain. The objective is to perform the recovery with minimum error and at the same time guarantee that the internal variables remain in their admissible spaces. The minimization of the error is achieved by a three-field finite element formulation. The fields in the formulation are the deformation mapping, the target or mapped internal variables and a Lagrange multiplier that enforces the equality between the source and target internal variables. This formulation leads to an L2 projection that minimizes the distance between the source and target internal variables as measured in the L2 norm of the internal variable space. To ensure that the target internal variables remain in their original space, their interpolation is performed by recourse to Lie groups, which allows for direct polynomial interpolation of the corresponding Lie algebras by means of the logarithmic map. Once the Lie algebras are interpolated, the mapped variables are recovered by the exponential map, thus guaranteeing that they remain in the appropriate space
Gravitational Lensing in Clusters of Galaxies
Gravitational lensing in clusters of galaxies is an efficient tool to probe
the mass distribution of galaxies and clusters, high redshift objects thanks to
the gravitational amplification, and the geometry of the universe. We review
some important aspects of cluster lensing and related issues in observational
cosmology.Comment: invited review of the journal: Progress of Theoretical Physics (in
press) 51 pages - 33 figure
Three dimensional numerical relativity: the evolution of black holes
We report on a new 3D numerical code designed to solve the Einstein equations
for general vacuum spacetimes. This code is based on the standard 3+1 approach
using cartesian coordinates. We discuss the numerical techniques used in
developing this code, and its performance on massively parallel and vector
supercomputers. As a test case, we present evolutions for the first 3D black
hole spacetimes. We identify a number of difficulties in evolving 3D black
holes and suggest approaches to overcome them. We show how special treatment of
the conformal factor can lead to more accurate evolution, and discuss
techniques we developed to handle black hole spacetimes in the absence of
symmetries. Many different slicing conditions are tested, including geodesic,
maximal, and various algebraic conditions on the lapse. With current
resolutions, limited by computer memory sizes, we show that with certain lapse
conditions we can evolve the black hole to about , where is the
black hole mass. Comparisons are made with results obtained by evolving
spherical initial black hole data sets with a 1D spherically symmetric code. We
also demonstrate that an ``apparent horizon locking shift'' can be used to
prevent the development of large gradients in the metric functions that result
from singularity avoiding time slicings. We compute the mass of the apparent
horizon in these spacetimes, and find that in many cases it can be conserved to
within about 5\% throughout the evolution with our techniques and current
resolution.Comment: 35 pages, LaTeX with RevTeX 3.0 macros. 27 postscript figures taking
7 MB of space, uuencoded and gz-compressed into a 2MB uufile. Also available
at http://jean-luc.ncsa.uiuc.edu/Papers/ and mpeg simulations at
http://jean-luc.ncsa.uiuc.edu/Movies/ Submitted to Physical Review
Manifold interpolation and model reduction
One approach to parametric and adaptive model reduction is via the
interpolation of orthogonal bases, subspaces or positive definite system
matrices. In all these cases, the sampled inputs stem from matrix sets that
feature a geometric structure and thus form so-called matrix manifolds. This
work will be featured as a chapter in the upcoming Handbook on Model Order
Reduction (P. Benner, S. Grivet-Talocia, A. Quarteroni, G. Rozza, W.H.A.
Schilders, L.M. Silveira, eds, to appear on DE GRUYTER) and reviews the
numerical treatment of the most important matrix manifolds that arise in the
context of model reduction. Moreover, the principal approaches to data
interpolation and Taylor-like extrapolation on matrix manifolds are outlined
and complemented by algorithms in pseudo-code.Comment: 37 pages, 4 figures, featured chapter of upcoming "Handbook on Model
Order Reduction
Grid generation for the solution of partial differential equations
A general survey of grid generators is presented with a concern for understanding why grids are necessary, how they are applied, and how they are generated. After an examination of the need for meshes, the overall applications setting is established with a categorization of the various connectivity patterns. This is split between structured grids and unstructured meshes. Altogether, the categorization establishes the foundation upon which grid generation techniques are developed. The two primary categories are algebraic techniques and partial differential equation techniques. These are each split into basic parts, and accordingly are individually examined in some detail. In the process, the interrelations between the various parts are accented. From the established background in the primary techniques, consideration is shifted to the topic of interactive grid generation and then to adaptive meshes. The setting for adaptivity is established with a suitable means to monitor severe solution behavior. Adaptive grids are considered first and are followed by adaptive triangular meshes. Then the consideration shifts to the temporal coupling between grid generators and PDE-solvers. To conclude, a reflection upon the discussion, herein, is given
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