9,755 research outputs found
Incomplete Orthogonal Factorization Methods Using Givens Rotations II: Implementation and Results
We present, implement and test a series of incomplete orthogonal factorization methods based on Givens rotations for large sparse unsymmetric matrices. These methods include: column-Incomplete Givens Orthogonalization (cIGO-method), which drops entries by position only; column-Threshold Incomplete Givens Orthogonalization (cTIGO-method) which drops entries dynamically by both their magnitudes and positions and where the reduction via Givens rotations is done in a column-wise fashion; and, row-Threshold Incomplete Givens Orthogonalization (r-TIGO-method) which again drops entries dynamically, but only magnitude is now taken into account and reduction is performed in a row-wise fashion. We give comprehensive accounts of how one would code these algorithms using a high level language to ensure efficiency of computation and memory use. The methods are then applied to a variety of square systems and their performance as preconditioners is tested against standard incomplete LU factorization techniques. For rectangular matrices corresponding to least-squares problems, the resulting incomplete factorizations are applied as preconditioners for conjugate gradients for the system of normal equations. A comprehensive discussion about the uses, advantages and shortcomings of these preconditioners is given
Dynamics of Scalar Fields in the Background of Rotating Black Holes
A numerical study of the evolution of a massless scalar field in the
background of rotating black holes is presented. First, solutions to the wave
equation are obtained for slowly rotating black holes. In this approximation,
the background geometry is treated as a perturbed Schwarzschild spacetime with
the angular momentum per unit mass playing the role of a perturbative
parameter. To first order in the angular momentum of the black hole, the scalar
wave equation yields two coupled one-dimensional evolution equations for a
function representing the scalar field in the Schwarzschild background and a
second field that accounts for the rotation. Solutions to the wave equation are
also obtained for rapidly rotating black holes. In this case, the wave equation
does not admit complete separation of variables and yields a two-dimensional
evolution equation. The study shows that, for rotating black holes, the late
time dynamics of a massless scalar field exhibit the same power-law behavior as
in the case of a Schwarzschild background independently of the angular momentum
of the black hole.Comment: 14 pages, RevTex, 6 Figure
A current disruption mechanism in the neutral sheet for triggering substorm expansions
Two main areas were addressed in support of an effort to understand mechanism responsible for the broadband electrostatic noise (BEN) observed in the magnetotail. The first area concerns the generation of BEN in the boundary layer region of the magnetotail whereas the second area concerns the occassional presence of BEN in the neutral sheet region. For the generation of BEN in the boundary layer region, a hybrid simulation code was developed to perform reliable longtime, quiet, highly resolved simulations of field aligned electron and ion beam flow. The result of the simulation shows that broadband emissions cannot be generated by beam-plasma instability if realistic values of the ion beam parameters are used. The waves generated from beam-plasma instability are highly discrete and are of high frequencies. For the plasma sheet boundary layer condition, the wave frequencies are in the kHz range, which is incompatible with the observation that the peak power in BEN occur in the 10's of Hz range. It was found that the BEN characteristics are more consistent with lower hybrid drift instability. For the occasional presence of BEN in the neutral sheet region, a linear analysis of the kinetic cross-field streaming instability appropriate to the neutral sheet condition just prior to onset of substorm expansion was performed. By solving numerically the dispersion relation, it was found that the instability has a growth time comparable to the onset time scale of substorm onset. The excited waves have a mixed polarization in the lower hybrid frequency range. The imposed drift driving the instability corresponds to unmagnetized ions undergoing current sheet acceleration in the presence of a cross-tail electric field. The required electric field strength is in the 10 mV/m range which is well within the observed electric field values detected in the neutral sheet during substorms. This finding can potentially account for the disruption of cross-tail current and its diversion to the ionosphere to form the substorm current wedge. Furthermore, a number of features associated with substorm expansion onset can be understood based on this substorm onset scenario
The spinorial geometry of supersymmetric heterotic string backgrounds
We determine the geometry of supersymmetric heterotic string backgrounds for
which all parallel spinors with respect to the connection with
torsion , the NSNS three-form field strength, are Killing. We find
that there are two classes of such backgrounds, the null and the timelike. The
Killing spinors of the null backgrounds have stability subgroups
K\ltimes\bR^8 in , for , SU(4), , and , and the Killing spinors of the timelike backgrounds have
stability subgroups , SU(3), SU(2) and . The former admit a single
null -parallel vector field while the latter admit a timelike and
two, three, five and nine spacelike -parallel vector fields,
respectively. The spacetime of the null backgrounds is a Lorentzian
two-parameter family of Riemannian manifolds with skew-symmetric torsion.
If the rotation of the null vector field vanishes, the holonomy of the
connection with torsion of is contained in . The spacetime of time-like
backgrounds is a principal bundle with fibre a Lorentzian Lie group and
base space a suitable Riemannian manifold with skew-symmetric torsion. The
principal bundle is equipped with a connection which determines the
non-horizontal part of the spacetime metric and of . The curvature of
takes values in an appropriate Lie algebra constructed from that of
. In addition has only horizontal components and contains the
Pontrjagin class of . We have computed in all cases the Killing spinor
bilinears, expressed the fluxes in terms of the geometry and determine the
field equations that are implied by the Killing spinor equations.Comment: 73pp. v2: minor change
Designing an Experimental and a Reference Robot to Test and Evaluate the Impact of Cultural Competence in Socially Assistive Robotics
The article focusses on the work performed in preparation for an experimental trial aimed at evaluating the impact of a culturally competent robot for care home assistance. Indeed, it has been estabilished that the user's cultural identity plays an important role during the interaction with a robotic system and cultural competence may be one of the key elements for increasing capabilities of socially assistive robots. Specifically, the paper describes part of the work carried out for the definition and implementation of two different robotic systems for the care of older adults: a culturally competent robot, that shows its awareness of the user's cultural identity, and a reference robot, non culturally competent, but with the same functionalities of the former. The design of both robots is here described in detail, together with the key elements that make a socially assistive robot culturally competent, which should be absent in the non-culturally competent counterpart. Examples of the experimental phase of the CARESSES project, with a fictional user are reported, giving a hint of the validness of the proposed approach
- âŠ