32,973 research outputs found
Axial symmetry and conformal Killing vectors
Axisymmetric spacetimes with a conformal symmetry are studied and it is shown
that, if there is no further conformal symmetry, the axial Killing vector and
the conformal Killing vector must commute. As a direct consequence, in
conformally stationary and axisymmetric spacetimes, no restriction is made by
assuming that the axial symmetry and the conformal timelike symmetry commute.
Furthermore, we prove that in axisymmetric spacetimes with another symmetry
(such as stationary and axisymmetric or cylindrically symmetric spacetimes) and
a conformal symmetry, the commutator of the axial Killing vector with the two
others mush vanish or else the symmetry is larger than that originally
considered. The results are completely general and do not depend on Einstein's
equations or any particular matter content.Comment: 15 pages, Latex, no figure
Spherical Orbifolds for Cosmic Topology
Harmonic analysis is a tool to infer cosmic topology from the measured
astrophysical cosmic microwave background CMB radiation. For overall positive
curvature, Platonic spherical manifolds are candidates for this analysis. We
combine the specific point symmetry of the Platonic manifolds with their deck
transformations. This analysis in topology leads from manifolds to orbifolds.
We discuss the deck transformations of the orbifolds and give eigenmodes for
the harmonic analysis as linear combinations of Wigner polynomials on the
3-sphere. These provide new tools for detecting cosmic topology from the CMB
radiation.Comment: 17 pages, 9 figures. arXiv admin note: substantial text overlap with
arXiv:1011.427
Fine-grain process modelling
In this paper, we propose the use of fine-grain process
modelling as an aid to software development. We suggest
the use of two levels of granularity, one at the level of the
individual developer and another at the level of the
representation scheme used by that developer. The
advantages of modelling the software development process
at these two levels, we argue, include respectively: (1) the
production of models that better reflect actual
development processes because they are oriented towards
the actors who enact them, and (2) models that are
vehicles for providing guidance because they may be
expressed in terms of the actual representation schemes
employed by those actors. We suggest that our previously
published approach of using multiple “ViewPoints” to
model software development participants, the perspectives
that they hold, the representation schemes that they
deploy and the process models that they maintain, is one
way of supporting the fine-grain modelling we advocate.
We point to some simple, tool-based experiments we have
performed that support our proposition
Research on output feedback control
In designing fixed order compensators, an output feedback formulation has been adopted by suitably augmenting the system description to include the compensator states. However, the minimization of the performance index over the range of possible compensator descriptions was impeded due to the nonuniqueness of the compensator transfer function. A controller canonical form of the compensator was chosen to reduce the number of free parameters to its minimal number in the optimization. In the MIMO case, the controller form requires a prespecified set of ascending controllability indices. This constraint on the compensator structure is rather innocuous in relation to the increase in convergence rate of the optimization. Moreover, the controller form is easily relatable to a unique controller transfer function description. This structure of the compensator does not require penalizing the compensator states for a nonzero or coupled solution, a problem that occurs when following a standard output feedback synthesis formulation
Long term monitoring of mode switching for PSR B0329+54
The mode switching phenomenon of PSR B0329+54 is investigated based on the
long-term monitoring from September 2003 to April 2009 made with the Urumqi 25m
radio telescope at 1540 MHz. At that frequency, the change of relative
intensity between the leading and trailing components is the predominant
feature of mode switching. The intensity ratios between the leading and
trailing components are measured for the individual profiles averaged over a
few minutes. It is found that the ratios follow normal distributions, where the
abnormal mode has a wider typical width than the normal mode, indicating that
the abnormal mode is less stable than the normal mode. Our data show that 84.9%
of the time for PSR B0329+54 was in the normal mode and 15.1% was in the
abnormal mode. From the two passages of eight-day quasi-continuous observations
in 2004, and supplemented by the daily data observed with 15 m telescope at 610
MHz at Jodrell Bank Observatory, the intrinsic distributions of mode timescales
are constrained with the Bayesian inference method. It is found that the gamma
distribution with the shape parameter slightly smaller than 1 is favored over
the normal, lognormal and Pareto distributions. The optimal scale parameters of
the gamma distribution is 31.5 minutes for the abnormal mode and 154 minutes
for the normal mode. The shape parameters have very similar values, i.e.
0.75^{+0.22}_{-0.17} for the normal mode and 0.84^{+0.28}_{-0.22} for the
abnormal mode, indicating the physical mechanisms in both modes may be the
same. No long-term modulation of the relative intensity ratios was found for
both the modes, suggesting that the mode switching was stable. The intrinsic
timescale distributions, for the first time constrained for this pulsar,
provide valuable information to understand the physics of mode switching.Comment: 31 pages,12 figures, Accepted by the Ap
Space-times admitting a three-dimensional conformal group
Perfect fluid space-times admitting a three-dimensional Lie group of
conformal motions containing a two-dimensional Abelian Lie subgroup of
isometries are studied. Demanding that the conformal Killing vector be proper
(i.e., not homothetic nor Killing), all such space-times are classified
according to the structure of their corresponding three-dimensional conformal
Lie group and the nature of their corresponding orbits (that are assumed to be
non-null). Each metric is then explicitly displayed in coordinates adapted to
the symmetry vectors. Attention is then restricted to the diagonal case, and
exact perfect fluid solutions are obtained in both the cases in which the fluid
four-velocity is tangential or orthogonal to the conformal orbits, as well as
in the more general "tilting" case.Comment: Latex 34 page
Orientational transition in nematic liquid crystals under oscillatory Poiseuille flow
We investigate the orientational behaviour of a homeotropically aligned
nematic liquid crystal subjected to an oscillatory plane Poiseuille flow
produced by an alternating pressure gradient. For small pressure amplitudes the
director oscillates within the flow plane around the initial homeotropic
position, whereas for higher amplitudes a spatially homogeneous transition to
out-of-plane director motion was observed for the first time. The orientational
transition was found to be supercritical and the measured frequency dependence
of the critical pressure amplitude in the range between 2 and 20 Hz was in
quantitative agreement with a recent theory.Comment: 11 pages, 4 figures, submitted to Europhys. Let
Revivals of quantum wave-packets in graphene
We investigate the propagation of wave-packets on graphene in a perpendicular
magnetic field and the appearance of collapses and revivals in the
time-evolution of an initially localised wave-packet. The wave-packet evolution
in graphene differs drastically from the one in an electron gas and shows a
rich revival structure similar to the dynamics of highly excited Rydberg
states.
We present a novel numerical wave-packet propagation scheme in order to solve
the effective single-particle Dirac-Hamiltonian of graphene and show how the
collapse and revival dynamics is affected by the presence of disorder. Our
effective numerical method is of general interest for the solution of the Dirac
equation in the presence of potentials and magnetic fields.Comment: 22 pages, 10 figures, 3 movies, to appear in New Journal of Physic
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