176,987 research outputs found
Cusp Summations and Cusp Relations of Simple Quad Lenses
We review five often used quad lens models, each of which has analytical
solutions and can produce four images at most. Each lens model has two
parameters, including one that describes the intensity of non-dimensional mass
density, and the other one that describes the deviation from the circular lens.
In our recent work, we have found that the cusp and the fold summations are not
equal to 0, when a point source infinitely approaches a cusp or a fold from
inner side of the caustic. Based on the magnification invariant theory, which
states that the sum of signed magnifications of the total images of a given
source is a constant, we calculate the cusp summations for the five lens
models. We find that the cusp summations are always larger than 0 for source on
the major cusps, while can be larger or smaller than 0 for source on the minor
cusps. We also find that if these lenses tend to the circular lens, the major
and minor cusp summations will have infinite values, and with positive and
negative signs respectively. The cusp summations do not change significantly if
the sources are slightly deviated from the cusps. In addition, through the
magnification invariants, we also derive the analytical signed cusp relations
on the axes for three lens models. We find that both on the major and the minor
axes the larger the lenses deviated from the circular lens, the larger the
signed cusp relations. The major cusp relations are usually larger than the
absolute minor cusp relations, but for some lens models with very large
deviation from circular lens, the minor cusp relations can be larger than the
major cusp relations.Comment: 8 pages, 4 figures, accepted for publication in MNRA
Multipole Gravitational Lensing and High-order Perturbations on the Quadrupole Lens
An arbitrary surface mass density of gravitational lens can be decomposed
into multipole components. We simulate the ray-tracing for the multipolar mass
distribution of generalized SIS (Singular Isothermal Sphere) model, based on
the deflection angles which are analytically calculated. The magnification
patterns in the source plane are then derived from inverse shooting technique.
As have been found, the caustics of odd mode lenses are composed of two
overlapping layers for some lens models. When a point source traverses such
kind of overlapping caustics, the image numbers change by \pm 4, rather than
\pm 2. There are two kinds of images for the caustics. One is the critical
curve and the other is the transition locus. It is found that the image number
of the fold is exactly the average value of image numbers on two sides of the
fold, while the image number of the cusp is equal to the smaller one. We also
focus on the magnification patterns of the quadrupole (m = 2) lenses under the
perturbations of m = 3, 4 and 5 mode components, and found that one, two, and
three butterfly or swallowtail singularities can be produced respectively. With
the increasing intensity of the high-order perturbations, the singularities
grow up to bring sixfold image regions. If these perturbations are large enough
to let two or three of the butterflies or swallowtails contact, eightfold or
tenfold image regions can be produced as well. The possible astronomical
applications are discussed.Comment: 24 pages, 6 figure
Defect chemistry and transport properties of BaxCe0.85M0.15O3-d
The site-incorporation mechanism of M3+ dopants into A2+B4+O3 perovskites controls the overall defect chemistry and thus their transport properties. For charge-balance reasons, incorporation onto the A2+-site would require the creation of negatively charged point defects (such as cation vacancies), whereas incorporation onto the B4+-site is accompanied by the generation of positively charged defects, typically oxygen vacancies. Oxygen-vacancy content, in turn, is relevant to proton-conducting oxides in which protons are introduced via the dissolution of hydroxyl ions at vacant oxygen sites. We propose here, on the basis of x-ray powder diffraction studies, electron microscopy, chemical analysis, thermal gravimetric analysis, and alternating current impedance spectroscopy, that nominally B-site doped barium cerate can exhibit dopant partitioning as a consequence of barium evaporation at elevated temperatures. Such partitioning and the presence of significant dopant concentrations on the A-site negatively impact proton conductivity. Specific materials examined are BaxCe0.85M0.15O3-d (x = 0.85 - 1.20; M = Nd, Gd, Yb). The compositional limits for the maximum A-site incorporation are experimentally determined to be: (Ba0.919Nd0.081)(Ce0.919Nd0.081)O3, (Ba0.974Gd0.026)(Ce0.872Gd0.128)O2.875, and Ba(Ce0.85Yb0.15)O2.925. As a consequence of the greater ability of larger cations to exist on the Ba site, the H2O adsorption and proton conductivities of large-cation doped barium cerates are lower than those of small-cation doped analogs
Fermi Coordinates for Weak Gravitational Fields
A Reference is corrected. (We derive the Fermi coordinate system of an
observer in arbitrary motion in an arbitrary weak gravitational field valid to
all orders in the geodesic distance from the worldline of the observer. In flat
space-time this leads to a generalization of Rindler space for arbitrary
acceleration and rotation. The general approach is applied to the special case
of an observer resting with respect to the weak gravitational field of a static
mass distribution. This allows to make the correspondence between general
relativity and Newtonian gravity more precise.)Comment: 7 Pages, Preprint KONS-RGKU-94-04, LaTe
Magnification relations of quad lenses and applications on Einstein crosses
In this work, we mainly study the magnification relations of quad lens models
for cusp, fold and cross configurations. By dividing and ray-tracing in
different image regions, we numerically derive the positions and magnifications
of the four images for a point source lying inside of the astroid caustic.
Then, based on the magnifications, we calculate the signed cusp and fold
relations for the singular isothermal elliptical lenses. The signed fold
relation map has positive and negative regions, and the positive region is
usually larger than the negative region as has been confirmed before. It can
also explain that for many observed fold image pairs, the fluxes of the Fermat
minimum images are apt to be larger than those of the saddle images. We define
a new quantity cross relation which describes the magnification discrepancy
between two minimum images and two saddle images. Distance ratio is also
defined as the ratio of the distance of two saddle images to that of two
minimum images. We calculate the cross relations and distance ratios for nine
observed Einstein crosses. In theory, for most of the quad lens models, the
cross relations decrease as the distance ratios increase. In observation, the
cross relations of the nine samples do not agree with the quad lens models very
well, nevertheless, the cross relations of the nine samples do not give obvious
evidence for anomalous flux ratio as the cusp and fold types do. Then, we
discuss several reasons for the disagreement, and expect good consistencies for
more precise observations and better lens models in the future.Comment: 12 pages, 11 figures, accepted for publication in MNRA
The Precise Formula in a Sine Function Form of the norm of the Amplitude and the Necessary and Sufficient Phase Condition for Any Quantum Algorithm with Arbitrary Phase Rotations
In this paper we derived the precise formula in a sine function form of the
norm of the amplitude in the desired state, and by means of he precise formula
we presented the necessary and sufficient phase condition for any quantum
algorithm with arbitrary phase rotations. We also showed that the phase
condition: identical rotation angles, is a sufficient but not a necessary phase
condition.Comment: 16 pages. Modified some English sentences and some proofs. Removed a
table. Corrected the formula for kol on page 10. No figure
Ratcheting Heat Flux against a Thermal Bias
Merely rocking the temperature in one heat bath can direct a steady heat flux
from cold to hot against a non-zero thermal bias in stylized nonlinear lattice
junctions that are sandwiched between two heat baths. Likewise, for an average
zero-temperature difference between the two contacts a net, ratchet-like heat
flux emerges. Computer simulations show that this very heat flux can be
controlled and reversed by suitably tailoring the frequency ( 100
MHz) of the alternating temperature field.Comment: 5 pages, 6 figure
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