29,518 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
Optimal paths on the road network as directed polymers
We analyze the statistics of the shortest and fastest paths on the road
network between randomly sampled end points. To a good approximation, these
optimal paths are found to be directed in that their lengths (at large scales)
are linearly proportional to the absolute distance between them. This motivates
comparisons to universal features of directed polymers in random media. There
are similarities in scalings of fluctuations in length/time and transverse
wanderings, but also important distinctions in the scaling exponents, likely
due to long-range correlations in geographic and man-made features. At short
scales the optimal paths are not directed due to circuitous excursions governed
by a fat-tailed (power-law) probability distribution.Comment: 5 pages, 7 figure
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
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
Characterization of the Noise in Secondary Ion Mass Spectrometry Depth Profiles
The noise in the depth profiles of secondary ion mass spectrometry (SIMS) is
studied using different samples under various experimental conditions. Despite
the noise contributions from various parts of the dynamic SIMS process, its
overall character agrees very well with the Poissonian rather than the Gaussian
distribution in all circumstances. The Poissonian relation between the measured
mean-square error (MSE) and mean can be used to describe our data in the range
of four orders. The departure from this relation at high counts is analyzed and
found to be due to the saturation of the channeltron used. Once saturated, the
detector was found to exhibit hysteresis between rising and falling input flux
and output counts.Comment: 14 pages, 4 postscript figures, to appear on J. Appl. Phy
Aharonov-Bohm Radiation of Fermions
We analyze Aharonov-Bohm radiation of charged fermions from oscillating
solenoids and cosmic strings. We find that the angular pattern of the radiation
has features that differ significantly from that for bosons. For example,
fermionic radiation in the lowest harmonic is approximately isotropically
distributed around an oscillating solenoid, whereas for bosons the radiation is
dipolar. We also investigate the spin polarization of the emitted
fermion-antifermion pair. Fermionic radiation from kinks and cusps on cosmic
strings is shown to depend linearly on the ultraviolet cut-off, suggesting
strong emission at an energy scale comparable to the string energy scale.Comment: 14 pages, 6 figures. Version 2: Expanded discussion on boundary
conditions obeyed by Dirac equation mode functions (in Section V B).
Acknowledgements and references added. Version 3: Minor changes made in
response to referee's comment
Designing a Biosensor Using a Photonic Quasi-Crystal Fiber with Fan-shaped Analyte Channel
Postprin
Molecular Breeding of White Clover for Transgenic Resistance to Alfalfa Mosaic Virus and Natural Resistance to Clover Yellow Vein Virus
Trifolium repens L. (white clover) is one of the most important pastoral plants in temperate Australia. Its productivity and persistence is being reduced significantly by Alfalfa mosaic virus (AMV), Clover yellow vein virus (ClYVV) and White clover mosaic virus (WClMV). These viruses are also widespread in other legumes and are inflicting large economic losses to farmers throughout the world (Campbell, 1984). To reduce the economic impact of these viruses, white clover plants resistant to both ClYVV and AMV are being developed for future commercial release. Since introducing viral transgenes from two or more viruses into a transgenic plant has the potential threat of viral recombination, we have decided to develop white clover with transgenic resistance to AMV and natural resistance to ClYVV
Calcium-gated calcium channels in sarcoplasmic reticulum of rabbit skinned skeletal muscle fibers
The action of ruthenium red (RR) on Ca2+ loading by and Ca2+ release from the sarcoplasmic reticulum (SR) of chemically skinned skeletal muscle fibers of the rabbit was investigated. Ca2+ loading, in the presence of the precipitating anion pyrophosphate, was monitored by a light-scattering method. Ca2+ release was indirectly measured by following tension development evoked by caffeine. Stimulation of the Ca2+ loading rate by 5 microM RR was dependent on free Ca2+, being maximal at pCa 5.56. Isometric force development induced by 5 mM caffeine was reversibly antagonized by RR. IC50 for the rate of tension rise was 0.5 microM; that for the extent of tension was 4 microM. RR slightly shifted the steady state isometric force/pCa curve toward lower pCa values. At 5 microM RR, the pCa required for half-maximal force was 0.2 log units lower than that of the control, and maximal force was depressed by approximately 16%. These results suggest that RR inhibited Ca2+ release from the SR and stimulated Ca2+ loading into the SR by closing Ca2+-gated Ca2+ channels. Previous studies on isolated SR have indicated the selective presence of such channels in junctional terminal cisternae
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