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