22,251 research outputs found

    Multipole Gravitational Lensing and High-order Perturbations on the Quadrupole Lens

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    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

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    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

    Neutrino mixing and masses in SO(10) GUTs with hidden sector and flavor symmetries

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    We consider the neutrino masses and mixing in the framework of SO(10) GUTs with hidden sector consisting of fermionic and bosonic SO(10) singlets and flavor symmetries. The framework allows to disentangle the CKM physics responsible for the CKM mixing and different mass hierarchies of quarks and leptons and the neutrino new physics which produces smallness of neutrino masses and large lepton mixing. The framework leads naturally to the relation UPMNSVCKMU0U_{PMNS} \sim V_{CKM}^{\dagger} U_0, where structure of U0U_0 is determined by the flavor symmetry. The key feature of the framework is that apart from the Dirac mass matrices mDm_D, the portal mass matrix MDM_D and the mass matrix of singlets MSM_S are also involved in generation of the lepton mixing. This opens up new possibilities to realize the flavor symmetries and explain the data. Using A4×Z4A_4 \times Z_4 as the flavor group, we systematically explore the flavor structures which can be obtained in this framework depending on field content and symmetry assignments. We formulate additional conditions which lead to U0UTBMU_0 \sim U_{TBM} or UBMU_{BM}. They include (i) equality (in general, proportionality) of the singlet flavons couplings, (ii) equality of their VEVs; (iii) correlation between VEVs of singlets and triplet, (iv) certain VEV alignment of flavon triplet(s). These features can follow from additional symmetries or be remnants of further unification. Phenomenologically viable schemes with minimal flavon content and minimal number of couplings are constructed

    E-cadherin and gastric cancer: Cause, consequence and applications

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    Structure of CdTe/ZnTe superlattices

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    The structure of CdTe/ZnTe superlattices has been analyzed through θ/2θ x‐ray diffraction, photoluminescence, and in situ reflection high‐energy electron diffraction (RHEED) measurements. Samples are found to break away from Cd_(x)Zn_(1−x)Te buffer layers as a consequence of the 6% lattice mismatch in this system. However, defect densities in these superlattices are seen to drop dramatically away from the buffer layer interface, accounting for the intense photoluminescence and high‐average strain fields seen in each of our samples. Observed variations in residual strains suggest that growth conditions play a role in forming misfit defects. This could explain discrepancies with calculated values of critical thickness based on models which neglect growth conditions. Photoluminescence spectra reveal that layer‐to‐layer growth proceeded with single monolayer uniformity, suggesting highly reproducible growth. Our results give hope for relatively defect‐free Cd_(x)Zn_(1−x)Te/Cd_(y)Zn_(1−y)Te superlattices with the potential for applications to optoelectronics offered by intense visible light emitters