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

Assessment of probability of detection of delaminations in fiber-reinforced composites

Delamination is one of the critical defects in composite materials and structures. An ultrasonic C-scan imaging technique which maps out the acoustic impedance mismatched areas with respect to the sample coordinates, is particularly well suited for detecting and characterizing delaminations in composites. To properly interpret the results, it is necessary to correlate the indications with the detection limits and probability of detection (POD) of the ultrasonic C-scan imaging technique. The baseline information on the assessment of POD of delaminations in composite materials and structures is very beneficial to the evaluation of spacecraft materials. In this study, we review the principle of POD, describe the laboratory set-up and procedure, and present the experimental results as well as assessment of POD of delaminations in fiber reinforced composite panels using ultrasonic C-scan techniques

Low Temperature Creep of a Titanium Alloy Ti-6Al-2Cb-1Ta-0.8Mo

This paper presents a methodology for the analysis of low temperature creep of titanium alloys in order to establish design limitations due to the effect of creep. The creep data on a titanium Ti-6Al-2Cb-1Ta-0.8Mo are used in the analysis. A creep equation is formulated to determine the allowable stresses so that creep at ambient temperatures can be kept within an acceptable limit during the service life of engineering structures or instruments. Microcreep which is important to design of precision instruments is included in the discussion also

Equilibrium orbit analysis in a free-electron laser with a coaxial wiggler

An analysis of single-electron orbits in combined coaxial wiggler and axial guide magnetic fields is presented. Solutions of the equations of motion are developed in a form convenient for computing orbital velocity components and trajectories in the radially dependent wiggler. Simple analytical solutions are obtained in the radially-uniform-wiggler approximation and a formula for the derivative of the axial velocity $v_{\|}$ with respect to Lorentz factor $\gamma$ is derived. Results of numerical computations are presented and the characteristics of the equilibrium orbits are discussed. The third spatial harmonic of the coaxial wiggler field gives rise to group $III$ orbits which are characterized by a strong negative mass regime.Comment: 13 pages, 9 figures, to appear in phys. rev.