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

Properties of superconducting MgB_2 wires: "in-situ" versus "ex-situ" reaction technique

We have fabricated a series of iron-sheathed superconducting wires prepared by the powder-in-tube technique from (MgB_2)_{1-x}:(Mg+2B)_x initial powder mixtures taken with different proportions, so that x varies from 0 to 1. It turned out that "ex-situ" prepared wire (x = 0) has considerable disadvantages compared to all the other wires in which "in-situ" assisted (0 < x < 1) or pure "in-situ" (x = 1) preparation was used due to weaker inter-grain connectivity. As a result, higher critical current densities J_c were measured over the entire range of applied magnetic fields B_a for all the samples with x > 0. Pinning of vortices in MgB_2 wires is shown to be due to grain boundaries. J_c(B_a) behavior is governed by an interplay between the transparency of grain boundaries and the amount of "pinning" grain boundaries. Differences between thermo-magnetic flux-jump instabilities in the samples and a possible threat to practical applications are also discussed.Comment: To be published in Supercond. Sci. Technol. (2003), in pres

Microwave-Induced Interfacial Nanobubbles

A new method for generating nanobubbles via microwave irradiation was verified and quantified. AFM measurement showed that nanobubbles with diameters ranging in 200 - 600 nm were generated at water-HOPG surface by applying microwave to aqueous solutions with 9.0 - 30.0 mg/L of dissolved oxygen. Graphite displays strong microwave absorption and transmits high thermal energy to surface. Due to high dielectric constant (20 °C, 80 F/m) and dielectric loss factor, water molecule has strong absorption ability for microwave. The thermal and non-thermal effects of microwave both had contributions to decrease gas solubility and that facilitated nanobubble nucleation. The yield of nanobubbles increased about ten times when irradiation time increased from 60 s to 120 s at 200 W microwave. The nanobubbles density increased from 0.8 to 15 numbers/μm2 by improving working power from 200 to 600 W. An apparent improvement of nanobubbles yield was obtained between 300 and 400 W, and the resulting temperature was 34 - 52 °C. When the initial dissolved oxygen increased from 11.3 to 30.0 mg/L, the density of nanobubbles increased from 1.2 to 13 numbers/μm2. The generation of nanobubbles could be well controlled by adjusting gas concentration, microwave power or irradiation time. The method maybe valuable in preparing surface nanobubbles quickly and conveniently for various applications, such as catalysis, hypoxia/anoxia remediation or as templates to prepare nanoscale materials

Various Correlations in Anisotropic Heisenberg XYZ Model with Dzyaloshinski-Moriya Interaction

Various thermal correlations as well as the effect of intrinsic decoherence on the correlations are studied in a two-qubit Heisenberg XYZ spin chain with the Dzyaloshinski--Moriya (DM) interaction along the z direction, i.e. Dz. It is found that tunable parameter Dz may play a constructive role on the concurrence (C), classical correlation (CC) and quantum discord (QD) in thermal equilibrium while it plays a destructive role on the correlations in the intrinsic decoherence case. The entanglement and quantum discord exhibit collapse and revival under the phase decoherence. With a proper combination of the system parameters, the correlations can effectively be kept at high steady state values despite the intrinsic decoherence.Comment: 4 pages, 4 figure