With the growing interest in and ability of using weak lensing studies to probe the non-Gaussian properties of the matter density field, there is an increasing need for the study of suitable statistical measures, e.g. shear three-point statistics. In this paper we establish the relations between the three-point configuration space shear and convergence statistics, which are an important missing link between different weak lensing three-point statistics and provide an alternative way of relating observation and theory. The method we use also allows us to derive the relations between other two- and three-point correlation functions. We show the consistency of the relations obtained with already established results and demonstrate how they can be evaluated numerically. As a direct application, we use these relations to formulate the condition for E/B-mode decomposition of lensing three-point statistics, which is the basis for constructing new three-point statistics which allow for exact E/B-mode separation. Our work applies also to other two-dimensional polarization fields such as that of the Cosmic Microwave Background.
Superconducting MgB2 strands with nanometer-scale SiC additions have been investigated systematically using transport and magnetic measurements. A comparative study of MgB2 strands with different nano-SiC addition levels has shown C-doping-enhanced critical current density Jc through enhancements in the upper critical field, Hc2, and decreased anisotropy. The critical current density and flux pinning force density obtained from magnetic measurements were found to greatly differ from the values obtained through transport measurements, particularly with regards to magnetic field dependence. The differences in magnetic and transport results are largely attributed to connectivity related effects. On the other hand, based on the scaling behavior of flux pinning force, there may be other effective pinning centers in MgB2 strands in addition to grain boundary pinning.
Magnetic hysteresis loops (MHLs) have been comparatively measured on both textured and single crystalline Sc5Ir4Si10 superconductors. Critical current densities and flux pinning forces are calculated from MHLs by Bean model. Three kinds of peaks of the flux pinning force are found at low fields near zero, intermediated fields, and high fields near the upper critical field, respectively. The characters and origins of these peaks are studied in detail.
The anisotropy of the critical current density (Jc) and its influence on measurement of irreversibility field (Birr) has been investigated for high quality, in-situ MgB2 strands. Comparison of transport and magnetization measurements has revealed the onset of a regime where large differences exist between transport and magnetically measured values of the critical current density and Birr. These effects, initially unexpected due to the lack of crystalline texture in these in-situ processed strands, appear to be due to a fibrous microstructure, connected with the details of the wire fabrication and MgB2 formation reactions. Scanning electron micrographs of in-situ-processed MgB2 monocore strands have revealed a fibrous microstructure. Grains (~100 nm) are randomly oriented, and there is no apparent local texture of the grains. However, this randomly oriented polycrystalline material has a fibrous texture at a larger length scale, with stringers of MgB2 (~ 60 {mu}m long and ~5 {mu}m in diameter) partially separated by elongated pores -- the spaces previously occupied by stringers of elemental Mg. This leads to an interpretation of the differences observed in transport and magnetically determined critical currents, in particular a large deviation between the two at higher fields, in terms of different transverse and longitudinal connectivities within the strand. The different values of connectivity also lead to different resistive transition widths, and thus irreversibility field values, as measured by transport and magnetic techniques. Finally, these considerations are seen to influence estimated pinning potentials for the strands.
We demonstrate a technique that allows to fully control the bandwidth of entangled photons independently of the frequency band of interest and of the nonlinear crystal. We show that this technique allows to generate nearly transform-limited biphotons with almost one octave of bandwidth (hundreds of THz) which corresponds to correlation times of just a few femtoseconds. The presented method becomes an enabling tool for attosecond entangled-photons quantum optics. The technique can also be used to generate paired photons with a very high degree of entanglement.
