Andreev Bound States and Self-Consistent Gap Functions for SNS and SNSNS Systems

Andreev bound states in clean, ballistic SNS and SNSNS junctions are calculated exactly and by using the Andreev approximation (AA). The AA appears to break down for junctions with transverse dimensions chosen such that the motion in the longitudinal direction is very slow. The doubly degenerate states typical for the traveling waves found in the AA are replaced by two standing waves in the exact treatment and the degeneracy is lifted. A multiple-scattering Green's function formalism is used, from which the states are found through the local density of states. The scattering by the interfaces in any layered system of ballistic normal metals and clean superconducting materials is taken into account exactly. The formalism allows, in addition, for a self-consistent determination of the gap function. In the numerical calculations the pairing coupling constant for aluminum is used. Various features of the proximity effect are shown

Andreev states, supercurrents and interface effects in clean SN multilayers

We present results for the local density of states in the S and N layers of a SN multilayer, and the supercurrent, based on a Green's function formalism, as an extension of previous calculations on NS, SNS and SNSNS systems. The gap function is determined selfconsistently. Our systems are chosen to have a finite transverse width. We focus on phenomena which occur at so-called critical transverse widths, at which a new transverse mode is starting to contribute. It appears, that for an arbitrary width the Andreev approximation (AA), which takes into account only Andreev reflection at the SN interfaces, works well. We show that at a critical width the AA breaks down. An exact treatment is required, which considers also ordinary reflections. In addition, we study the influence of an interface barrier on the coupling between the S-layers

The Influence of the Transverse Width on the Andreev Bound States and Self-Consistent Gap Function in Clean SNS System

Intro:In clean layered structure of normal metal andsuperconductor, Andreev-bound states are formed inthe normal metallic part through multiple Andreevreflections (Andreev, 1964 & 1967) of the electron andhole waves. In the Andreev approximation (AA)(Andreev, 1964 & 1967), the incident electron towardsa normal metal-superconductor (NS) interface will bereflected as a hole. Exact analysis, however, shows asmall amplitude of a normally reflected electron (Sipr& Gyorffy, 1996). In most studies (Larkin & Yu, 1975),Andreev-bound states are described using thequasiclassical description, which can be shown to beequivalent to AA (Ashida et al., 1982). Interestingly,Andreev approximation works remarkably well(Blaauboer et al., 1996). In this paper, we want toinvestigate the reliability of AA by varying the transversedimensions (dimensions perpendicular to the flow ofcurrent) of a mesoscopic superconductor-normal metalsuperconductor (SNS) sample (Bagwell, 1999). In mostsystems considered so far (Tanaka & Tsukada, 1991),the transverse dimensions which the breakdown of theAndreev approximation can hardly show up areconsidered infinite

TREE CANOPY COVER MAPPING USING LiDAR IN URBAN BARANGAYS OF CEBU CITY, CENTRAL PHILIPPINES

This paper investigates tree canopy cover mapping of urban barangays (smallest administrative division in the Philippines) in Cebu City using LiDAR (Light Detection and Ranging). Object-Based Image Analysis (OBIA) was used to extract tree canopy cover. Multi-resolution segmentation and a series of assign-class algorithm in eCognition software was also performed to extract different land features. Contextual features of tree canopies such as height, area, roundness, slope, length-width and elliptic fit were also evaluated. The results showed that at the time the LiDAR data was collected (June 24, 2014), the tree cover was around 25.11 % (or 15,674,341.8 m2) of the city’s urban barangays (or 62,426,064.6 m2). Among all urban barangays in Cebu City, Barangay Busay had the highest cover (55.79 %) while barangay Suba had the lowest (0.8 %). The 16 barangays with less than 10 % tree cover were generally located in the coastal area, presumably due to accelerated urbanization. Thirty-one barangays have tree cover ranging from 10.59–-27.3 %. Only 3 barangays (i.e., Lahug, Talamban, and Busay) have tree cover greater than 30 %. The overall accuracy of the analysis was 96.6 % with the Kappa Index of Agreement or KIA of 0.9. From the study, a grouping can be made of the city’s urban barangays with regards to tree cover. The grouping will be useful to urban planners not only in allocating budget to the tree planting program of the city but also in planning and creation of urban parks and playgrounds

AN OBJECT-BASED WORKFLOW DEVELOPED TO EXTRACT AQUACULTURE PONDS FROM AIRBORNE LIDAR DATA: A TEST CASE IN CENTRAL VISAYAS, PHILIPPINES

Traditional remote sensing approach for mapping aquaculture ponds typically involves the use of aerial photography and high resolution images. The current study demonstrates the use of object-based image processing and analyses of LiDAR-data-generated derivative images with 1-meter resolution, namely: CHM (canopy height model) layer, DSM (digital surface model) layer, DTM (digital terrain model) layer, Hillshade layer, Intensity layer, NumRet (number of returns) layer, and Slope layer. A Canny edge detection algorithm was also performed on the Hillshade layer in order to create a new image (Canny layer) with more defined edges. These derivative images were then used as input layers to perform a multi-resolution segmentation algorithm best fit to delineate the aquaculture ponds. In order to extract the aquaculture pond feature, three major classes were identified for classification, including land, vegetation and water. Classification was first performed by using assign class algorithm to classify Flat Surfaces to segments with mean Slope values of 10 or lower. Out of these Flat Surfaces, assign class algorithm was then performed to determine Water feature by using a threshold value of 63.5. The segments identified as Water were then merged together to form larger bodies of water which comprises the aquaculture ponds. The present study shows that LiDAR data coupled with object-based classification can be an effective approach for mapping coastal aquaculture ponds. The workflow currently presented can be used as a model to map other areas in the Philippines where aquaculture ponds exist

An empirical model of the quiet daily geomagnetic field variation

An empirical model of the quiet daily geomagnetic field variation has been constructed based on geomagnetic data obtained from 21 stations along the 210 Magnetic Meridian of the Circum-pan Pacific Magnetometer Network (CPMN) from 1996 to 2007. Using the least squares fitting method for geomagnetically quiet days (Kp ≤ 2+), the quiet daily geomagnetic field variation at each station was described as a function of solar activity SA, day of year DOY, lunar age LA, and local time LT. After interpolation in latitude, the model can describe solar-activity dependence and seasonal dependence of solar quiet daily variations (S) and lunar quiet daily variations (L). We performed a spherical harmonic analysis (SHA) on these S and L variations to examine average characteristics of the equivalent external current systems. We found three particularly noteworthy results. First, the total current intensity of the S current system is largely controlled by solar activity while its focus position is not significantly affected by solar activity. Second, we found that seasonal variations of the S current intensity exhibit north-south asymmetry; the current intensity of the northern vortex shows a prominent annual variation while the southern vortex shows a clear semi-annual variation as well as annual variation. Thirdly, we found that the total intensity of the L current system changes depending on solar activity and season; seasonal variations of the L current intensity show an enhancement during the December solstice, independent of the level of solar activity