The Screen representation of spin networks. Images of 6j symbols and semiclassical features

This article presents and discusses in detail the results of extensive exact calculations of the most basic ingredients of spin networks, the Racah coefficients (or Wigner 6j symbols), exhibiting their salient features when considered as a function of two variables - a natural choice due to their origin as elements of a square orthogonal matrix - and illustrated by use of a projection on a square "screen" introduced recently. On these screens, shown are images which provide a systematic classification of features previously introduced to represent the caustic and ridge curves (which delimit the boundaries between oscillatory and evanescent behaviour according to the asymptotic analysis of semiclassical approaches). Particular relevance is given to the surprising role of the intriguing symmetries discovered long ago by Regge and recently revisited; from their use, together with other newly discovered properties and in conjunction with the traditional combinatorial ones, a picture emerges of the amplitudes and phases of these discrete wavefunctions, of interest in wide areas as building blocks of basic and applied quantum mechanics.Comment: 16 pages, 13 figures, presented at ICCSA 2013 13th International Conference on Computational Science and Applicatio

A detailed study of spring soil test nutrients along a catena sequence in a thin Black Chernozem

Non-Peer Reviewe

Relationships among landform elements, soil properties, and crop yields on Blaine Lake-Hamlin Soils

Non-Peer ReviewedSoil properties are an important part of the complex framework in the crop production system. Soil properties may vary over short distances, but are related to position within the landscape. This study investigated the relationships among pH, salinity, bulk density, horizon thickness, depth to carbonates, and soil moisture according to landform position. Four catenas were studied under different crop rotations: summerfallow-canola-wheat, summerfallow-wheat-wheat, continuous cereals, and continuous cereals plus a legume. Total plant biomass and crop yields were determined on hand harvested samples from each slope position. Best yields in 1989, generally occurred in back and shoulder slopes and lowest yield in footslope areas that were flooded out by intense summer showers

The influence of non-imaging detector design on heralded ghost-imaging and ghost-diffraction examined using a triggered ICCD came

Ghost imaging and ghost diffraction can be realized by using the spatial correlations between signal and idler photons produced by spontaneous parametric down-conversion. If an object is placed in the signal (idler) path, the spatial correlations between the transmitted photons as measured by a single, non-imaging, “bucket” detector and a scanning detector placed in the idler (signal) path can reveal either the image or diffraction pattern of the object, whereas neither detector signal on its own can. The details of the bucket detector, such as its collection area and numerical aperture, set the number of transverse modes supported by the system. For ghost imaging these details are less important, affecting mostly the sampling time required to produce the image. For ghost diffraction, however, the bucket detector must be filtered to a single, spatially coherent mode. We examine this difference in behavour by using either a multi-mode or single-mode fibre to define the detection aperture. Furthermore, instead of a scanning detector we use a heralded camera so that the image or diffraction pattern produced can be measured across the full field of view. The importance of a single mode detection in the observation of ghost diffraction is equivalent to the need within a classical diffraction experiment to illuminate the aperture with a spatially coherent mode

The Screen representation of spin networks: 2D recurrence, eigenvalue equation for 6j symbols, geometric interpretation and Hamiltonian dynamics

This paper treats 6j symbols or their orthonormal forms as a function of two variables spanning a square manifold which we call the "screen". We show that this approach gives important and interesting insight. This two dimensional perspective provides the most natural extension to exhibit the role of these discrete functions as matrix elements that appear at the very foundation of the modern theory of classical discrete orthogonal polynomials. Here we present 2D and 1D recursion relations that are useful for the direct computation of the orthonormal 6j, which we name U. We present a convention for the order of the arguments of the 6j that is based on their classical and Regge symmetries, and a detailed investigation of new geometrical aspects of the 6j symbols. Specifically we compare the geometric recursion analysis of Schulten and Gordon with the methods of this paper. The 1D recursion relation, written as a matrix diagonalization problem, permits an interpretation as a discrete Schr\"odinger-like equations and an asymptotic analysis illustrates semiclassical and classical limits in terms of Hamiltonian evolution.Comment: 14 pages,9 figures, presented at ICCSA 2013 13th International Conference on Computational Science and Applicatio

Dehydrated Alfalfa Meal in Growing-Finishing Swine Rations

It has been suggested by many investigations that certain ingredients contain unidentified growth factors of bene fit to the growing pig. One of the ingredients that has been suggested as a source of unidentified growth factors is alfalfa meal. This trial was part of a larger experiment participated in by several states in the North Central region. The objectives were to determine the effects of low levels of dehydrated alfalfa meal in a com-soybean meal type ration fed to growing-finishing swine

Fish Solubles in Rations for Early Weaned Pigs

This experiment was a continuation of a project covering several aspects of the nutrition of young pigs. The results of previous work reported at the 1966 Swine Field Day ( A.S. Series 66-21) showed that a simple corn-soybean meal fortified ration was equal to a more complex diet that also contained rolled oats, dried skim milk and sugar. Therefore, the current experiment was designed to compare a basal corn-soybean meal type ration with a similar ration containing 3% fish solubles. Fish solubles are a good source of high quality protein and also may contain an identified growth factor(s). The experiment was designed to study the effect of fish solubles on palatability of the ration as well as its effect on growth and feed conversion

The Influence of Alfalfa Coumestrol on the Reproductive Performance of Gilts

In Australia during the early 1940\u27sa syndrome known as clover disease was observed in sheep grazing subterranean clover. This syndrome was characterized by a marked reduction in fertility which was later proved to be due to a high content of estrogenic substances in the clover. Alfalfa has since been shown to contain varying levels of these plant estrogens. The most important of the plant estrogens present in alfalfa is coumestrol because of its relatively greater biological potency than the other plant estrogens and because of its more frequent occurrence. Plant physiologists have shown that alfalfa infected with certain fungus diseases contains a level of coumestrol which increases with the amount of disease present in the alfalfa plants. Since alfalfa meal is such an important source of nutrients for farm animals and is often included in swine rations this study was conducted to determine if alfalfa plants with coumestrol levels in excess of 100 parts per million (ppm) would have any effect on the reproductive performance of gilts when included in their ration

Exact and asymptotic computations of elementary spin networks: classification of the quantum-classical boundaries

Increasing interest is being dedicated in the last few years to the issues of exact computations and asymptotics of spin networks. The large-entries regimes (semiclassical limits) occur in many areas of physics and chemistry, and in particular in discretization algorithms of applied quantum mechanics. Here we extend recent work on the basic building block of spin networks, namely the Wigner 6j symbol or Racah coefficient, enlightening the insight gained by exploiting its self-dual properties and studying it as a function of two (discrete) variables. This arises from its original definition as an (orthogonal) angular momentum recoupling matrix. Progress also derives from recognizing its role in the foundation of the modern theory of classical orthogonal polynomials, as extended to include discrete variables. Features of the imaging of various regimes of these orthonormal matrices are made explicit by computational advances -based on traditional and new recurrence relations- which allow an interpretation of the observed behaviors in terms of an underlying Hamiltonian formulation as well. This paper provides a contribution to the understanding of the transition between two extreme modes of the 6j, corresponding to the nearly classical and the fully quantum regimes, by studying the boundary lines (caustics) in the plane of the two matrix labels. This analysis marks the evolution of the turning points of relevance for the semiclassical regimes and puts on stage an unexpected key role of the Regge symmetries of the 6j.Comment: 15 pages, 11 figures. Talk presented at ICCSA 2012 (12th International Conference on Computational Science and Applications, Salvador de Bahia (Brazil) June 18-21, 2012