Wigner transform and pseudodifferential operators on symmetric spaces of non-compact type

We obtain a general expression for a Wigner transform (Wigner function) on symmetric spaces of non-compact type and study the Weyl calculus of pseudodifferential operators on them

Unmanned aerial vehicle remote sensing of snow: improving snowmelt prediction

Non-Peer Reviewe

Greenhouse gas intensity of an irrigated cropping system in Saskatchewan

Non-Peer ReviewedIn response to increasing global food demands, the proportion of irrigated agricultural land within the Canadian Prairies is likely to increase. However, the implications of this with respect to the agricultural greenhouse gas (GHG) balance are not well understood. This study investigates and compares the greenhouse gas intensity of a typical irrigated and dryland cropping system in Saskatchewan, a semi-arid region of the Canadian Prairies. Compared to their dryland counterpart, irrigated cropping systems have higher GHG emissions which are a result of the energy used for pumping and larger nitrous oxide (N2O) production rates associated with higher N-fertilizer application and moist soil conditions. These emissions may be partially offset by increased carbon sequestration from the greater productivity realized through irrigation. This investigation focuses on the quantification of soil GHG emissions through chamber-based flux measurements. Factors driving these emissions have been determined through in-situ soil temperature, matric potential, and moisture measurements. The emissions associated with pumping and other crop management activities are accounted for using the Intergovernmental Panel on Climate Change (IPCC) literature and methodology. Preliminary results from the first season of study confirm that irrigated cropping systems have greater greenhouse gas intensity. Soil N2O emissions from the irrigated system were four times greater than the dryland and were the greatest source of emissions for the irrigated system. Diesel combustion used to power equipment was comparable between cropping systems. Emissions associated with pumping were notable; however, due to the wet growing season they remained smaller than could be expected most years. The information derived from this study will aid in the development of regional specific soil emission factors, improved management strategies, and will identify new approaches for mitigating emissions

Pre-irrigation of a severely-saline soil with in-situ water to establish dryland forages

Non-Peer ReviewedAlfalfa serves as one of the most important forage plants in North America. It is also the recommended remedial crop for dryland salinity control. But, because of its limited salt tolerance, it does not establish satisfactorily in severely or moderately saline soils. A series of irrigations with the in-situ ground water located beneath a severely-saline site were delivered across seedbeds prepared within the same site prior to seeding ‘Beaver’ alfalfa (Medicago sativa) and ‘ AC Saltlander’ green wheatgrass (Elymus Hoffmannii). In this field study conducted in semiarid Saskatchewan, fall irrigations with 4.6 dS/m-water from a shallow, on-site, backhoe-dug well fitted with a solar-powered pump preceded spring seeding. Irrigation treatments ranged from zero to 2530 mm in total applied water. Plant emergence, spacing, height, cover, and forage yield of the alfalfa were significantly improved following pre-irrigation. Mean plant emergence increased from 20 to 79% for the alfalfa. The wheatgrass height and forage yield also improved significantly, but showed only an upward trend in emergence, spacing, height, and cover. The mean plant height in July increased from 90 to 159 mm for the wheatgrass and from 35 to 140 mm for the alfalfa. Based on linear regression of irrigated volume, every 119.3 mm of irrigated, in-situ water up to 2530 mm increased alfalfa forage yield by 10 g/m2

Aerodynamic and Radiative Controls on the Snow Surface Temperature

Abstract The snow surface temperature (SST) is essential for estimating longwave radiation fluxes from snow. SST can be diagnosed using finescale multilayer snow physics models that track changes in snow properties and internal energy; however, these models are heavily parameterized, have high predictive uncertainty, and require continuous simulation to estimate prognostic state variables. Here, a relatively simple model to estimate SST that is not reliant on prognostic state variables is proposed. The model assumes that the snow surface is poorly connected thermally to the underlying snowpack and largely transparent for most of the shortwave radiation spectrum, such that a snow surface energy balance among only sensible heat, latent heat, longwave radiation, and near-infrared radiation is possible and is called the radiative psychrometric model (RPM). The RPM SST is sensitive to air temperature, humidity, ventilation, and longwave irradiance and is secondarily affected by absorption of near-infrared radiation at the snow surface that was higher where atmospheric deposition of particulates was more likely to be higher. The model was implemented with neutral stability, an implicit windless exchange coefficient, and constant shortwave absorption factors and aerodynamic roughness lengths. It was evaluated against radiative SST measurements from the Canadian Prairies and Rocky Mountains, French Alps, and Bolivian Andes. With optimized and global shortwave absorption and aerodynamic roughness length parameters, the model is shown to accurately predict SST under a wide range of conditions, providing superior predictions when compared to air temperature, dewpoint, or ice bulb calculation approaches.</jats:p

Volume of the set of unistochastic matrices of order 3 and the mean Jarlskog invariant

A bistochastic matrix B of size N is called unistochastic if there exists a unitary U such that B_ij=|U_{ij}|^{2} for i,j=1,...,N. The set U_3 of all unistochastic matrices of order N=3 forms a proper subset of the Birkhoff polytope, which contains all bistochastic (doubly stochastic) matrices. We compute the volume of the set U_3 with respect to the flat (Lebesgue) measure and analytically evaluate the mean entropy of an unistochastic matrix of this order. We also analyze the Jarlskog invariant J, defined for any unitary matrix of order three, and derive its probability distribution for the ensemble of matrices distributed with respect to the Haar measure on U(3) and for the ensemble which generates the flat measure on the set of unistochastic matrices. For both measures the probability of finding |J| smaller than the value observed for the CKM matrix, which describes the violation of the CP parity, is shown to be small. Similar statistical reasoning may also be applied to the MNS matrix, which plays role in describing the neutrino oscillations. Some conjectures are made concerning analogous probability measures in the space of unitary matrices in higher dimensions.Comment: 33 pages, 6 figures version 2 - misprints corrected, explicit formulae for phases provide

Symmetric spaces of higher rank do not admit differentiable compactifications

Any nonpositively curved symmetric space admits a topological compactification, namely the Hadamard compactification. For rank one spaces, this topological compactification can be endowed with a differentiable structure such that the action of the isometry group is differentiable. Moreover, the restriction of the action on the boundary leads to a flat model for some geometry (conformal, CR or quaternionic CR depending of the space). One can ask whether such a differentiable compactification exists for higher rank spaces, hopefully leading to some knew geometry to explore. In this paper we answer negatively.Comment: 13 pages, to appear in Mathematische Annale

Generalized quantum tomographic maps

Some non-linear generalizations of classical Radon tomography were recently introduced by M. Asorey et al [Phys. Rev. A 77, 042115 (2008), where the straight lines of the standard Radon map are replaced by quadratic curves (ellipses, hyperbolas, circles) or quadratic surfaces (ellipsoids, hyperboloids, spheres). We consider here the quantum version of this novel non-linear approach and obtain, by systematic use of the Weyl map, a tomographic encoding approach to quantum states. Non-linear quantum tomograms admit a simple formulation within the framework of the star-product quantization scheme and the reconstruction formulae of the density operators are explicitly given in a closed form, with an explicit construction of quantizers and dequantizers. The role of symmetry groups behind the generalized tomographic maps is analyzed in some detail. We also introduce new generalizations of the standard singular dequantizers of the symplectic tomographic schemes, where the Dirac delta-distributions of operator-valued arguments are replaced by smooth window functions, giving rise to the new concept of "thick" quantum tomography. Applications for quantum state measurements of photons and matter waves are discussed.Comment: 8 page

On the scattering theory of the classical hyperbolic C(n) Sutherland model

In this paper we study the scattering theory of the classical hyperbolic Sutherland model associated with the C(n) root system. We prove that for any values of the coupling constants the scattering map has a factorized form. As a byproduct of our analysis, we propose a Lax matrix for the rational C(n) Ruijsenaars-Schneider-van Diejen model with two independent coupling constants, thereby setting the stage to establish the duality between the hyperbolic C(n) Sutherland and the rational C(n) Ruijsenaars-Schneider-van Diejen models.Comment: 15 page

Nonnegatively curved homogeneous metrics obtained by scaling fibers of submersions

We consider invariant Riemannian metrics on compact homogeneous spaces G/H where an intermediate subgroup K between G and H exists, so that the homogeneous space G/H is the total space of a Riemannian submersion. We study the question as to whether enlarging the fibers of the submersion by a constant scaling factor retains the nonnegative curvature in the case that the deformation starts at a normal homogeneous metric. We classify triples of groups (H,K,G) where nonnegative curvature is maintained for small deformations, using a criterion proved by Schwachh\"ofer and Tapp. We obtain a complete classification in case the subgroup H has full rank and an almost complete classification in the case of regular subgroups.Comment: 23 pages; minor revisions, to appear in Geometriae Dedicat