Differential Algebras in Non-Commutative Geometry

We discuss the differential algebras used in Connes' approach to Yang-Mills theories with spontaneous symmetry breaking. These differential algebras generated by algebras of the form functions $\otimes$ matrix are shown to be skew tensorproducts of differential forms with a specific matrix algebra. For that we derive a general formula for differential algebras based on tensor products of algebras. The result is used to characterize differential algebras which appear in models with one symmetry breaking scale.Comment: 21 page

Multiple scattered radiation emerging from continental haze layers. 1: Radiance, polarization, and neutral points

The complete radiation field is calculated for scattering layers of various optical thicknesses. Results obtained for Rayleigh and haze scattering are compared. Calculated radiances show differences as large as 23% compared to the approximate scalar theory of radiative transfer, while the same differences are approximately 0.1% for a continental haze phase function. The polarization of reflected and transmitted radiation is given for various optical thicknesses, solar zenith angles, and surface albedos. Two types of neutral points occur for aerosol phase functions. Rayleigh-like neutral points arise from zero polarization that occurs at scattering angles of 0 deg and 180 deg. For Rayleigh phase functions, the position of these points varies with the optical thickness of the scattering layer. Non-Rayleigh neutral points are associated with the zeros of polarization which occur between the end points of the single scattering curve, and are found over a wide range of azimuthal angles

Multiple scattered radiation emerging from continental haze layers. 2: Ellipticity and direction of polarization

The ellipticity and the direction of polarization are calculated for radiation that has undergone multiple scattering from plane parallel layers. Both the radiation emerging from the top of the layer and that transmitted through the bottom are considered. Two different phase functions are used for the scattering layer: Rayleigh and haze L. The direction of polarization of the reflected radiation shows little variation as the optical depth of the layer increases, while there is a much larger variation for the transmitted radiation. When the optical thickness is small, the direction of polarization for haze L varies rapidly with zenith angle near those angles at which the single scattered polarization is zero. The ellipticity of the radiation from haze L layers increases at first in direct proportion to the optical thickness of the layer. In general the ellipticity of the transmitted radiation is considerably greater than that of the reflected because of the greater average number of photon collisions in the former case

Radiance, polarization, and ellipticity of the radiation in the earth's atmosphere

The complete radiation field including polarization is calculated for a model of the real atmosphere by the matrix operator method. The radiance, direction and amount of polarization, and ellipticity are obtained at the top and bottom of the atmosphere for three values of the surface albedo (0; 0.15 0.90) and five solar zenith angles. Scattering and absorption by molecules (including ozone) and by aerosols are taken into account together with the variation of the number density of these substances with height. All results are calculated for both a normal aerosol number and a distribution which is one-third of the normal amount at all heights. The calculated values show general qualitative agreement with the available experimental measurements. The position of the neutral points of the polarization in the principal plane is a sensitive indicator of the characteristics of the aerosol particles in the atmosphere, since it depends on the sign and value of the single scattered polarization for scattering angles around 20 deg and 160 deg for transmitted and reflected photons respectively

How Might Synthetic Fuels from Coal Affect Natural Resources and Environment?

Energy self-sufficiency for the U. S. requires substantially increased use of coal. Direct combustion of coal without adequate environmental controls, as would occur if coal were used as a fuel for homes and offices throughout the country, would result in severe air pollution problems„ Synthetic fuels from coal such as methane, low BTU gas, or hydrogen, when utilized by the homes and businesses as gas or as electricity from gas, will contribute a much smaller amount of air pollution. However, to make these synthetic fuels available, it is necessary to mine more coal than would have to be mined for direct combustion, as the conversion processes all have energy losses. It is also necessary to make more extraction equipment, more fuels processing equipment and more distribution equipment which places a heavier burden on mineral resources, with associated added requirements for energy to make the equipment. This paper explores the effects on energy resources, and the environment by carefully- taking account of extra coal needed, extra equipment required, and the associated environmental costs due to all forms of pollution resulting from the mining operation, conversion of coal to synthetic fuels, and the combustion of the synthetic fuels. Resource depletion and environmental impact are compared for the present system and a synthetic gas system which provides all of our electric power

A Comprehensive Emission Inventory of Bbiogenic Volatile Organic Compounds in Europe: Improved Seasonality and Land-cover

Biogenic volatile organic compounds (BVOC) emitted from vegetation are important for the formation of secondary pollutants such as ozone and secondary organic aerosols (SOA) in the atmosphere. Therefore, BVOC emission are an important input for air quality models. To model these emissions with high spatial resolution, the accuracy of the underlying vegetation inventory is crucial. We present a BVOC emission model that accommodates different vegetation inventories and uses satellite-based measurements of greenness instead of pre-defined vegetation periods. This approach to seasonality implicitly treats effects caused by water or nutrient availability, altitude and latitude on a plant stand. Additionally, we test the influence of proposed seasonal variability in enzyme activity on BVOC emissions. In its present setup, the emission model calculates hourly emissions of isoprene, monoterpenes, sesquiterpenes and the oxygenated volatile organic compounds (OVOC) methanol, formaldehyde, formic acid, ethanol, acetaldehyde, acetone and acetic acid. In this study, emissions based on three different vegetation inventories are compared with each other and diurnal and seasonal variations in Europe are investigated for the year 2006. Two of these vegetation inventories require information on tree-cover as an input. We compare three different land-cover inventories (USGS GLCC, GLC2000 and Globcover 2.2) with respect to tree-cover. The often-used USGS GLCC land-cover inventory leads to a severe reduction of BVOC emissions due to a potential miss-attribution of broad-leaved trees and reduced tree-cover compared to the two other land-cover inventories. To account for uncertainties in the land-cover classification, we introduce land-cover correction factors for each relevant land-use category to adjust the tree-cover. The results are very sensitive to these factors within the plausible range. For June 2006, total monthly BVOC emissions decreased up to −27% with minimal and increased up to +71% with maximal factors, while in January 2006, the changes in monthly BVOC emissions were −54 and +56% with minimal and maximal factors, respectively. The new seasonality approach leads to a reduction in the annual emissions compared with non-adjusted data. The strongest reduction occurs in OVOC (up to −32 %), the weakest in isoprene (as little as −19 %). If also enzyme seasonality is taken into account, however, isoprene reacts with the steepest decrease of annual emissions, which are reduced by −44% to −49 %, annual emissions of monoterpenes reduce between −30 and −35 %. The sensitivity of the model to changes in temperature depends on the climatic zone but not on the vegetation inventory. The sensitivity is higher for temperature increases of 3K (+31% to +64 %) than decreases by the same amount (−20 to −35 %). The climatic zones “Cold except summer” and “arid” are most sensitive to temperature changes in January for isoprene and monoterpenes, respectively, while in June, “polar” is most sensitive to temperature for both isoprene and monoterpenes. Our model predicts the oxygenated volatile organic compounds to be the most abundant fraction of the annual European emissions (3571–5328 Gg yr−1), followed by monoterpenes (2964–4124 Gg yr−1), isoprene (1450–2650 Gg yr−1) and sesquiterpenes (150–257 Gg yr−1). We find regions with high isoprene emissions (most notably the Iberian Peninsula), but overall, oxygenated VOC dominate with 43–45% (depending on the vegetation inventory) contribution to the total annual BVOC emissions in Europe. Isoprene contributes between 18–21 %, monoterpenes 33–36% and sesquiterpenes contribute 1–2 %.We compare the concentrations of biogenic species simulated by an air quality model with measurements of isoprene and monoterpenes in Hohenpeissenberg (Germany) for both summer and winter. The agreement between observed and modelled concentrations is better in summer than in winter. This can partly be explained with the difficulty to model weather conditions in winter accurately, but also with the increased anthropogenic influence on the concentrations of BVOC compounds in winter. Our results suggest that land-cover inventories used to derive tree-cover must be chosen with care. Also, uncertainties in the classification of land-cover pixels must be taken into account and remain high. This problem must be addressed together with the remote sensing community. Our new approach using a greenness index for addressing seasonality of vegetation can be implemented easily in existing models. The importance of OVOC for air quality should be more deeply addressed by future studies, especially in smog chambers. Also, the fate of BVOC from the dominant region of the Iberian Peninsula should be studied more in detail