Abstract:
We discuss exact analytical solutions of a variety of statistical models recently obtained for finite systems by a novel powerful mathematical method, the Laplace-Fourier transform. Among them are a constrained version of the statistical multifragmentation model, the Gas of Bags Model and the Hills and Dales Model of surface partition. Thus, the Laplace-Fourier transform allows one to study the nuclear matter equation of state, the equation of state of hadronic and quark gluon matter and surface partitions on the same footing. A complete analysis of the isobaric partition singularities of these models is done for finite systems. The developed formalism allows us, for the first time, to exactly define the finite volume analogs of gaseous, liquid and mixed phases of these models from the first principles of statistical mechanics and demonstrate the pitfalls of earlier works. The found solutions may be used for building up a new theoretical apparatus to rigorously study phase transitions in finite systems. The strategic directions of future research opened by these exact results are also discussed.

Abstract:
For the statistical multifragmentation model the critical indices $\alpha^\prime, \beta, \gamma^\prime, \delta$ are calculated as functions of the Fisher parameter $\tau$. It is found that these indices have different values than in Fisher's droplet model. Some peculiarities of the scaling relations are discussed. The basic model predicts for the index $\tau$ a narrow range of values, $1.799< \tau < 1.846$, which is consistent with two experiments on nuclear multifragmentation.

Abstract:
A canonical partition function for the two-component excluded volume model is derived, leading to two different van der Waals approximations. The one is known as the Lorentz-Berthelot mixture and the other has been proposed recently. Both models are analysed in the canonical and grand canonical ensemble. In comparison with the one-component van der Waals excluded volume model the suppression of particle densities is reduced in these two-component formulations, but in two essentially different ways. Presently used multi-component models have no such reduction. They are shown to be not correct when used for components with different hard-core radii. For high temperatures the excluded volume interaction is refined by accounting for the Lorentz contraction of the spherical excluded volumes, which leads to a distinct enhancement of lighter particles. The resulting effects on pion yield ratios are studied for AGS and SPS data.

Abstract:
A general effective action for quark matter at nonzero temperature and/or nonzero density is derived. Irrelevant quark modes are distinguished from relevant quark modes, and hard from soft gluon modes, by introducing two separate cut-offs in momentum space, one for quarks, $\Lambda_q$, and one for gluons, $\Lambda_g$. Irrelevant quark modes and hard gluon modes are then exactly integrated out in the functional integral representation of the QCD partition function. Depending on the specific choice for $\Lambda_q$ and $\Lambda_g$, the resulting effective action contains well-known effective actions for hot and/or dense quark matter, for instance the ``Hard Thermal Loop'' (HTL) or the ``Hard Dense Loop'' (HDL) action, as well as the high-density effective theory proposed by Hong and others.

Abstract:
I derive a general effective theory for hot and/or dense quark matter. After introducing general projection operators for hard and soft quark and gluon degrees of freedom, I explicitly compute the functional integral for the hard quark and gluon modes in the QCD partition function. Upon appropriate choices for the projection operators one recovers various well-known effective theories such as the Hard Thermal Loop/ Hard Dense Loop Effective Theories as well as the High Density Effective Theory by Hong and Schaefer. I then apply the effective theory to cold and dense quark matter and show how it can be utilized to simplify the weak-coupling solution of the color-superconducting gap equation. In general, one considers as relevant quark degrees of freedom those within a thin layer of width 2 Lambda_q around the Fermi surface and as relevant gluon degrees of freedom those with 3-momenta less than Lambda_gl. It turns out that it is necessary to choose Lambda_q << Lambda_gl, i.e., scattering of quarks along the Fermi surface is the dominant process. Moreover, this special choice of the two cutoff parameters Lambda_q and Lambda_gl facilitates the power-counting of the numerous contributions in the gap-equation. In addition, it is demonstrated that both the energy and the momentum dependence of the gap function has to be treated self-consistently in order to determine the imaginary part of the gap function. For quarks close to the Fermi surface the imaginary part is calculated explicitly and shown to be of sub-subleading order in the gap equation.

Abstract:
We solve the gap equation for color-superconducting quark matter in the 2SC phase, including both the energy and the momentum dependence of the gap, \phi=\phi(k_0,\vk). For that purpose a complex Ansatz for \phi is made. The calculations are performed within an effective theory for cold and dense quark matter. The solution of the complex gap equation is valid to subleading order in the strong coupling constant g and in the limit of zero temperature. We find that, for momenta sufficiently close to the Fermi surface and for small energies, the dominant contribution to the imaginary part of $\phi$ arises from Landau-damped magnetic gluons. Further away from the Fermi surface and for larger energies the other gluon sectors have to be included into Im\phi. We confirm that Im$ \phi$ contributes a correction of order g to the prefactor of \phi for on-shell quasiquarks sufficiently close to the Fermi surface, whereas further away from the Fermi surface Im\phi and Re\phi are of the same order. Finally, we discuss the relevance of Im\phi for the damping of quasiquark excitations.

Abstract:
We derive an effective theory for dense, cold and massive quark matter. To this end, we employ a general effective action formalism where antiquarks and quarks far from the Fermi surface, as well as hard gluons, are integrated out explicitly. We show that the resulting effective action depends crucially on the projectors used to separate quarks from antiquarks. If one neglects the quark masses in these projectors, the Feynman rules of the effective theory involve quark mass insertions which connect quark with antiquark propagators. Including the quark masses into these projectors, mass insertions do not appear and the Feynman rules are identical to those found in the zero-mass limit.

Abstract:
Carbon dioxide (CO2) and methane (CH4) are the two most important anthropogenic greenhouse gases. SCIAMACHY on ENVISAT is the first satellite instrument whose measurements are sensitive to concentration changes of the two gases at all altitude levels down to the Earth's surface where the source/sink signals are largest. We have processed three years (2003–2005) of SCIAMACHY near-infrared nadir measurements to simultaneously retrieve vertical columns of CO2 (from the 1.58 μm absorption band), CH4 (1.66 μm) and oxygen (O2 A-band at 0.76 μm) using the scientific retrieval algorithm WFM-DOAS. We show that the latest version of WFM-DOAS, version 1.0, which is used for this study, has been significantly improved with respect to its accuracy compared to the previous versions while essentially maintaining its high processing speed (~1 min per orbit, corresponding to ~6000 single measurements, and per gas on a standard PC). The greenhouse gas columns are converted to dry air column-averaged mole fractions, denoted XCO2 (in ppm) and XCH4 (in ppb), by dividing the greenhouse gas columns by simultaneously retrieved dry air columns. For XCO2 dry air columns are obtained from the retrieved O2 columns. For XCH4 dry air columns are obtained from the retrieved CO2 columns because of better cancellation of light path related errors compared to using O2 columns retrieved from the spectrally distant O2 A-band. Here we focus on a discussion of the XCO2 data set. The XCH4 data set is discussed in a separate paper (Part 2). In order to assess the quality of the retrieved XCO2 we present comparisons with Fourier Transform Spectroscopy (FTS) XCO2 measurements at two northern hemispheric mid-latitude ground stations. To assess the quality globally, we present detailed comparisons with global XCO2 fields obtained from NOAA's CO2 assimilation system CarbonTracker. For the Northern Hemisphere we find good agreement with the reference data for the CO2 seasonal cycle and the CO2 annual increase. For the Southern Hemisphere, where significantly less data are available for averaging compared to the Northern Hemisphere, the CO2 annual increase is also in good agreement with CarbonTracker but the amplitude and phase of the seasonal cycle show systematic differences (up to several ppm) arising partially from the O2 normalization most likely caused by unconsidered scattering effects due to subvisual cirrus clouds. The retrieved XCO2 regional pattern at monthly resolution over various regions show clear correlations with CarbonTracker but also significant differences. Typically the retrieved variability is about 4 ppm (1% of 380 ppm) higher but depending on time and location differences can reach or even exceed 8 ppm. Based on the error analysis and on the comparison with the reference data we conclude that the XCO2 data set can be characterized by a single measurement retrieval precision (random error) of 1–2%, a systematic low bias of about 1.5%, and by a relative accuracy of about

Abstract:
Carbon dioxide (CO2) is the most important man-made greenhouse gas (GHG) that cause global warming. With electricity generation through fossil-fuel power plants now being the economic sector with the largest source of CO2, power plant emissions monitoring has become more important than ever in the fight against global warming. In a previous study done by Bovensmann et al. (2010), random and systematic errors of power plant CO2 emissions have been quantified using a single overpass from a proposed CarbonSat instrument. In this study, we quantify errors of power plant annual emission estimates from a hypothetical CarbonSat and constellations of several CarbonSats while taking into account that power plant CO2 emissions are time-dependent. Our focus is on estimating systematic errors arising from the sparse temporal sampling as well as random errors that are primarily dependent on wind speeds. We used hourly emissions data from the US Environmental Protection Agency (EPA) combined with assimilated and re-analyzed meteorological fields from the National Centers of Environmental Prediction (NCEP). CarbonSat orbits were simulated as a sun-synchronous low-earth orbiting satellite (LEO) with an 828-km orbit height, local time ascending node (LTAN) of 13:30 (01:30 p.m. LT) and achieves global coverage after 5 days. We show, that despite the variability of the power plant emissions and the limited satellite overpasses, one CarbonSat has the potential to verify reported US annual CO2 emissions from large power plants (≥5 Mt CO2 yr 1) with a systematic error of less than ~4.9% and a random error of less than ~6.7% for 50% of all the power plants. For 90% of all the power plants, the systematic error was less than ~12.4% and the random error was less than ~13%. We additionally investigated two different satellite configurations using a combination of 5 CarbonSats. One achieves global coverage everyday but only samples the targets at fixed local times. The other configuration samples the targets five times at two-hour intervals approximately every 6th day but only achieves global coverage after 5 days. From the statistical analyses, we found, as expected, that the random errors improve by approximately a factor of two if 5 satellites are used. On the other hand, more satellites do not result in a large reduction of the systematic error. The systematic error is somewhat smaller for the CarbonSat constellation configuration achieving global coverage everyday. Therefore, we recommend the CarbonSat constellation configuration that achieves daily global coverage.

Abstract:
A microscopic study of the individual annealed (In,Ga)As/GaAs quantum dots is done by means of high-resolution transmission electron microscopy. The Cauchy-Green strain-tensor component distribution and the chemical composition of the (In,Ga)As alloy are extracted from the microscopy images. The image processing allows for the reconstruction of the strain-induced electric-field gradients at the individual atomic columns extracting thereby the magnitude and asymmetry parameter of the nuclear quadrupole interaction. Nuclear magnetic resonance absorption spectra are analyzed for parallel and transverse mutual orientations of the electric-field gradient and a static magnetic field.