Abstract:
Before radar estimates of the raindrop size distribution (DSD) can be assimilated into numerical weather prediction models, the DSD estimate must also include an uncertainty estimate. Ensemble statistics are based on using the same observations as inputs into several different models with the spread in the outputs providing an uncertainty estimate. In this study, Doppler velocity spectra from collocated vertically pointing profiling radars operating at 50 and 920 MHz were the input data for 42 different DSD retrieval models. The DSD retrieval models were perturbations of seven different DSD models (including exponential and gamma functions), two different inverse modeling methodologies (convolution or deconvolution), and three different cost functions (two spectral and one moment cost functions). Two rain events near Darwin, Australia, were analyzed in this study producing 26 725 independent ensembles of mass-weighted mean raindrop diameter Dm and rain rate R. The mean and the standard deviation (indicated by the symbols and σx) of Dm and R were estimated for each ensemble. For small ranges of or , histograms of σDm and σR were found to be asymmetric, which prevented Gaussian statistics from being used to describe the uncertainties. Therefore, 10, 50, and 90 percentiles of σDm and σR were used to describe the uncertainties for small intervals of or . The smallest Dm uncertainty occurred for between 0.8 and 1.8 mm with the 90th and 50th percentiles being less than 0.15 and 0.11 mm, which correspond to relative errors of less than 20% and 15%, respectively. The uncertainty increased for smaller and larger values. The uncertainty of R increased with . While the 90th percentile uncertainty approached 0.6 mm h 1 for a 2 mm h 1 rain rate (30% relative error), the median uncertainty was less than 0.15 mm h 1 at the same rain rate (less than 8% relative error). This study addresses retrieval error and does not attempt to quantify absolute or representativeness errors.

Abstract:
It has recently been suggested \cite{Chang:2006bm} that a reliable and unambiguous definition of the non-perturbative massive quark condensate could be provided by considering a non positive-definite class of solutions to the Schwinger Dyson Equation for the quark propagator. In this paper we show that this definition is incomplete without considering a third class of solutions. Indeed, studying these three classes reveals a degeneracy of possible condensate definitions leading to a whole range of values. However, we show that the {\it physical} condensate may in fact be extracted by simple fitting to the Operator Product Expansion, a procedure which is stabilised by considering the three classes of solution together. We find that for current quark masses in the range from zero to 25 MeV or so (defined at a scale of 2 GeV in the $\bar{MS}$ scheme), the dynamically generated condensate increases from the chiral limit in a wide range of phenomenologically successful models of the confining QCD interaction. Lastly, the role of a fourth class of noded solutions is briefly discussed.

Abstract:
We determine the q-bar q condensate for quark masses from zero up to that of the strange quark within a phenomenologically successful modelling of continuum QCD by solving the quark Schwinger-Dyson equation. The existence of multiple solutions to this equation is the key to an accurate and reliable extraction of this condensate using the operator product expansion. We explain why alternative definitions fail to give the physical condensate.

Abstract:
The use of a dynamic "accordion" lattice with ultracold atoms is demonstrated. Ultracold atoms of $^{87}$Rb are trapped in a two-dimensional optical lattice, and the spacing of the lattice is then increased in both directions from 2.2 to 5.5 microns. Atoms remain bound for expansion times as short as a few milliseconds, and the experimentally measured minimum ramp time is found to agree well with numerical calculations. This technique allows an experiment such as quantum simulations to be performed with a lattice spacing smaller than the resolution limit of the imaging system, while allowing imaging of the atoms at individual lattice sites by subsequent expansion of the optical lattice.

Abstract:
We report the observation of vortex nucleation in a rotating optical lattice. A 87Rb Bose-Einstein condensate was loaded into a static two-dimensional lattice and the rotation frequency of the lattice was then increased from zero. We studied how vortex nucleation depended on optical lattice depth and rotation frequency. For deep lattices above the chemical potential of the condensate we observed a linear dependence of the number of vortices created with the rotation frequency,even below the thermodynamic critical frequency required for vortex nucleation. At these lattice depths the system formed an array of Josephson-coupled condensates. The effective magnetic field produced by rotation introduced characteristic relative phases between neighbouring condensates, such that vortices were observed upon ramping down the lattice depth and recombining the condensates.

Abstract:
We summarize our results for the impact of anisotropic fermionic velocities in (2+1)-dimensional QED on the critical number of fermion flavors, N^c_f, and dynamical mass generation. We apply different approximation schemes for the gauge boson vacuum polarization and the fermion-boson vertex to analyze the according Dyson-Schwinger equations in a finite volume. Our results point towards large variations of N^c_f away from the isotropic point in agreement with other approaches.

Abstract:
We investigate transport in a gate-defined graphene quantum point contact in the quantum Hall regime. Edge states confined to the interface of p and n regions in the graphene sheet are controllably brought together from opposite sides of the sample and allowed to mix in this split-gate geometry. Among the expected quantum Hall features, an unexpected additional plateau at 0.5 h/e^2 is observed. We propose that chaotic mixing of edge channels gives rise to the extra plateau.

The central importance of quantum chemistry is to obtain solutions of the Schr?dinger equation for the accurate determination of the properties of atomic and molecular systems that occurred from the calculation of wave functions accurate for many diatomic and polyatomic molecules, using Self Consistent Field method (SCF). The application of quantum chemical methods in the study and planning of bioactive compounds has become a common practice nowadays. From the point of view of planning it is important to note, when it comes to the use of molecular modeling, a collective term that refers to methods and theoretical modeling and computational techniques to mimic the behavior of molecules, not intend to reach a bioactive molecule simply through the use of computer programs. The choice of method for energy minimization depends on factors related to the size of the molecule, parameters of availability, stored data and computational resources. Molecular models generated by the computer are the result of mathematical equations that estimate the positions and properties of the electrons and nuclei, the calculations exploit experimentally, the characteristics of a structure, providing a new perspective on the molecule. In this work we show that studies of Highest Occupied Molecular Orbital Energy (HOMO), Low Unoccupied Molecular Orbital Energy (LUMO) and Map of molecular electrostatic potential (MEP) using Hatree-Fock method with different basis sets (HF/3-21G*, HF/3-21G**, HF/6-31G, HF/6-31G*, HF/6-31G** and HF/6-311G), that are of great importance in modern chemistry, biochemistry, molecular biology, and other fields of knowledge of health sciences. In order to obtain a significant correlation, it is essential that the descriptors are used appropriately. Thus, the quantum chemical calculations are an attractive source of new molecular descriptors that can, in principle, express all the geometrical and electronic properties of molecules and their interactions with biological receptor.

Abstract:
We have investigated three SNRs in the LMC using multi-wavelength data. These SNRs are generally fainter than the known sample and may represent a previously missed population. One of our SNRs is the second LMC remnant analyzed which is larger than any Galactic remnant for which a definite size has been established. The analysis of such a large remnant contributes to the understanding of the population of highly evolved SNRs. We have obtained X-ray images and spectra of three of these recently identified SNRs using the XMM-Newton observatory. These data, in conjunction with pre-existing optical emission-line images and spectra, were used to determine the physical conditions of the optical- and X-ray-emitting gas in the SNRs. We have compared the morphologies of the SNRs in the different wavebands. The physical properties of the warm ionized shell were determined from the H-alpha surface brightness and the SNR expansion velocity. The X-ray spectra were fit with a thermal plasma model and the physical conditions of the hot gas were derived from the model fits. Finally, we have compared our observations with simulations of SNR evolution.

Abstract:
We describe interacting mixtures of ultracold bosonic and fermionic atoms in harmonically confined optical lattices. For a suitable choice of parameters we study the emergence of superfluid and Fermi liquid (non-insulating) regions out of Bose-Mott and Fermi-band insulators, due to finite Boson and Fermion hopping. We obtain the shell structure for the system and show that angular momentum can be transferred to the non-insulating regions from Laguerre-Gaussian beams, which combined with Bragg spectroscopy can reveal all superfluid and Fermi liquid shells.