Regularly varying probability densities

The convolution of regularly varying probability densities is proved asymptotic to their sum, and hence is also regularly varying. Extensions to rapid variation, O-regular variation, and other types of asymptotic decay are also given

Ab Initio Study of Phase Stability in Doped TiO2

Ab-initio density functional theory (DFT) calculations of the relative stability of anatase and rutile polymorphs of TiO2 were carried using all-electron atomic orbitals methods with local density approximation (LDA). The rutile phase exhibited a moderate margin of stability of ~ 3 meV relative to the anatase phase in pristine material. From computational analysis of the formation energies of Si, Al, Fe and F dopants of various charge states across different Fermi level energies in anatase and in rutile, it was found that the cationic dopants are most stable in Ti substitutional lattice positions while formation energy is minimised for F- doping in interstitial positions. All dopants were found to considerably stabilise anatase relative to the rutile phase, suggesting the anatase to rutile phase transformation is inhibited in such systems with the dopants ranked F>Si>Fe>Al in order of anatase stabilisation strength. Al and Fe dopants were found to act as shallow acceptors with charge compensation achieved through the formation of mobile carriers rather than the formation of anion vacancies

The structure of the hard sphere solid

We show that near densest-packing the perturbations of the HCP structure yield higher entropy than perturbations of any other densest packing. The difference between the various structures shows up in the correlations between motions of nearest neighbors. In the HCP structure random motion of each sphere impinges slightly less on the motion of its nearest neighbors than in the other structures.Comment: For related papers see: http://www.ma.utexas.edu/users/radin/papers.htm

Blade-mounted trailing edge flap control for BVI noise reduction

Numerical procedures based on the 2-D and 3-D full potential equations and the 2-D Navier-Stokes equations were developed to study the effects of leading and trailing edge flap motions on the aerodynamics of parallel airfoil-vortex interactions and on the aerodynamics and acoustics of the more general self-generated rotor blade vortex interactions (BVI). For subcritical interactions, the 2-D results indicate that the trailing edge flap can be used to alleviate the impulsive loads experienced by the airfoil. For supercritical interactions, the results show the necessity of using a leading edge flap, rather than a trailing edge flap, to alleviate the interaction. Results for various time dependent flap motions and their effect on the predicted temporal sectional loads, differential pressures, and the free vortex trajectories are presented. For the OLS model rotor, contours of a BVI noise metric were used to quantify the effects of the trailing edge flap on the size and directivity of the high/low intensity noise region(s). Average reductions in the BVI noise levels on the order of 5 dB with moderate power penalties on the order of 18 pct. for a four bladed rotor and 58 pct. for a two bladed rotor were obtained

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

Statistics of Cosmological Black Hole Jet Sources: Blazar Predictions for GLAST

A study of the statistics of cosmological black-hole jet sources is applied to EGRET blazar data, and predictions are made for GLAST. Black-hole jet sources are modeled as collimated relativistic plasma outflows with radiation beamed along the jet axis due to strong Doppler boosting. The comoving rate density of blazar flares is assumed to follow a blazar formation rate (BFR), modeled by analytic functions based on astronomical observations and fits to EGRET data. The redshift and size distributions of gamma-ray blazars observed with EGRET, separated into BL Lac object (BL) and flat spectrum radio quasar (FSRQ) distributions, are fit with monoparametric functions for the distributions of the jet Lorentz factor \Gamma, comoving directional power l'_e, and spectral slope. A BFR factor ~10 x greater at z ~ 1 than at present is found to fit the FSRQ data. A smaller comoving rate density and greater luminosity of BL flares at early times compared to the present epoch fits the BL data. Based on the EGRET observations, ~1000 blazars consisting of ~800 FSRQs and FR2 radio galaxies and ~200 BL Lacs and FR1 radio galaxies will be detected with GLAST during the first year of the mission. Additional AGN classes, such as hard-spectrum BL Lacs that were mostly missed with EGRET, could add more GLAST sources. The FSRQ and BL contributions to the EGRET gamma-ray background at 1 GeV are estimated at the level of ~10 - 15% and ~2 - 4%, respectively. EGRET and GLAST sensitivities to blazar flares are considered in the optimal case, and a GLAST analysis method for blazar detection is outlined.Comment: 17 pages, 9 figures, ApJ, in press, v.660, May 1, 2007 (minor changes from previous version

Modelling the spread of Wolbachia in spatially heterogeneous environments

The endosymbiont Wolbachia infects a large number of insect species and is capable of rapid spread when introduced into a novel host population. The bacteria spread by manipulating their hosts' reproduction, and their dynamics are influenced by the demographic structure of the host population and patterns of contact between individuals. Reaction–diffusion models of the spatial spread of Wolbachia provide a simple analytical description of their spatial dynamics but do not account for significant details of host population dynamics. We develop a metapopulation model describing the spatial dynamics of Wolbachia in an age-structured host insect population regulated by juvenile density-dependent competition. The model produces similar dynamics to the reaction–diffusion model in the limiting case where the host's habitat quality is spatially homogeneous and Wolbachia has a small effect on host fitness. When habitat quality varies spatially, Wolbachia spread is usually much slower, and the conditions necessary for local invasion are strongly affected by immigration of insects from surrounding regions. Spread is most difficult when variation in habitat quality is spatially correlated. The results show that spatial variation in the density-dependent competition experienced by juvenile host insects can strongly affect the spread of Wolbachia infections, which is important to the use of Wolbachia to control insect vectors of human disease and other pests

Alternative Methods of Describing Structure Formation in the Lemaitre-Tolman Model

We describe several new ways of specifying the behaviour of Lemaitre-Tolman (LT) models, in each case presenting the method for obtaining the LT arbitrary functions from the given data, and the conditions for existence of such solutions. In addition to our previously considered `boundary conditions', the new ones include: a simultaneous big bang, a homogeneous density or velocity distribution in the asymptotic future, a simultaneous big crunch, a simultaneous time of maximal expansion, a chosen density or velocity distribution in the asymptotic future, only growing or only decaying fluctuations. Since these conditions are combined in pairs to specify a particular model, this considerably increases the possible ways of designing LT models with desired properties.Comment: Accepted by Phys Rev D. RevTeX 4, 13 pages, no figures. Part of a series: gr-qc/0106096, gr-qc/0303016, gr-qc/0309119. Replacement contains very minor correction