A theoretical study on the XeF(2) molecule

A relativistic four-component study was performed for the XeF(2) molecule by using the Dirac-Coulomb (DC) Hamiltonian and the relativistic adapted Gaussian basis sets (RAGBSs). The comparison of bond lengths obtained showed that relativistic effects on this property are small (increase of only 0.01 angstrom) while the contribution of electron correlation, obtained at CCSD(T) or CCSD-T levels, is more important (increase of 0.05 angstrom). Electron correlation is also dominant over relativistic effects for dissociation energies. Moreover, the correlation-relativity interaction is shown to be negligible for these properties. The electron affinity, the first ionization potential and the double ionization potential are obtained by means of the Fock-space coupled cluster (FSCC) method, resulting in DC-CCSD-T values of 0.3 eV, 12.5 eV and 32.3 eV, respectively. Vibrational frequencies and some anharmonicity constants were also calculated under the four-component formalism by means of standard perturbation equations. All these molecular properties are, in general, ill satisfactory agreement with available experimental results. Finally, a partition in terms of charge-charge flux-dipole flux (CCFDF) contributions derived by means of the quantum theory of atoms in molecules (QTAIM) in non-relativistic QCISD(FC)/3-21G* calculations was carried out for XeF(2) and KrF(2). This analysis showed that the most remarkable difference between both molecules lies on the charge flux contribution to the asymmetric stretching mode, which is negligible in KrF(2) but important in XeF(2). (c) 2008 Elsevier B.V. All rights reserved.

Detection of complex point targets with distributed assets in a MIMO radar system

The report explores the problem of detecting complex point target models in a MIMO radar system. A complex point target is a mathematical and statistical model for a radar target that is not resolved in space, but exhibits varying complex reflectivity across the different bistatic view angles. The complex reflectivity can be modeled as a complex stochastic process whose index set is the set of all the bistatic view angles, and the parameters of the stochastic process follow from an analysis of a target model comprising a number of ideal point scatterers randomly located within some radius of the targets center of mass. The proposed complex point targets may be applicable to statistical inference in multistatic or MIMO radar system. Six different target models are summarized here – three 2-dimensional (Gaussian, Uniform Square, and Uniform Circle) and three 3-dimensional (Gaussian, Uniform Cube, and Uniform Sphere). They are assumed to have different distributions on the location of the point scatterers within the target. We develop data models for the received signals from such targets in the MIMO radar system with distributed assets and partially correlated signals, and consider the resulting detection problem which reduces to the familiar Gauss-Gauss detection problem. We illustrate that the target parameter and transmit signal have an influence on the detector performance through target extent and the SNR respectively. A series of the receiver operator characteristic (ROC) curves are generated to notice the impact on the detector for varying SNR. Kullback–Leibler (KL) divergence is applied to obtain the approximate mean difference between density functions the scatterers assume inside the target models to show the change in the performance of the detector with target extent of the point scatterers.

Energy and structure of dilute hard- and soft-sphere gases

The energy and structure of dilute hard- and soft-sphere Bose gases are systematically studied in the framework of several many-body approaches, such as the variational correlated theory, the Bogoliubov model, and the uniform limit approximation, valid in the weak-interaction regime. When possible, the results are compared with the exact diffusion Monte Carlo ones. Jastrow-type correlation provides a good description of the systems, both hard- and soft-spheres, if the hypernetted chain energy functional is freely minimized and the resulting Euler equation is solved. The study of the soft-sphere potentials confirms the appearance of a dependence of the energy on the shape of the potential at gas paremeter values of x~0.001. For quantities other than the energy, such as the radial distribution functions and the momentum distributions, the dependence appears at any value of x. The occurrence of a maximum in the radial distribution function, in the momentum distribution, and in the excitation spectrum is a natural effect of the correlations when x increases. The asymptotic behaviors of the functions characterizing the structure of the systems are also investigated. The uniform limit approach is very easy to implement and provides a good description of the soft-sphere gas. Its reliability improves when the interaction weakens.

Voronoi, Delaunay, and Block-Structured Mesh Refinement for Solution of the Shallow-Water Equations on the Sphere

Alternative meshes of the sphere and adaptive mesh refinement could be immensely beneficial for weather and climate forecasts, but it is not clear how mesh refinement should be achieved. A finite-volume model that solves the shallow-water equations on any mesh of the surface of the sphere is presented. The accuracy and cost effectiveness of four quasi-uniform meshes of the sphere are compared: a cubed sphere, reduced latitude–longitude, hexagonal–icosahedral, and triangular–icosahedral. On some standard shallow-water tests, the hexagonal–icosahedral mesh performs best and the reduced latitude–longitude mesh performs well only when the flow is aligned with the mesh. The inclusion of a refined mesh over a disc-shaped region is achieved using either gradual Delaunay, gradual Voronoi, or abrupt 2:1 block-structured refinement. These refined regions can actually degrade global accuracy, presumably because of changes in wave dispersion where the mesh is highly nonuniform. However, using gradual refinement to resolve a mountain in an otherwise coarse mesh can improve accuracy for the same cost. The model prognostic variables are height and momentum collocated at cell centers, and (to remove grid-scale oscillations of the A grid) the mass flux between cells is advanced from the old momentum using the momentum equation. Quadratic and upwind biased cubic differencing methods are used as explicit corrections to a fast implicit solution that uses linear differencing.

Computational modes and grid imprinting on five quasi-uniform spherical C-grids

Currently, most operational forecasting models use latitude-longitude grids, whose convergence of meridians towards the poles limits parallel scaling. Quasi-uniform grids might avoid this limitation. Thuburn et al, JCP, 2009 and Ringler et al, JCP, 2010 have developed a method for arbitrarily-structured, orthogonal C-grids (TRiSK), which has many of the desirable properties of the C-grid on latitude-longitude grids but which works on a variety of quasi-uniform grids. Here, five quasi-uniform, orthogonal grids of the sphere are investigated using TRiSK to solve the shallow-water equations. We demonstrate some of the advantages and disadvantages of the hexagonal and triangular icosahedra, a Voronoi-ised cubed sphere, a Voronoi-ised skipped latitude-longitude grid and a grid of kites in comparison to a full latitude-longitude grid. We will show that the hexagonal-icosahedron gives the most accurate results (for least computational cost). All of the grids suffer from spurious computational modes; this is especially true of the kite grid, despite it having exactly twice as many velocity degrees of freedom as height degrees of freedom. However, the computational modes are easiest to control on the hexagonal icosahedron since they consist of vorticity oscillations on the dual grid which can be controlled using a diffusive advection scheme for potential vorticity.

Metallochlorophylls of magnesium, copper and zinc: evaluation of the influence of the first coordination sphere on their solvatochromism and aggregation properties

In this study the role of different metal centers (magnesium, zinc and copper) on the enhancement of the hydrophilic character of metallochlorophylls, was evaluated. The solvatochromism as well as the aggregation process for these compounds in water/ethanol mixtures at different volume ratios were evaluated using Fluorescence, and Resonant Light Scattering (RLS) measurements, aiming to characterize the behavior of these compounds. Independently on the studied metallochlorophyll, the presence of at least 60% of water results in a considerable increase in the fluorescence emission, probably a direct consequence of a lower aggregation of these compounds, which is confirmed by the results from RLS measurements. Additionally, the results suggest that magnesium and zinc chlorophyll should be promising phototherapeutic agents for Photodynamic Therapy.

The Genomic Ancestry of Individuals from Different Geographical Regions of Brazil Is More Uniform Than Expected

Based on pre-DNA racial/color methodology, clinical and pharmacological trials have traditionally considered the different geographical regions of Brazil as being very heterogeneous. We wished to ascertain how such diversity of regional color categories correlated with ancestry. Using a panel of 40 validated ancestry-informative insertion-deletion DNA polymorphisms we estimated individually the European, African and Amerindian ancestry components of 934 self-categorized White, Brown or Black Brazilians from the four most populous regions of the Country. We unraveled great ancestral diversity between and within the different regions. Especially, color categories in the northern part of Brazil diverged significantly in their ancestry proportions from their counterparts in the southern part of the Country, indicating that diverse regional semantics were being used in the self-classification as White, Brown or Black. To circumvent these regional subjective differences in color perception, we estimated the general ancestry proportions of each of the four regions in a form independent of color considerations. For that, we multiplied the proportions of a given ancestry in a given color category by the official census information about the proportion of that color category in the specific region, to arrive at a ""total ancestry"" estimate. Once such a calculation was performed, there emerged a much higher level of uniformity than previously expected. In all regions studied, the European ancestry was predominant, with proportions ranging from 60.6% in the Northeast to 77.7% in the South. We propose that the immigration of six million Europeans to Brazil in the 19(th) and 20(th) centuries - a phenomenon described and intended as the ""whitening of Brazil"" -is in large part responsible for dissipating previous ancestry dissimilarities that reflected region-specific population histories. These findings, of both clinical and sociological importance for Brazil, should also be relevant to other countries with ancestrally admixed populations.

Soliton dynamics at an interface between a uniform medium and a nonlinear optical lattice

We study trapping and propagation of a matter-wave soliton through the interface between uniform medium and a nonlinear optical lattice. Different regimes for transmission of a broad and a narrow solitons are investigated. Reflections and transmissions of solitons are predicted as a function of the lattice phase. The existence of a threshold in the amplitude of the nonlinear optical lattice, separating the transmission and reflection regimes, is verified. The localized nonlinear surface state, corresponding to the soliton trapped by the interface, is found. Variational approach predictions are confirmed by numerical simulations for the original Gross-Pitaevskii equation with nonlinear periodic potentials.

Free-fall in a uniform gravitational field in noncommutative quantum mechanics

We study the free-fall of a quantum particle in the context of noncommutative quantum mechanics (NCQM). Assuming noncommutativity of the canonical type between the coordinates of a two-dimensional configuration space, we consider a neutral particle trapped in a gravitational well and exactly solve the energy eigenvalue problem. By resorting to experimental data from the GRANIT experiment, in which the first energy levels of freely falling quantum ultracold neutrons were determined, we impose an upper-bound on the noncommutativity parameter. We also investigate the time of flight of a quantum particle moving in a uniform gravitational field in NCQM. This is related to the weak equivalence principle. As we consider stationary, energy eigenstates, i.e., delocalized states, the time of flight must be measured by a quantum clock, suitably coupled to the particle. By considering the clock as a small perturbation, we solve the (stationary) scattering problem associated and show that the time of flight is equal to the classical result, when the measurement is made far from the turning point. This result is interpreted as an extension of the equivalence principle to the realm of NCQM. (C) 2010 American Institute of Physics. [doi:10.1063/1.3466812]

THE LOWER CENTRAL AND DERIVED SERIES OF THE BRAID GROUPS OF THE SPHERE

In this paper, we determine the lower central and derived series for the braid groups of the sphere. We are motivated in part by the study of Fadell-Neuwirth short exact sequences, but the problem is important in its own right. The braid groups of the 2-sphere S(2) were studied by Fadell, Van Buskirk and Gillette during the 1960s, and are of particular interest due to the fact that they have torsion elements (which were characterised by Murasugi). We first prove that for all n epsilon N, the lower central series of the n-string braid group B(n)(S(2)) is constant from the commutator subgroup onwards. We obtain a presentation of Gamma(2)(Bn(S(2))), from which we observe that Gamma(2)(B(4)(S(2))) is a semi-direct product of the quaternion group Q(8) of order 8 by a free group F(2) of rank 2. As for the derived series of Bn(S(2)), we show that for all n >= 5, it is constant from the derived subgroup onwards. The group Bn(S(2)) being finite and soluble for n <= 3, the critical case is n = 4 for which the derived subgroup is the above semi-direct product Q(8) (sic) F(2). By proving a general result concerning the structure of the derived subgroup of a semi-direct product, we are able to determine completely the derived series of B(4)(S(2)) which from (B(4)(S(2)))(4) onwards coincides with that of the free group of rank 2, as well as its successive derived series quotients.

Dissolution of a solid sphere in an unbounded, stagnant liquid

An exact analytical solution is obtained for the transient dissolution of solid spheres in a diffusion-controlled environment. This result provides a useful reference point for drug testing in humans. The dimensionless solution is expressed in terms of a single parameter, which accounts for solubility, bulk flow, and stagnant fluid composition. A simple, explicit and exact expression was found to predict time-to-complete dissolution (TCD). An approximate solution was also found which tracks the exact case for low solubility conditions.

Entropy generation for forced convection in a porous saturated circular tube with uniform wall temperature

A numerical study is reported to investigate both the First and the Second Law of Thermodynamics for thermally developing forced convection in a circular tube filled by a saturated porous medium, with uniform wall temperature, and with the effects of viscous dissipation included. A theoretical analysis is also presented to study the problem for the asymptotic region applying the perturbation solution of the Brinkman momentum equation reported by Hooman and Kani [1]. Expressions are reported for the temperature profile, the Nusselt number, the Bejan number, and the dimensionless entropy generation rate in the asymptotic region. Numerical results are found to be in good agreement with theoretical counterparts.

Compact tiled display with uniform illumination

The demand for more pixels is beginning to be met as manufacturers increase the native resolution of projector chips. Tiling several projectors still offers a solution to augment the pixel capacity of a display. However, problems of color and illumination uniformity across projectors need to be addressed as well as the computer software required to drive such devices. We present the results obtained on a desktop-size tiled projector array of three D-ILA projectors sharing a common illumination source. A short throw lens (0.8:1) on each projector yields a 21-in. diagonal for each image tile; the composite image on a 3×1 array is 3840×1024 pixels with a resolution of about 80 dpi. The system preserves desktop resolution, is compact, and can fit in a normal room or laboratory. The projectors are mounted on precision six-axis positioners, which allow pixel level alignment. A fiber optic beamsplitting system and a single set of red, green, and blue dichroic filters are the key to color and illumination uniformity. The D-ILA chips inside each projector can be adjusted separately to set or change characteristics such as contrast, brightness, or gamma curves. The projectors were then matched carefully: photometric variations were corrected, leading to a seamless image. Photometric measurements were performed to characterize the display and are reported here. This system is driven by a small PC cluster fitted with graphics cards and running Linux. It can be scaled to accommodate an array of 2×3 or 3×3 projectors, thus increasing the number of pixels of the final image. Finally, we present current uses of the display in fields such as astrophysics and archaeology (remote sensing).

On the applicability of the Aris' equivalent sphere in multicomponent reacting systems

The validity of the concept of equivalent sphere introduced by Aris in 1957 to multicomponent reacting systems is investigated in this paper. A network of C6 hydrocarbon reforming reaction and a fixed bed reactor are taken as the model reaction network and the reactor configuration, respectively.