Intercomparison of general circulation models for hot extrasolar planets

We compare five general circulation models (GCMs) which have been recently used to study hot extrasolar planet atmospheres (BOB, CAM, IGCM, MITgcm, and PEQMOD), under three test cases useful for assessing model convergence and accuracy. Such a broad, detailed intercomparison has not been performed thus far for extrasolar planets study. The models considered all solve the traditional primitive equations, but employ di↵erent numerical algorithms or grids (e.g., pseudospectral and finite volume, with the latter separately in longitude-latitude and ‘cubed-sphere’ grids). The test cases are chosen to cleanly address specific aspects of the behaviors typically reported in hot extrasolar planet simulations: 1) steady-state, 2) nonlinearly evolving baroclinic wave, and 3) response to fast timescale thermal relaxation. When initialized with a steady jet, all models maintain the steadiness, as they should—except MITgcm in cubed-sphere grid. A very good agreement is obtained for a baroclinic wave evolving from an initial instability in pseudospectral models (only). However, exact numerical convergence is still not achieved across the pseudospectral models: amplitudes and phases are observably di↵erent. When subject to a typical ‘hot-Jupiter’-like forcing, all five models show quantitatively di↵erent behavior—although qualitatively similar, time-variable, quadrupole-dominated flows are produced. Hence, as have been advocated in several past studies, specific quantitative predictions (such as the location of large vortices and hot regions) by GCMs should be viewed with caution. Overall, in the tests considered here, pseudospectral models in pressure coordinate (PEBOB and PEQMOD) perform the best and MITgcm in cubed-sphere grid performs the worst.

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.

Non-orthogonal version of the arbitrary polygonal C-grid and a new diamond grid

Quasi-uniform grids of the sphere have become popular recently since they avoid parallel scaling bottle- necks associated with the poles of latitude–longitude grids. However quasi-uniform grids of the sphere are often non- orthogonal. A version of the C-grid for arbitrary non- orthogonal grids is presented which gives some of the mimetic properties of the orthogonal C-grid. Exact energy conservation is sacrificed for improved accuracy and the re- sulting scheme numerically conserves energy and potential enstrophy well. The non-orthogonal nature means that the scheme can be used on a cubed sphere. The advantage of the cubed sphere is that it does not admit the computa- tional modes of the hexagonal or triangular C-grids. On var- ious shallow-water test cases, the non-orthogonal scheme on a cubed sphere has accuracy less than or equal to the orthog- onal scheme on an orthogonal hexagonal icosahedron. A new diamond grid is presented consisting of quasi- uniform quadrilaterals which is more nearly orthogonal than the equal-angle cubed sphere but with otherwise similar properties. It performs better than the cubed sphere in ev- ery way and should be used instead in codes which allow a flexible grid structure.

A theory of electron collection by a grid sphere

Use of a spherical grid as electron collector at the anodic end of a tether, as recently proposed, is considered. The standard analysis of space-charge limited current to a solid sphere (with neither magnetic nor plasma-motion effects), which has been shown to best fit TSS1R in-orbit results at very high bias, is used to determine effects from grid transparency on current collected; the analysis is first reformulated in the formalism recently introduced in the two-dimensional analysis of bare-tethers. A discussion of the electric potential created by a spherical grid in vacuum is then carried out; it is shown that each grid-wire collects current well below its maximum OML current, the effective grid transparency being close to its optical value. Formulae for the current to a spherical grid, showing the effects of grid transparency, is determined. A fully consistent analysis of electric potential and electron density, outside and inside the grid, is completed.

Controlling the computational modes of the arbitrarily structured C-grid

The arbitrarily structured C-grid, TRiSK (Thuburn, Ringler, Skamarock and Klemp, 2009, 2010) is being used in the ``Model for Prediction Across Scales'' (MPAS) and is being considered by the UK Met Office for their next dynamical core. However the hexagonal C-grid supports a branch of spurious Rossby modes which lead to erroneous grid-scale oscillations of potential vorticity (PV). It is shown how these modes can be harmlessly controlled by using upwind-biased interpolation schemes for PV. A number of existing advection schemes for PV are tested, including that used in MPAS, and none are found to give adequate results for all grids and all cases. Therefore a new scheme is proposed; continuous, linear-upwind stabilised transport (CLUST), a blend between centred and linear-upwind with the blend dependent on the flow direction with respect to the cell edge. A diagnostic of grid-scale oscillations is proposed which gives further discrimination between schemes than using potential enstrophy alone and indeed some schemes are found to destroy potential enstrophy while grid-scale oscillations grow. CLUST performs well on hexagonal-icosahedral grids and unrotated skipped latitude-longitude grids of the sphere for various shallow water test cases. Despite the computational modes, the hexagonal icosahedral grid performs well since these modes are easy and harmless to filter. As a result TRiSK appears to perform better than a spectral shallow water model.

Distribution of microservices for hardware interoperability in the Smart Grid

Due to the significant increase of population and their natural desire of improving their standard of living, usage of energy extracted from world commodities, especially shaped as electricity, has increased in an intense manner during the last decades. This fact brings up a challenge with a complicated solution, which is how to guarantee that there will be enough energy so as to satisfy the energy demand of the world population. Among all the possible solutions that can be adopted to mitigate this problem one of them is almost of mandatory adoption, which consists of rationalizing energy utilization, in a way that its wasteful usage is minimized and it can be leveraged during a longer period of time. One of the ways to achieve it is by means of the improvement of the power distribution grid, so that it will be able to react in a more efficient manner against common issues, such as energy demand peaks or inaccurate electricity consumption forecasts. However, in order to be able to implement this improvement it is necessary to use technologies from the ICT (Information and Communication Technologies) sphere that often present challenges in some key areas: advanced metering infrastructure integration, interoperability and interconnectivity of the devices, interfaces to offer the applications, security measures design, etc. All these challenges may imply slowing down the adoption of the smart grid as a system to prolong the lifespan and utilization of the available energy. A proposal for an intermediation architecture that will make possible solving these challenges is put forward in this Master Thesis. Besides, one implementation and the tests that have been carried out to know the performance of the presented concepts have been included as well, in a way that it can be proved that the challenges set out by the smart grid can be resolved. RESUMEN. Debido al incremento significativo de la población y su deseo natural de mejorar su nivel de vida, la utilización de la energía extraída de las materias primas mundiales, especialmente en forma de electricidad, ha aumentado de manera intensa durante las últimas décadas. Este hecho plantea un reto de solución complicada, el cual es cómo garantizar que se dispondrá de la energía suficiente como para satisfacer la demanda energética de la población mundial. De entre todas las soluciones posibles que se pueden adoptar para mitigar este problema una de ellas es de casi obligatoria adopción, la cual consiste en racionalizar la utilización de la energía, de tal forma que se minimice su malgasto y pueda aprovecharse durante más tiempo. Una de las maneras de conseguirlo es mediante la mejora de la red de distribución de electricidad para que ésta pueda reaccionar de manera más eficaz contra problemas comunes, tales como los picos de demanda de energía o previsiones imprecisas acerca del consumo de electricidad. Sin embargo, para poder implementar esta mejora es necesario utilizar tecnologías del ámbito de las TIC (Tecnologías de la Información y la Comunicación) que a menudo presentan problemas en algunas áreas clave: integración de infraestructura de medición avanzada, interoperabilidad e interconectividad de los dispositivos, interfaces que ofrecer a las aplicaciones, diseño de medidas de seguridad, etc. Todos estos retos pueden implicar una ralentización en la adopción de la red eléctrica inteligente como un sistema para alargar la vida y la utilización de la energía disponible. En este Trabajo Fin de Máster se sugiere una propuesta para una arquitectura de intermediación que posibilite la resolución de estos retos. Además, una implementación y las pruebas que se han llevado a cabo para conocer el rendimiento de los conceptos presentados también han sido incluidas, de tal forma que se demuestre que los retos que plantea la red eléctrica inteligente pueden ser solventados.

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 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.

A Study on the Relationship of Embedded Sensitivity With Measuring Grid and Mode Shapes

Embedded sensitivity analysis has proven to be a useful tool in finding optimum positions of structure reinforcements. However, it was not clear how sensitivities obtained from the embedded sensitivity method were related to the normal mode, or operational mode, associated to the frequency of interest. In this work, this relationship is studied based on a finite element of a slender sheet metal piece, with preponderant bending modes. It is shown that higher sensitivities always occur at nodes or antinodes of the vibrating system. [DOI: 10.1115/1.4002127]

Applying semantics to grid middleware

Scheduling parallel and distributed applications efficiently onto grid environments is a difficult task and a great variety of scheduling heuristics has been developed aiming to address this issue. A successful grid resource allocation depends, among other things, on the quality of the available information about software artifacts and grid resources. In this article, we propose a semantic approach to integrate selection of equivalent resources and selection of equivalent software artifacts to improve the scheduling of resources suitable for a given set of application execution requirements. We also describe a prototype implementation of our approach based on the Integrade grid middleware and experimental results that illustrate its benefits. Copyright (C) 2009 John Wiley & Sons, Ltd.

Coarse-grid higher order finite-difference time-domain algorithm with low dispersion errors

Higher order (2,4) FDTD schemes used for numerical solutions of Maxwell`s equations are focused on diminishing the truncation errors caused by the Taylor series expansion of the spatial derivatives. These schemes use a larger computational stencil, which generally makes use of the two constant coefficients, C-1 and C-2, for the four-point central-difference operators. In this paper we propose a novel way to diminish these truncation errors, in order to obtain more accurate numerical solutions of Maxwell`s equations. For such purpose, we present a method to individually optimize the pair of coefficients, C-1 and C-2, based on any desired grid size resolution and size of time step. Particularly, we are interested in using coarser grid discretizations to be able to simulate electrically large domains. The results of our optimization algorithm show a significant reduction in dispersion error and numerical anisotropy for all modeled grid size resolutions. Numerical simulations of free-space propagation verifies the very promising theoretical results. The model is also shown to perform well in more complex, realistic scenarios.

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.

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.