A family of quantum projective spaces and related q-hypergeometric orthogonal polynomials

We define a one-parameter family of two-sided coideals in U_q(gl(n)) and study the corresponding algebras of infinitesimally right invariant functions on the quantum unitary group U_q(n). The Plancherel decomposition of these algebras with respect to the natural transitive U_q(n)-action is shown to be the same as in the case of a complex projective space. By computing the radial part of a suitable Casimir operator, we identify the zonal spherical functions (i.e. infinitesimally bi-invariant matrix coefficients of finite-dimensional irreducible representations) as Askey-Wilson polynomials containing two continuous and one discrete parameter. In certain limit cases, the zonal spherical functions are expressed as big and little q-Jacobi polynomials depending on one discrete parameter.Comment: 31 pages, AMS-TeX 2.1, no figure

Direct numerical simulation of the drag force in bubble swarms

This paper studies the swarm effect on the drag force in bubbly flows. From literature it is well-known that for relatively small bubbles, the drag force increases with the bubble hold-up due to additional hindrance experienced by the bubbles caused by the modified flow field. Very large (spherical cap) bubbles on the other hand may rise cooperatively. The unique capabilities of a 3D Front Tracking model were used to investigate the influence of important parameters like the gas fraction, Reynolds number and the bubble size independently. It was found that the relative drag force increases for bubbles in the range of 2 to 5 mm when the gas fraction is increased up to 13%, while the bubbles become more spherical. Also the influence of the Reynolds number and the bubble aspect ratio on the increased drag force has been determined. It can be concluded that there is only a very weak effect over several decades of the Reynolds number, while there is a strong effect of the bubble aspect ratio.\ud This also helps explaining why the increase in drag is smaller for larger bubbles: when the gas fraction is increased deformable bubbles become more spherical, thus reducing the drag force

Validation of the granular temperature prediction of the kinetic theory of granular flow by particle image velocimetry and discrete particle model

In order to give a detailed description of the hydrodynamics in large industrial scale fluidized beds, continuum models are required. Continuum models often use the kinetic theory of granular flow (KTGF) to provide closure equations for the internal momentum transport in the particulate phase. In this work the outcome of the continuum model is compared with both an experimental technique and detailed simulations, i.e. particle image velocimetry (PIV) and the discrete particle model (DPM).\ud PIV is used for the measurement of an instantaneous velocity field of the flow in the front plane of a fluid bed. The classical PIV analysis is extended to enable the measurement of the local velocity fluctuations in the interrogation area, i.e. the granular temperature. In the DPM, each particle is tracked individually. In this model detailed collision models can be incorporated, rendering the DPM a valuable research tool to validate the underlying assumptions in the KTGF concerning the particle-particle interactions and the particle velocity distribution functions.\ud The aforementioned experimental and numerical techniques are used to measure the granular temperature distribution around a single bubble rising in a gas-fluidized bed. It was found that the results of PIV and the DPM are very similar. Although the initial bubble shape and size are well predicted by the continuum model, it fails once the bubble has detached from the bottom plate. Further research in the area of KTGF closures is needed to improve the predictions of the TFM

Sponsorship behaviour of the BRICS in the United Nations General Assembly

The formation of informal groupings of states is a manifestation of the global shift in economic power. One such a grouping is the BRICS, consisting of Brazil, Russia, India, China and South Africa, which stands out for its importance due to its economic weight, its coverage across continents and the numerous internal differences. The BRICS have collectively flexed their muscle and expressed their intentions to extend their cooperation at the United Nations (UN). Proposals in the United Nations General Assembly (UN GA) take the form of resolutions, which can be written and co-written by the UN member states. This so-called sponsoring of resolutions is a way to push agenda items forward. Using a large-N network analysis, we examine the patterns of co-sponsorship of the BRICS of resolutions adopted in the UN GA plenary sessions. We find that the BRICS cooperate on fields such as economic issues, however, they do not form a coherent bloc when it comes to resolution sponsorship. These results raise the question in what way the BRICS actually cooperate at the UN level

Conversion of a cyclodextrin glucanotransferase into an alpha-amylase:Assessment of directed evolution strategies

Glycoside hydrolase family 13 (GH13) members have evolved to possess various distinct reaction specificities despite the overall structural similarity. In this study we investigated the evolutionary input required to effeciently interchange these specificities and also compared the effectiveness of laboratory evolution techniques applied, i.e., error-prone PCR and saturation mutagenesis. Conversion of our model enzyme, cyclodextrin glucanotransferase (CGTase), into an cc-amylase like hydrolytic enzyme by saturation mutagenesis close to the catalytic core yielded a triple mutant (A231V/F260W/F184Q) with the highest hydrolytic rate ever recorded for a CGTase, similar to that of a highly active alpha-anaylase, while cyclodextrin production was virtually abolished. Screening of a much larger, error-prone PCR generated library yielded far less effective mutants. Our results demonstrate that it requires only three mutations to change CGTase reaction specificity into that of another GH13 enzyme. This suggests that GH13 members may have diversified by introduction of a limited number of mutations to the common ancestor, and that interconversion of reaction specificites may prove easier than previously thought

The coisotropic subgroup structure of SL_q(2,R)

We study the coisotropic subgroup structure of standard SL_q(2,R) and the corresponding embeddable quantum homogeneous spaces. While the subgroups S^1 and R_+ survive undeformed in the quantization as coalgebras, we show that R is deformed to a family of quantum coisotropic subgroups whose coalgebra can not be extended to an Hopf algebra. We explicitly describe the quantum homogeneous spaces and their double cosets.Comment: LaTex2e, 10pg, no figure

Numerical investigation of the lift force acting on single air bubbles in liquids with different viscosities using a 3D Front Tracking method

No abstract

Modelling disease activity in juvenile dermatomyositis: A Bayesian approach

Juvenile dermatomyositis is the most common form of the juvenile idiopathic inflammatory myopathies characterised by muscle and skin inflammation, leading to symmetric proximal muscle weakness and cutaneous symptoms. It has a fluctuating course and varying prognosis. In a Bayesian framework, we develop a joint model for four longitudinal outcomes, which accounts for within individual variability as well as inter-individual variability. Correlations among the outcome variables are introduced through a subject-specific random effect. Moreover, we exploit an approach similar to a hurdle model to account for excess of a specific outcome in the response. Clinical markers and symptoms are used as covariates in a regression set-up. Data from an ongoing observational cohort study are available, providing information on 340 subjects, who contributed 2725 clinical visits. The model shows good performance and yields efficient estimations of model parameters, as well as accurate predictions of the disease activity parameters, corresponding well to observed clinical patterns over time. The posterior distribution of the by-subject random intercepts shows a substantial correlation between two of the outcome variables. A subset of clinical markers and symptoms are identified as associated with disease activity. These findings have the potential to influence clinical practice as they can be used to stratify patients according to their prognosis and guide treatment decisions, as well as contribute to on-going research about the most relevant outcome markers for patients affected by juvenile dermatomyositis

DNS of gas bubbles behaviour using an improved 3D front tracking model—Model development

In recent years CFD has proven to be a valuable and powerful tool to advance our understanding of complex multiphase flow systems arising in industrial applications. However, the predictive capabilities of this tool are determined by many factors of physical and numerical origin but in particular by the quality of the closures adopted for the description of the interface forces. The objective of this study is to improve the front tracking method in order to compute such forces with sufficient accuracy. This paper describes the further development of a 3D front tracking model to achieve improved volume conservation and circumvent problems related to the representation of surface tension. First, we have included a method to handle the pressure jump at the interface. This causes the spurious currents, observed in conventional front tracking, to decrease with two orders of magnitude. Also the advection scheme has been adapted, using higher order velocity interpolation (using cubic splines), and Runge–Kutta time-stepping, in order to prevent considerable volume changes of the dispersed phase. Test simulations involving a stationary bubble, a standard advection test and an oscillating droplet, demonstrate the effect of these improvements. The implementation of these procedures enlarged the computational window and in particular enabled the simulation of very small bubbles, where large surface forces dominate, without any significant spurious currents or volume loss