A new family of multivariate heavy-tailed distributions with variable marginal amounts of tailweight: Application to robust clustering

We propose a family of multivariate heavy-tailed distributions that allow variable marginal amounts of tailweight. The originality comes from introducing multidimensional instead of univariate scale variables for the mixture of scaled Gaussian family of distributions. In contrast to most existing approaches, the derived distributions can account for a variety of shapes and have a simple tractable form with a closed-form probability density function whatever the dimension. We examine a number of properties of these distributions and illustrate them in the particular case of Pearson type VII and t tails. For these latter cases, we provide maximum likelihood estimation of the parameters and illustrate their modelling flexibility on simulated and real data clustering examples.

Bayesian mixture model estimation of aerosol particle size distributions

In this paper, we examine approaches to estimate a Bayesian mixture model at both single and multiple time points for a sample of actual and simulated aerosol particle size distribution (PSD) data. For estimation of a mixture model at a single time point, we use Reversible Jump Markov Chain Monte Carlo (RJMCMC) to estimate mixture model parameters including the number of components which is assumed to be unknown. We compare the results of this approach to a commonly used estimation method in the aerosol physics literature. As PSD data is often measured over time, often at small time intervals, we also examine the use of an informative prior for estimation of the mixture parameters which takes into account the correlated nature of the parameters. The Bayesian mixture model offers a promising approach, providing advantages both in estimation and inference.

Turbulence measurements in an equilibrium axisymmetric wall jet

This paper reports measurements of turbulent quantities in an axisymmetric wall jet subjected to an adverse pressure gradient in a conical diffuser, in such a way that a suitably defined pressure-gradient parameter is everywhere small. Self-similarity is observed in the mean velocity profile, as well as the profiles of many turbulent quantities at sufficiently large distances from the injection slot. Autocorrelation measurements indicate that, in the region of turbulent production, the time scale of ν fluctuations is very much smaller than the time scale of u fluctuations. Based on the data on these time scales, a possible model is proposed for the Reynolds stress. One-dimensional energy spectra are obtained for the u, v and w components at several points in the wall jet. It is found that self-similarity is exhibited by the one-dimensional wavenumber spectrum of $\overline{q^2}(=\overline{u^2}+\overline{v^2}+\overline{w^2})$, if the half-width of the wall jet and the local mean velocity are used for forming the non-dimensional wavenumber. Both the autocorrelation curves and the spectra indicate the existence of periodicity in the flow. The rate of dissipation of turbulent energy is estimated from the $\overline{q^2}$ spectra, using a slightly modified version of a previously suggested method.

Factors influencing kinetic and equilibrium behaviour of sodium ion exchange with strong acid cation resin

This study reports an investigation of the ion exchange treatment of sodium chloride solutions in relation to use of resin technology for applications such as desalination of brackish water. In particular, a strong acid cation (SAC) resin (DOW Marathon C) was studied to determine its capacity for sodium uptake and to evaluate the fundamentals of the ion exchange process involved. Key questions to answer included: impact of resin identity; best models to simulate the kinetics and equilibrium exchange behaviour of sodium ions; difference between using linear least squares (LLS) and non-linear least squares (NLLS) methods for data interpretation; and, effect of changing the type of anion in solution which accompanied the sodium species. Kinetic studies suggested that the exchange process was best described by a pseudo first order rate expression based upon non-linear least squares analysis of the test data. Application of the Langmuir Vageler isotherm model was recommended as it allowed confirmation that experimental conditions were sufficient for maximum loading of sodium ions to occur. The Freundlich expression best fitted the equilibrium data when analysing the information by a NLLS approach. In contrast, LLS methods suggested that the Langmuir model was optimal for describing the equilibrium process. The Competitive Langmuir model which considered the stoichiometric nature of ion exchange process, estimated the maximum loading of sodium ions to be 64.7 g Na/kg resin. This latter value was comparable to sodium ion capacities for SAC resin published previously. Inherent discrepancies involved when using linearized versions of kinetic and isotherm equations were illustrated, and despite their widespread use, the value of this latter approach was questionable. The equilibrium behaviour of sodium ions form sodium fluoride solution revealed that the sodium ions were now more preferred by the resin compared to the situation with sodium chloride. The solution chemistry of hydrofluoric acid was suggested as promoting the affinity of the sodium ions to the resin.

Electron energy distributions and transport coefficients in N2 in E times B fields

Using the concept of energy-dependent effective field intensity, electron transport coefficients in nitrogen have been determined in E times B fields (E = electric field intensity, B = magnetic flux density) by the numerical solution of the Boltzmann transport equation for the energy distribution of electrons. It has been observed that as the value of B/p (p = gas pressure) is increased from zero, the perpendicular drift velocity increased linearly at first, reaches a maximum value, and then decreases with increasing B/p. In general, the electron mean energy is found to be a function of Eavet/p( Eavet = averaged effective electric field intensity) only, but the other transport coefficients, such as transverse drift velocity, perpendicular drift velocity, and the Townsend ionization coefficient, are functions of both E/p and B/p.

Determination of skin friction in strong pressure-gradient equilibrium and near-equilibrium turbulent boundary layers

The conventional Clauser-chart method for determination of local skin friction in zero or weak pressure-gradient turbulent boundary layer flows fails entirely in strong pressure-gradient situations. This failure occurs due to the large departure of the mean velocity profile from the universal logarithmic law upon which the conventional Clauser-chart method is based. It is possible to extend this method,even for strong pressure-gradient situations involving equilibrium or near-equilibrium turbulent boundary layers by making use of the so-called non-universal logarithmic laws. These non-universal log laws depend on the local strength of the pressure gradient and may be regarded as perturbations of the universal log law.The present paper shows that the modified Clauser-chart method, so developed, yields quit satisfactory results in terms of estimation of local skin friction in strongly accelerated or retarded equilibrium and near-equilibrium turbulent boundary layers that are not very close to relaminarization or separation.

CFD analysis of high frequency miniature pulse tube refrigerators for space applications with thermal non-equilibrium model

High frequency, miniature, pulse tube cryocoolers are extensively used in space applications because of their simplicity. Parametric studies of inertance type pulse tube cooler are performed with different length-to-diameter ratios of the pulse tube with the help of the FLUENT (R) package. The local thermal non-equilibrium of the gas and the matrix is taken into account for the modeling of porous zones, in addition to the wall thickness of the components. Dynamic characteristics and the actual mechanism of energy transfer in pulse are examined with the help of the pulse tube wall time constant. The heat interaction between pulse tube wall and the oscillating gas, leading to surface heat pumping, is quantified. The axial heat conduction is found to reduce the performance of the pulse tube refrigerator. The thermal non-equilibrium predicts a higher cold heat exchanger temperature compared to thermal equilibrium. The pressure drop through the porous medium has a strong non-linear effect due to the dominating influence of Forchheimer term over that of the linear Darcy term at high operating frequencies. The phase angle relationships among the pressure, temperature and the mass flow rate in the porous zones are also important in determining the performance of pulse tuberefrigerator.

Phytoplankton ecology of subarctic lakes in Finnish Lapland

Climate is warming and it is especially seen in arctic areas, where the warming trend is expected to be greatest. Arctic freshwater ecosystems, which are a very characteristic feature of the arctic landscape, are especially sensitive to climate change. They could be used as early warning systems, but more information about the ecosystem functioning and responses are needed for proper interpretation of the observations. Phytoplankton species and assemblages could be especially suitable for climate-related studies, since they have short generation times and react rapidly to changes in the environment. In addition, phytoplankton provides a good tool for lake classifications, since different species have different requirements and tolerance ranges for various environmental factors. The use of biological indicators is especially useful in arctic areas, were many of the chemical factors commonly fall under the detection limit and therefore do not provide much information about the environment. This work brings new information about species distribution and dynamics of arctic freshwater phytoplankton in relation to environmental factors. The phytoplankton of lakes in Finnish Lapland and other European high-altitude or high-latitude areas were compared. Most lakes were oligotrophic and dominated by flagellated species belonging to chrysophytes, cryptophytes and dinoflagellates. In Finnish Lapland cryptophytes were of less importance, whereas desmids had high species richness in many of the lakes. In Pan-European scale, geographical and catchment-related factors were explaining most of the differences in species distributions between different districts, whereas lake water chemistry (especially conductivity, SiO2 and pH) was most important regionally. Seasonal and interannual variation of phytoplankton was studied in subarctic Lake Saanajärvi. Characteristic phytoplankton species in this oligotrophic, dimictic lake belonged mainly to chrysophytes and diatoms. The maximum phytoplankton biomass in Lake Saanajärvi occurs during autumn, while spring biomass is very low. During years with heavy snow cover the lake suffers from pH drop caused by melt waters, but the effects of this acid pulse are restricted to surface layers and last for a relatively short period. In addition to some chemical parameters (mainly Ca and nutrients), length of the mixing cycle and physical factors such as lake water temperature and thermal stability of water column had major impact on phytoplankton dynamics. During a year with long and strong thermal stability, the phytoplankton community developed towards an equilibrium state, with heavy dominance of only a few taxa for a longer period of time. During a year with higher windiness and less thermal stability, the species composition was more diverse and species with different functional strategies were able to occur simultaneously. The results of this work indicate that although arctic lakes in general share many common features concerning their catchment and water chemistry, large differences in biological features can be found even in a relatively small area. Most likely the lakes with very different algal flora do not respond in a similar way to differences in the environmental factors, and more information about specific arctic lake types is needed. The results also show considerable year to year differences in phytoplankton species distribution and dynamics, and these changes are most likely linked to climatic factors.

Wigner distributions for finite-state systems without redundant phase-point operators

We set up Wigner distributions for N-state quantum systems following a Dirac-inspired approach. In contrast to much of the work in this study, requiring a 2N x 2N phase space, particularly when N is even, our approach is uniformly based on an N x N phase-space grid and thereby avoids the necessity of having to invoke a `quadrupled' phase space and hence the attendant redundance. Both N odd and even cases are analysed in detail and it is found that there are striking differences between the two. While the N odd case permits full implementation of the marginal property, the even case does so only in a restricted sense. This has the consequence that in the even case one is led to several equally good definitions of the Wigner distributions as opposed to the odd case where the choice turns out to be unique.

Convective heat-transfer rate distributions over a missile shaped body flying at hypersonic speeds

Experiments are carried out with air as the test gas to obtain the surface convective heating rate on a missile shaped body flying at hypersonic speeds. The effect of fins on the surface heating rates of missile frustum is also investigated. The tests are performed in a hypersonic shock tunnel at stagnation enthalpy of 2 MJ/kg and zero degree angle of attack. The experiments are conducted at flow Mach number of 5.75 and 8 with an effective test time of 1 ms. The measured stagnation-point heat-transfer data compares well with the theoretical value estimated using Fay and Riddell expression. The measured heat-transfer rate with fin configuration is slightly higher than that of model without fin. The normalized values of experimentally measured heat transfer rate and Stanton number compare well with the numerically estimated results. (C) 2009 Elsevier Inc. All rights reserved.

Nash equilibrium based semantic cache in mobile sensor grid database systems

Mobile applications are being increasingly deployed on a massive scale in various mobile sensor grid database systems. With limited resources from the mobile devices, how to process the huge number of queries from mobile users with distributed sensor grid databases becomes a critical problem for such mobile systems. While the fundamental semantic cache technique has been investigated for query optimization in sensor grid database systems, the problem is still difficult due to the fact that more realistic multi-dimensional constraints have not been considered in existing methods. To solve the problem, a new semantic cache scheme is presented in this paper for location-dependent data queries in distributed sensor grid database systems. It considers multi-dimensional constraints or factors in a unified cost model architecture, determines the parameters of the cost model in the scheme by using the concept of Nash equilibrium from game theory, and makes semantic cache decisions from the established cost model. The scenarios of three factors of semantic, time and locations are investigated as special cases, which improve existing methods. Experiments are conducted to demonstrate the semantic cache scheme presented in this paper for distributed sensor grid database systems.

Nickel(II) meso-hydroxyporphyrin complexes revisited: Palladium-catalysed synthesis, electronic structures of derived oxy radicals, and oxidative coupling to a dioxoporphodimethene dyad

We report the synthesis and characterisation of new examples of meso-hydroxynickel(II) porphyrins with 5,15-diphenyl and 10-phenyl-5,15-diphenyl/diaryl substitu- tion. The OH group was introduced by using carbonate or hydroxide as nucleophile by using palladium/phosphine cat- alysis. The NiPor OHs exist in solution in equilibrium with the corresponding oxy radicals NiPor OC. The 15-phenyl group stabilises the radicals, so that the 1H NMR spectra of {NiPor OH} are extremely broad due to chemical exchange with the paramagnetic species. The radical concentration for the diphenylporphyrin analogue is only 1%, and its NMR line-broadening was able to be studied by variable-tempera- ture NMR spectroscopy. The EPR signals of NiPor OC are con- sistent with somewhat delocalised porphyrinyloxy radicals, and the spin distributions calculated by using density func- tional theory match the EPR and NMR spectroscopic obser- vations. Nickel(II) meso-hydroxy-10,20-diphenylporphyrin was oxidatively coupled to a dioxo-terminated porphodimethene dyad, the strongly red-shifted electronic spectrum of which was successfully modelled by using time-dependent DFT calculations.