Structure and Thermodynamics of NaF-AlF(3) Melts with Addition of CaF(2) and MgF(2)

The NaF-AlF(3) system with additions of CaF(2) and MgF(2) has been studied with Raman and vapor pressure measurements for 3 >/= CR (NaF/AlF(3) molar ratio) >/= 1 and up to 50 mol % additive. The results show that the binary melt can be described using the two equilibria AlF(6)(3)(-) = AlF(6)(2)(-) + F(-) and AlF(5)(2)(-) = AlF(4)(-) + F(-) with equilibrium constants 0.25 and 0.05, respectively, at 1293 K. Both reactions have positive reaction enthalpies. The first equilibrium is strongly shifted to the right resulting in a melt mixture with very low AlF(6)(3)(-) concentrations even at the Na(3)AlF(6) composition. Evidence for nonideal mixing of anions was found. For the ternaries, models based on Raman data are presented and compared with vapor pressure measurements. Good agreement is observed when association between the additives, CaF(2) or MgF(2), with the AlF(5)(2)(-) ions in the melt was considered. This association could be experimentally observed through a band broadening and a slight shift in the AlF(5)(2)(-) band frequency. Our vapor pressures and Raman data both indicate that MgF(2) clearly acts as an acid when added to NaF-AlF(3) melts of any composition. When CaF(2) is added, a slight decrease of vapor pressure occurs. Raman data indicate a decrease of AlF(4)(-) concentration, corresponding to a dissociation of CaF(2) with liberation of F(-) ions. All these results are, however, very much dependent on the initial melt composition. These data are explained in terms of acid-base, dilution, and association reactions of the solute with the solvent.     

On integrating vertex singularities using extrapolation

A new approach to the integration of vertex singularities is described. This approach is based on a non-uniform subdivision of the region of integration and the technique fits well to the subdivision strategy used in many adaptive algorithms. A nice feature with this approach is that it can be used in any dimension and on any region of integration which can be subdivided into subregions of the same form. The strategy can be applied both to vertex singularities and internal point singularities. In the latter case this can be done without an initial subdivision of the region in order to put the singular point in a vertex. It turns out that the technique has excellent numerical stability properties.Dedicated to Carl-Erik Fröberg on the occasion of his 75th birthday.This work was supported by The Norwegian Research Council for Science and the Humanities.     

On replacement selection and Dinsmore's improvement

An improvement on replacement selection when used in the first phase of external sorting is studied. A modified version of a snowplow model introduced by Moore [7] is used giving a theoretical estimate of the improvement. The results are in good agreement with experiments. It is the author's opinion that Dinsmore's modification of replacement selection should be considered seriously when implementing sorting software. Under certain conditions the timegain may reach 30%.     

Fully symmetric integration rules for the 4-cube

In this paper we discuss fully symmetric integration rules of degree 7 and 9 for the 4-cube. In particular we are interested in good rules. (i.e. rules with all the evaluation points inside the cube and all the weights positive).This work was supported by the Norwegian Research Council for Sciences and Humanities.     

Isolated points in duals of certain locally compact groups

Summary LetG be a separable locally compact group with dual space. consists of all equivalence classes of irreducible unitary representations ofG, and is endowed with the Fell-topology. We study the topological properties in of the square-integrable representations ofG. [ is square-integrable provided there is a coordinate functiong((g)v, v),gG, for which is inL ²(G) w.r.t. left Haar measure onG.]SupposeG contains an open normal subgroupN of the formeKN ⁿ e whereK is compact. (All groups with a compact invariant neighborhood of the identity, [IN] groups, satisfy this condition.) In this case we show that if is square-integrable then {} is an open point of.Finally, our techniques are used to prove this result for arbitrary (non connected) nilpotent Lie groups.     

Visualization of network structure by the application of hypernodes

In the literature several authors describe methods to construct simplified models of networks. These methods are motivated by the need to gain insight into the main properties of medium sized or large networks. The present paper contributes to this research by setting focus on weighted networks, the geographical component of networks and introducing a class of functions to model how the weights propagate from one level of abstraction to the next. Hierarchies of network models can be constructed from reordering of the adjacency matrix of the network; this is how “hypernodes” are derived in the present paper. The hypernode algorithm is explored and it is shown how it can be formulated to handle weighted networks. Weighted networks enable handling the uncertainty or the strength of the components which make up the network. The hypernode algorithm can be run in an iterative manner so that a hierarchy of simplified models of the network can be derived. Some case studies demonstrate the hypernode algorithm. In the first case the algorithm is compared with a similar implementation described in the literature. In the second case an airline dataset is analysed. This study shows that when networks are embedded in the geographical space hypernodes may relate to clusters in the spatial domain. The selection of the visual variables to illustrate the strength of the edges and nodes in a weighted network is discussed.     

Liquid and gas chromatographic studies of the anaerobic degradation of baker’s yeast wastewater

The digestion of baker’s yeast wastewater was monitored by gas production intensity and composition of gaseous and liquid phases. Favorable coexistence of sulfate reducing bacteria and methanogens was explained by the presence and metabolism of trimethylamine, a degradation product of betaine. Concentration of sulfides decreased at the expense of betaine degradation with final products S₀ and N₂. Since biological wastewater treatment was complicated by both high content of SO₄^2-, eventually becoming reduced to toxic H₂S, and high total nitrogen content, a technological solution that links sulfate reduction to elemental sulfur coupled with reactions producing gaseous nitrogen may have great practical value.     

Stochastic binding of Ca2+ ions in the dyadic cleft; continuous vs random walk description of diffusion

Ca²⁺ signaling in the dyadic cleft in ventricular myocytes is fundamentally discrete and stochastic. In this paper we study the stochastic binding of single Ca²⁺ ions to receptors in the cleft using two different models of diffusion; a stochastic and discrete Random walk (RW) model, and a deterministic continuous model. We investigate if the latter model, together with a stochastic receptor model, can reproduce binding events registered in fully stochastic RW simulations. By evaluating the continuous model goodness-of-fit, we present evidences that it can. The large fluctuations in binding rate observed at the time level of single time steps are integrated and smoothed at the larger time scale of binding events, explaining the continuous model goodness-of-fit. With this we demonstrate that the stochasticity and discreteness of the Ca²⁺ signaling in the dyadic cleft, determined by single binding events, can be described with a deterministic model of Ca²⁺ diffusion together with a stochastic model of the binding events. Time consuming RW simulations can thus be avoided. We also present a new analytical model of bi-molecular binding probabilities that is used in the RW simulations, and in the statistical analysis. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Initial attachment and spreading of MG63 cells on nanopatterned titanium surfaces via through-mask anodization

It is well established that nanosized surface topography significantly affects cell response at a biomaterial surface. Here we used a through-mask anodization technique to fabricate well-defined titania nanopillars with tunable feature sizes from 15 to 100 nm on bulk titanium (Ti) substrates and studied their effects on initial attachment and spreading of osteoblast-like cells (MG63). An increase of titania pillar height from 15 to 100 nm resulted in reduced spreading of MG63 osteoblast-like cells and the higher pillar structures also gave rise to heavily elongated cells. By using a FIB/SEM dual beam microscope the interface between MG63 cells and nanopatterned Ti surfaces could be studied in more detail. It was found that the higher pillar structures prevented the cells to conform to the surface topography leaving voids in between the cells and the substrates. The results found in this study agree with previous studies that cells response better to surfaces with smaller (<20 nm) features.