Towards the Assessment of the Predictive Capacity of the β-σ Two-Fluid Model for Pseudo-Homogeneous Slurry Flow in Pipes

This paper focuses on the numerical simulation of turbulent, pseudo-homogeneous slurry flows in pipes through the β-σ two-fluid model, developed by the authors and collaborators in previous research. The two-fluid model gives its name to the presence of two main calibration coefficients, namely, σ, associated with the turbulent dispersion of the particles, and β, related to the inter-phase friction and to the wall shear stress produced by the solid phase. In a recently published article, the role played by β and σ on different features of the CFD solution has been established for different flow conditions, and a procedure for the calibration of the two coefficients has been proposed. The present contribution investigates the extrapolability of previously calibrated coefficients to different conditions in terms of pipe diameter, particle type, and in-situ concentration. The experimental data used to support the conclusions and recommendations from the numerical study were obtained from previously published literature. The findings of this study not only contribute to a deeper comprehension of the β-σ two-fluid model, but they also provide a methodological background for the development of computational tools for industrial practitioners and academic researchers

A new technique for elucidating β\beta-decay schemes which involve daughter nuclei with very low energy excited states

A new technique of elucidating $\beta$-decay schemes of isotopes with large density of states at low excitation energies has been developed, in which a Broad Energy Germanium (BEGe) detector is used in conjunction with coaxial hyper-pure germanium detectors. The power of this technique has been demonstrated on the example of 183Hg decay. Mass-separated samples of 183Hg were produced by a deposition of the low-energy radioactive-ion beam delivered by the ISOLDE facility at CERN. The excellent energy resolution of the BEGe detector allowed $\gamma$ rays energies to be determined with a precision of a few tens of electronvolts, which was sufficient for the analysis of the Rydberg-Ritz combinations in the level scheme. The timestamped structure of the data was used for unambiguous separation of $\gamma$ rays arising from the decay of 183Hg from those due to the daughter decays

Rapid quantification of low level polymorph content in a solid dose form using transmission Raman spectroscopy

This proof of concept study demonstrates the application of transmission Raman spectroscopy (TRS) to the non-invasive and non-destructive quantification of low levels (0.62-1.32% w/w) of an active pharmaceutical ingredient's polymorphic forms in a pharmaceutical formulation. Partial least squares calibration models were validated with independent validation samples resulting in prediction RMSEP values of 0.03-0.05% w/w and a limit of detection of 0.1-0.2% w/w. The study further demonstrates the ability of TRS to quantify all tablet constituents in one single measurement. By analysis of degraded stability samples, sole transformation between polymorphic forms was observed while excipient levels remained constant. Additionally, a beam enhancer device was used to enhance laser coupling to the sample, which allowed comparable prediction performance at 60 times faster rates (0.2 s) than in standard mode

Quantum Sign Permutation Polytopes

Convex polytopes are convex hulls of point sets in the $n$-dimensional space \E^n that generalize 2-dimensional convex polygons and 3-dimensional convex polyhedra. We concentrate on the class of $n$-dimensional polytopes in \E^n called sign permutation polytopes. We characterize sign permutation polytopes before relating their construction to constructions over the space of quantum density matrices. Finally, we consider the problem of state identification and show how sign permutation polytopes may be useful in addressing issues of robustness

A Novel Approach for Ellipsoidal Outer-Approximation of the Intersection Region of Ellipses in the Plane

In this paper, a novel technique for tight outer-approximation of the intersection region of a finite number of ellipses in 2-dimensional (2D) space is proposed. First, the vertices of a tight polygon that contains the convex intersection of the ellipses are found in an efficient manner. To do so, the intersection points of the ellipses that fall on the boundary of the intersection region are determined, and a set of points is generated on the elliptic arcs connecting every two neighbouring intersection points. By finding the tangent lines to the ellipses at the extended set of points, a set of half-planes is obtained, whose intersection forms a polygon. To find the polygon more efficiently, the points are given an order and the intersection of the half-planes corresponding to every two neighbouring points is calculated. If the polygon is convex and bounded, these calculated points together with the initially obtained intersection points will form its vertices. If the polygon is non-convex or unbounded, we can detect this situation and then generate additional discrete points only on the elliptical arc segment causing the issue, and restart the algorithm to obtain a bounded and convex polygon. Finally, the smallest area ellipse that contains the vertices of the polygon is obtained by solving a convex optimization problem. Through numerical experiments, it is illustrated that the proposed technique returns a tighter outer-approximation of the intersection of multiple ellipses, compared to conventional techniques, with only slightly higher computational cost

Bregman Voronoi Diagrams: Properties, Algorithms and Applications

The Voronoi diagram of a finite set of objects is a fundamental geometric structure that subdivides the embedding space into regions, each region consisting of the points that are closer to a given object than to the others. We may define many variants of Voronoi diagrams depending on the class of objects, the distance functions and the embedding space. In this paper, we investigate a framework for defining and building Voronoi diagrams for a broad class of distance functions called Bregman divergences. Bregman divergences include not only the traditional (squared) Euclidean distance but also various divergence measures based on entropic functions. Accordingly, Bregman Voronoi diagrams allow to define information-theoretic Voronoi diagrams in statistical parametric spaces based on the relative entropy of distributions. We define several types of Bregman diagrams, establish correspondences between those diagrams (using the Legendre transformation), and show how to compute them efficiently. We also introduce extensions of these diagrams, e.g. k-order and k-bag Bregman Voronoi diagrams, and introduce Bregman triangulations of a set of points and their connexion with Bregman Voronoi diagrams. We show that these triangulations capture many of the properties of the celebrated Delaunay triangulation. Finally, we give some applications of Bregman Voronoi diagrams which are of interest in the context of computational geometry and machine learning.Comment: Extend the proceedings abstract of SODA 2007 (46 pages, 15 figures