A Finite-Difference Numerical Method for Onsager's Pancake Approximation for Fluid Flow in a Gas Centrifuge

Gas centrifuges exhibit very complex flows. Within the centrifuge there is a rarefied region, a transition region, and a region with an extreme density gradient. The flow moves at hypersonic speeds and shock waves are present. However, the flow is subsonic in the axisymmetric plane. The analysis may be simplified by treating the flow as a perturbation of wheel flow. Wheel flow implies that the fluid is moving as a solid body. With the very large pressure gradient, the majority of the fluid is located very close to the rotor wall and moves at an azimuthal velocity proportional to its distance from the rotor wall; there is no slipping in the azimuthal plane. The fluid can be modeled as incompressible and subsonic in the axisymmetric plane. By treating the centrifuge as long, end effects can be appropriately modeled without performing a detailed boundary layer analysis. Onsager's pancake approximation is used to construct a simulation to model fluid flow in a gas centrifuge. The governing 6th order partial differential equation is broken down into an equivalent coupled system of three equations and then solved numerically. In addition to a discussion on the baseline solution, known problems and future work possibilities are presented

Modularity and Optimality in Social Choice

Marengo and the second author have developed in the last years a geometric model of social choice when this takes place among bundles of interdependent elements, showing that by bundling and unbundling the same set of constituent elements an authority has the power of determining the social outcome. In this paper we will tie the model above to tournament theory, solving some of the mathematical problems arising in their work and opening new questions which are interesting not only from a mathematical and a social choice point of view, but also from an economic and a genetic one. In particular, we will introduce the notion of u-local optima and we will study it from both a theoretical and a numerical/probabilistic point of view; we will also describe an algorithm that computes the universal basin of attraction of a social outcome in O(M^3 logM) time (where M is the number of social outcomes).Comment: 42 pages, 4 figures, 8 tables, 1 algorithm

Fractal geometry of spin-glass models

Stability and diversity are two key properties that living entities share with spin glasses, where they are manifested through the breaking of the phase space into many valleys or local minima connected by saddle points. The topology of the phase space can be conveniently condensed into a tree structure, akin to the biological phylogenetic trees, whose tips are the local minima and internal nodes are the lowest-energy saddles connecting those minima. For the infinite-range Ising spin glass with p-spin interactions, we show that the average size-frequency distribution of saddles obeys a power law $\sim w^{-D}$, where w=w(s) is the number of minima that can be connected through saddle s, and D is the fractal dimension of the phase space

Templated growth of metal-organic coordination chains at surfaces

Line them up: Metal\u2013organic chains (see scanning tunneling microscopy image) have been created in situ by self\u2010organized growth at a metal surface under ultrahigh vacuum. These 1D arrangements of metal centers (Fe, Cu), regularly spaced by organic linkers such as trimesitylic acid, open new possibilities for the study of low\u2010dimensional magnetism

The Optical System for the Large Size Telescope of the Cherenkov Telescope Array

The Large Size Telescope (LST) of the Cherenkov Telescope Array (CTA) is designed to achieve a threshold energy of 20 GeV. The LST optics is composed of one parabolic primary mirror 23 m in diameter and 28 m focal length. The reflector dish is segmented in 198 hexagonal, 1.51 m flat to flat mirrors. The total effective reflective area, taking into account the shadow of the mechanical structure, is about 368 m$^2$. The mirrors have a sandwich structure consisting of a glass sheet of 2.7 mm thickness, aluminum honeycomb of 60 mm thickness, and another glass sheet on the rear, and have a total weight about 47 kg. The mirror surface is produced using a sputtering deposition technique to apply a 5-layer coating, and the mirrors reach a reflectivity of $\sim$94% at peak. The mirror facets are actively aligned during operations by an active mirror control system, using actuators, CMOS cameras and a reference laser. Each mirror facet carries a CMOS camera, which measures the position of the light spot of the optical axis reference laser on the target of the telescope camera. The two actuators and the universal joint of each mirror facet are respectively fixed to three neighboring joints of the dish space frame, via specially designed interface plate.Comment: In Proceedings of the 34th International Cosmic Ray Conference (ICRC2015), The Hague, The Netherlands. All CTA contributions at arXiv:1508.0589

The effects of grain shape and frustration in a granular column near jamming

We investigate the full phase diagram of a column of grains near jamming, as a function of varying levels of frustration. Frustration is modelled by the effect of two opposing fields on a grain, due respectively to grains above and below it. The resulting four dynamical regimes (ballistic, logarithmic, activated and glassy) are characterised by means of the jamming time of zero-temperature dynamics, and of the statistics of attractors reached by the latter. Shape effects are most pronounced in the cases of strong and weak frustration, and essentially disappear around a mean-field point.Comment: 17 pages, 19 figure

The helicase HAGE prevents interferon-a-induced PML expression in ABCB5+ malignant melanoma-initiating cells by promoting the expression of SOCS1

The tumour suppressor PML (promyelocytic leukaemia protein) regulates several cellular pathways involving cell growth, apoptosis, differentiation and senescence. PML also has an important role in the regulation of stem cell proliferation and differentiation. Here, we show the involvement of the helicase HAGE in the transcriptional repression of PML expression in ABCB5 + malignant melanoma-initiating cells (ABCB5 + MMICs), a population of cancer stem cells which are responsible for melanoma growth, progression and resistance to drug-based therapy. HAGE prevents PML gene expression by inhibiting the activation of the JAK-STAT (janus kinase-signal transducers and activators of transcription) pathway in a mechanism which implicates the suppressor of cytokine signalling 1 (SOCS1). Knockdown of HAGE led to a significant decrease in SOCS1 protein expression, activation of the JAK-STAT signalling cascade and a consequent increase of PML expression. To confirm that the reduction in SOCS1 expression was dependent on the HAGE helicase activity, we showed that SOCS1, effectively silenced by small interfering RNA, could be rescued by re-introduction of HAGE into cells lacking HAGE. Furthermore, we provide a mechanism by which HAGE promotes SOCS1 mRNA unwinding and protein expression in vitro

High-precision Studies of the 3^{\bf{3}}He(e,e′^{\bf{\prime}}p) Reaction at the Quasielastic Peak

Precision studies of the reaction $^{3}$He(e,e$^\prime$p) using the three-spectrometer facility at the Mainz microtron MAMI are presented. All data are for quasielastic kinematics at $|\vec{q} | =685$ MeV/c. Absolute cross sections were measured at three electron kinematics. For the measured missing momenta range from 10 to 165 MeV/c, no strength is observed for missing energies higher than 20 MeV. Distorted momentum distributions were extracted for the two-body breakup and the continuum. The longitudinal and transverse behavior was studied by measuring the cross section for three photon polarizations. The longitudinal and transverse nature of the cross sections is well described by a currently accepted and widely used prescription of the off-shell electron-nucleon cross-section. The results are compared to modern three-body calculations and to previous data.Comment: 4 pages, 3 figures. Submitted for publication in Phys. Rev. Let

Self-Assembly of Supramolecular Triblock Copolymer Complexes

Four different poly(tert-butoxystyrene)-b-polystyrene-b-poly(4-vinylpyridine) (PtBOS-b-PS-b-P4VP) linear triblock copolymers, with the P4VP weight fraction varying from 0.08 to 0.39, were synthesized via sequential anionic polymerization. The values of the unknown interaction parameters between styrene and tert-butoxystyrene and between tert-butoxystyrene and 4-vinylpyridine were determined from random copolymer blend miscibility studies and found to satisfy 0.031<χS,tBOS<0.034 and 0.39<χ4VP,tBOS<0.43, the latter being slightly larger than the known 0.30<χS,4VP≤0.35 value range. All triblock copolymers synthesized adopted a P4VP/PS core/shell cylindrical self-assembled morphology. From these four triblock copolymers supramolecular complexes were prepared by hydrogen bonding a stoichiometric amount of pentadecylphenol (PDP) to the P4VP blocks. Three of these complexes formed a triple lamellar ordered state with additional short length scale ordering inside the P4VP(PDP) layers. The self-assembled state of the supramolecular complex based on the triblock copolymer with the largest fraction of P4VP consisted of alternating layers of PtBOS and P4VP(PDP) layers with PS cylinders inside the latter layers. The difference in morphology between the triblock copolymers and the supramolecular complexes is due to two effects: (i) a change in effective composition and, (ii) a reduction in interfacial tension between the PS and P4VP containing domains. The small angle X-ray scattering patterns of the supramolecules systems are very temperature sensitive. A striking feature is the disappearance of the first order scattering peak of the triple lamellar state in certain temperature intervals, while the higher order peaks (including the third order) remain. This is argued to be due to the thermal sensitivity of the hydrogen bonding and thus directly related to the very nature of these systems.