Dissipative Taylor-Couette flows under the influence of helical magnetic fields

The linear stability of MHD Taylor-Couette flows in axially unbounded cylinders is considered, for magnetic Prandtl number unity. Magnetic fields varying from purely axial to purely azimuthal are imposed, with a general helical field parameterized by \beta=B_\phi/B_z. We map out the transition from the standard MRI for \beta=0 to the nonaxisymmetric Azimuthal MagnetoRotational Instability (AMRI) for \beta\to \infty. For finite \beta, positive and negative wave numbers m, corresponding to right and left spirals, are no longer identical. The transition from \beta=0 to \beta\to\infty includes all the possible forms of MRI with axisymmetric and nonaxisymmetric modes. For the nonaxisymmetric modes, the most unstable mode spirals in the opposite direction to the background field. The standard (\beta=0) MRI is axisymmetric for weak fields (including the instability with the lowest Reynolds number) but is nonaxisymmetric for stronger fields. If the azimuthal field is due in part to an axial current flowing through the fluid itself (and not just along the central axis), then it is also unstable to the nonaxisymmetric Tayler instability, which is most effective without rotation. For large \beta this instability has wavenumber m=1, whereas for \beta\simeq 1 m=2 is most unstable. The most unstable mode spirals in the same direction as the background field.Comment: 9 pages, 11 figure

Curricular orientations to real-world contexts in mathematics

A common claim about mathematics education is that it should equip students to use mathematics in the ‘real world’. In this paper, we examine how relationships between mathematics education and the real world are materialised in the curriculum across a sample of eleven jurisdictions. In particular, we address the orientation of the curriculum towards application of mathematics, the ways that real-world contexts are positioned within the curriculum content, the ways in which different groups of students are expected to engage with real-world contexts, and the extent to which high-stakes assessments include real-world problem solving. The analysis reveals variation across jurisdictions and some lack of coherence between official orientations towards use of mathematics in the real world and the ways that this is materialised in the organisation of the content for students

Pervasively Altered Hematite-Rich Deposits Southeast of Home Plate, Gusev Crater, Mars

The investigation of Home Plate and its surroundings in the Inner Basin of the Columbia Hills in Gusev Crater has added substantially to the water story on Mars. Textural, morphological, and geochemical evidence from Home Plate point towards an explosive origin, probably a hydrovolcanic explosion [1]. High silica deposits in the immediate vicinity of Home Plate suggest hydrothermal alteration [e.g. 2,3]. Pervasively altered deposits rich in hematite were investigated to the southeast of Home Plate. Of these, the target Halley, the target KingGeorgeIsland on the GrahamLand outcrop, and the targets Montalva and Riquelme on the Troll outcrop were investigated in situ with the Alpha Particle X-ray spectrometer (APXS), the Microscopic Imager (MI), and the Moessbauer (MB) spectrometer (Fig. 1)

Surface Enhanced Second Harmonic Generation from Macrocycle, Catenane, and Rotaxane Thin Films: Experiments and Theory

Surface enhanced second harmonic generation (SE SHG) experiments on molecular structures, macrocycles, catenanes, and rotaxanes, deposited as monolayers and multilayers by vacuum sublimation on silver, are reported. The measurements show that the molecules form ordered thin films, where the highest degree of order is observed in the case of macrocycle monolayers and the lowest in the case of rotaxane multilayers. The second harmonic generation activity is interpreted in terms of electric field induced second harmonic (EFISH) generation where the electric field is created by the substrate silver atoms. The measured second order nonlinear optical susceptibility for a rotaxane thin film is compared with that obtained by considering only EFISH contribution to SHG intensity. The electric field on the surface of a silver layer is calculated by using the Delphi4 program for structures obtained with TINKER molecular mechanics/dynamics simulations. An excellent agreement is observed between the calculated and the measured SHG susceptibilities.

On the relevance of the mathematics curriculum to young people

In this paper we draw upon focus group data from a large study of learner trajectories through 14-19 mathematics education to think about the notion of relevance in the mathematics curriculum. Drawing on data from three socially distanced sites we explore how different emphases on what might be termed practical, process and/or professional forms of relevance affect the experiences and aspirations of learners of mathematics. We consider whether an emphasis on practical relevance in schools serving relatively disadvantaged communities might aid the reproduction of students’ social position. This leads us to suggest that a fourth category of curriculum relevance – political relevance – is largely missing from classrooms

Mineralogy of Vera Rubin Ridge in Gale Crater from the Mars Science Laboratory CheMin instrument

Gale crater was selected as the landing site for the Mars Science Laboratory Curiosity rover because of orbital evidence for a variety of secondary minerals in the lower slopes of Aeolis Mons (aka Mount Sharp) that indicate changes in aqueous conditions over time. Distinct units demonstrate orbital spectral signatures of hematite, phyllosilicate (smectite), and sulfate minerals, which suggest that ancient aqueous environments in Gale crater varied in oxidation potential, pH, and water activity. Vera Rubin ridge (VRR) is the first of these units identified from orbit to have been studied by Curiosity. Orbital near-infrared data from VRR show a strong band at 860 nm indicative of hematite. Before Curiosity arrived at VRR, the hypotheses to explain the formation of hematite included (1) precipitation at a redox interface where aqueous Fe2+ was oxidized to Fe3+, and (2) acidic alteration of olivine in oxic fluids. Studying the composition and sedimentology of the rocks on VRR allow us to test and refine these hypotheses and flesh out the depositional and diagenetic history of the ridge. Here, we focus on the mineralogical results of four rock powders drilled from and immediately below VRR as determined by CheMin

Evidence for a Global Martian Soil Composition Extends to Gale Crater

The eolian bedform within Gale Crater referred to as "Rocknest" was investigated by the science instruments of the Curiosity Mars rover. Physical, chemical and mineralogical results are consistent with data collected from soils at other landing sites, suggesting a globally-similar composition. Results from the Curiosity payload from Rocknest should be considered relevant beyond a single, localized region with Gale Crater, providing key insights into planetary scale processes

Transport properties of the azimuthal magnetorotational instability

The magnetorotational instability (MRI) is thought to be a powerful source of turbulence in Keplerian accretion disks. Motivated by recent laboratory experiments, we study the MRI driven by an azimuthal magnetic field in an electrically conducting fluid sheared between two concentric rotating cylinders. By adjusting the rotation rates of the cylinders, we approximate angular velocity profiles ω ∝ r q . We perform direct numerical simulations of a steep profile close to the Rayleigh line q & −2 and a quasiKeplerian profile q ≈ −3/2 and cover wide ranges of Reynolds (Re ≤ 4 · 104 ) and magnetic Prandtl numbers (0 ≤ Pm ≤ 1). In the quasi-Keplerian case, the onset of instability depends on the magnetic Reynolds number, with Rmc ≈ 50, and angular momentum transport scales as √ PmRe2 in the turbulent regime. The ratio of Maxwell to Reynolds stresses is set by Rm. At the onset of instability both stresses have similar magnitude, whereas the Reynolds stress vanishes or becomes even negative as Rm increases. For the profile close to the Rayleigh line, the instability shares these properties as long as Pm & 0.1, but exhibits a markedly different character if Pm → 0, where the onset of instability is governed by the Reynolds number, with Rec ≈ 1250, transport is via Reynolds stresses and scales as Re2 . At intermediate Pm = 0.01 we observe a continuous transition from one regime to the other, with a crossover at Rm = O(100). Our results give a comprehensive picture of angular momentum transport of the MRI with an imposed azimuthal field

Germanium Enrichments in Sedimentary Rocks in Gale Crater, Mars: Constraining the Timing of Alteration and Character of the Protolith

Rocks enriched in Ge have been discovered in Gale Crater, Mars, by the Alpha-particle X-ray spectrometer (APXS) on the Mars Science Lab (MSL) rover, Curiosity. The Ge concentrations in Gale Crater (commonly >50 ppm) are remarkably high in comparison to Earth, where Ge ranges from 0.5-4.0 ppm in igneous rocks and 0.2-3.3 ppm in siliciclastic sediment. Primary meteoritic input is not likely the source of high Ge because Ge/Ni in chondrites (approx.0.003) and irons (<0.04) is lower than in Gale rocks (0.08-0.2). Earth studies show Ge is a useful geochemical tracer because it is coherent with Si during magmatic processes and Ge/Si varies less than 20% in basalts. Ge and Si fractionate during soil/regolith weathering, with Ge preferentially sequestered in clays. Ge is also concentrated in Cu- and Zn-rich hydrothermal sulfide deposits and Fe- and Mnrich oxide deposits. Other fluid-mobile elements (K, Zn, Cl, Br, S) are also enriched at Gale and further constrain aqueous alteration processes. Here, we interpret the sediment alteration history and present a possible model for Ge enrichments at Gale involving fluid alteration of the protolith

Moessbauer Mineralogy of Rock, Soil, and Dust at Gusev Crater, Mars: Spirit's Journey through Weakly Altered Olivine Basalt on the Plains and Pervasively Altered Basalt in the Columbia Hills

The Moessbauer spectrometer on Spirit measured the oxidation state of Fe, identified Fe-bearing phases, and measured relative abundances of Fe among those phases for surface materials on the plains and in the Columbia Hills of Gusev crater. Eight Fe-bearing phases were identified: olivine, pyroxene, ilmenite, magnetite, nanophase ferric oxide (npOx), hematite, goethite, and a Fe(3+)-sulfate. Adirondack basaltic rocks on the plains are nearly unaltered (Fe(3+)/Fe(sub T)Px), and minor npOx and magnetite. Columbia Hills basaltic rocks are nearly unaltered (Peace and Backstay), moderately altered (WoolyPatch, Wishstone, and Keystone), and pervasively altered (e.g., Clovis, Uchben, Watchtower, Keel, and Paros with Fe(3+)/Fe(sub T) approx.0.6-0.9). Fe from pyroxene is greater than Fe from olivine (Ol sometimes absent), and Fe(2+) from Ol+Px is 40-49% and 9-24% for moderately and pervasively altered materials, respectively. Ilmenite (Fe from Ilm approx.3-6%) is present in Backstay, Wishstone, Keystone, and related rocks along with magnetite (Fe from Mt approx. 10-15%). Remaining Fe is present as npOx, hematite, and goethite in variable proportions. Clovis has the highest goethite content (Fe from Gt=40%). Goethite (alpha-FeOOH) is mineralogical evidence for aqueous processes because it has structural hydroxide and is formed under aqueous conditions. Relatively unaltered basaltic soils (Fe(3+)/Fe(sub T) approx. 0.3) occur throughout Gusev crater (approx. 60-80% Fe from Ol+Px, approx. 10-30% from npOx, and approx. 10% from Mt). PasoRobles soil in the Columbia Hills has a unique occurrence of high concentrations of Fe(3+)-sulfate (approx. 65% of Fe). Magnetite is identified as a strongly magnetic phase in Martian soil and dust