Quasi-geostrophic modes in the Earth's fluid core with an outer stably stratified layer

Seismic waves sensitive to the outermost part of the Earth's liquid core seem to be affected by a stably stratified layer at the core-mantle boundary. Such a layer could have an observable signature in both long-term and short-term variations of the magnetic field of the Earth, which are used to probe the flow at the top of the core. Indeed, with the recent SWARM mission, it seems reasonable to be able to identify waves propagating in the core with period of several months, which may play an important role in the large-scale dynamics. In this paper, we characterize the influence of a stratified layer at the top of the core on deep quasi-geostrophic (Rossby) waves. We compute numerically the quasi-geostrophic eigenmodes of a rapidly rotating spherical shell, with a stably stratified layer near the outer boundary. Two simple models of stratification are taken into account, which are scaled with commonly adopted values of the Brunt-V{\"a}is{\"a}l{\"a} frequency in the Earth's core. In the absence of magnetic field, we find that both azimuthal wavelength and frequency of the eigenmodes control their penetration into the stratified layer: the higher the phase speed, the higher the permeability of the stratified layer to the wave motion. We also show that the theory developed by Takehiro and Lister [2001] for thermal convection extends to the whole family of Rossby waves in the core. Adding a magnetic field, the penetrative behaviour of the quasi-geostrophic modes (the so-called fast branch) is insensitive to the imposed magnetic field and only weakly sensitive to the precise shape of the stratification. Based on these results, the large-scale and high frequency modes (1 to 2 month periods) may be detectable in the geomagnetic data measured at the Earth's surface, especially in the equatorial area where the modes can be trapped

The spectrum of the Poincar{\'e} operator in an ellipsoid

We reprove the fact, due to Backus, that the Poincar{\'e} operator in ellipsoids admits a pure point spectrum with polynomial eigenfunctions.We then show that the eigenvalues of the Poincar{\'e} operator restricted to polynomial vector fields of fixed degree admitsa limit repartition given by a probability measure that we construct explicitely. For that, we use Fourier integral operators and ideas comingfrom Alan Weinstein and the first author in the seventies. The starting observation is that the orthogonal polynomials in ellipsoids satisfy a PDE

Optimal finite measurements and Gauss quadratures

We exhibit measurements for optimal state estimation which have a finite number of outcomes. This is achieved by a connection between finite optimal measurements and Gauss quadratures. The example we consider to illustrate this connection is that of state estimation on $N$ qubits, all in a same pure state. Extensions to state estimation of mixed states are also discussed.Comment: 7 pages, 2 figures, paragraph added at the end of the article (extension of the problem to general states

HETEROGENEITY OF ZOOXANTHELLAE DENSITY IN THE CORAL ACROPORA GLOBICEPS AROUND MOOREA (FRENCH POLYNESIA)

Understanding the natural heterogeneity of coral zooxanthellae density appears as very important to understand variations in coral survival due to bleaching (the loss of these micro-algal symbionts). Heterogeneity of coral bleaching at different observation scales (within a colony, among neighbouring colonies of the same species or on a wider scale) remains largely misunderstood. The present work explores intracolonial, spatial and temporal variations of zooxanthellae density in the coral Acropora globiceps Dana 1846, over a period of three months on the forereef of Moorea, French Polynesia. In our study, intracolonial zooxanthellae densities did not vary significantly. However, zooxanthellae densities differed slightly between inner and outer branches but this trend was not significant at 6, 12 and 18 meters depth. On a wider scale, zooxanthellae densities also vary spatially : a positive correlation was observed between depth and symbiont density (density increases when light intensity decreases, so according to depth). Moreover, the location of colonies exposed to different hydrodynamical conditions was not a parameter controling the concentration of zooxanthellae. Finally, the temporal variation of zooxanthellae densities did not show significant variations even if it decreased slightly over the study period. The results of this study highlight the importance of accounting for variations within and among colonies to determine zooxanthellae densities and to assess the evolution of zooxanthellae populations

High temperature structural and magnetic properties of cobalt nanowires

We present in this paper the structural and magnetic properties of high aspect ratio Co nanoparticles (~10) at high temperatures (up to 623 K) using in situ X ray diffraction (XRD) and SQUID characterizations. We show that the anisotropic shapes, the structural and texture properties are preserved up to 500 K. The coercivity can be modelled by u0Hc=2(Kmc+Kshape)/Ms with Kmc the magnetocrystalline anisotropy constant, Kshape the shape anisotropy constant and Ms the saturation magnetization. Hc decreases linearly when the temperature is increased due to the loss of the Co magnetocrystalline anisotropy contribution. At 500K, 50% of the room temperature coercivity is preserved corresponding to the shape anisotropy contribution only. We show that the coercivity drop is reversible in the range 300 - 500 K in good agreement with the absence of particle alteration. Above 525 K, the magnetic properties are irreversibly altered either by sintering or by oxidation.Comment: 8 pages, 7 figures, submitted to Journal of Solid State Chemistr

Preliminary results of lifetime measurements in neutron-rich 53Ti

To study the nuclear structure of neutron-rich titanium isotopes, a lifetime measurement was performed at the Grand Accélérateur National d'Ions Lourds (GANIL) facility in Caen, France. The nucleiwere produced in a multinucleon-transfer reaction by using a 6.76 MeV/u 238U beam. The Advanced Gamma Tracking Array (AGATA) was employed for the γ-ray detection and target-like recoils were identified event-by-event by the large-acceptance variable mode spectrometer (VAMOS++). Preliminary level lifetimes of the (5/2−) to 13/2− states of the yrast band in the neutron-rich nucleus 53Ti were measured for the first time employing the recoil distance Doppler-shift (RDDS) method and the compact plunger for deep inelastic reactions. The differential decay curve method (DDCM) was used to obtain the lifetimes from the RDDS data

Microfossils from the late Mesoproterozoic – early Neoproterozoic Atar/El Mreïti Group, Taoudeni Basin, Mauritania, northwestern Africa

The well-preserved Meso-Neoproterozoic shallow marine succession of the Atar/El Mreïti Group, in the Taoudeni Basin, Mauritania, offers a unique opportunity to investigate the mid-Proterozoic eukaryotic record in Western Africa. Previous investigations focused on stromatolites, biomarkers, chemostratigraphy and palaeoredox conditions. However, only a very modest diversity of organic-walled microfossils (acritarchs) has been documented. Here, we present a new, exquisitely well-preserved and morphologically diverse assemblage of organic-walled microfossils from three cores drilled through the Atar/El Mreïti Group. A total of 48 distinct entities including 11 unambiguous eukaryotes (ornamented and process-bearing acritarchs), and 37 taxonomically unresolved taxa (including 9 possible eukaryotes, 6 probable prokaryotes, and 22 other prokaryotic or eukaryotic taxa) were observed. Black shales preserve locally abundant fragments of benthic microbial mats. We also document one of the oldest records of Leiosphaeridia kulgunica, a species showing a pylome interpreted as a sophisticated circular excystment structure, and one of the oldest records of Trachyhystrichosphaera aimika and T. botula, two distinctive process-bearing acritarchs present in well-dated 1.1 Ga formations at the base of the succession. The general assemblage composition and the presence of three possible index fossils (A. tetragonala, S. segmentata and T. aimika) support a late Mesoproterozoic to early Neoproterozoic (Tonian) age for the Atar/El Mreïti Group, consistent with published lithostratigraphy, chemostratigraphy and geochronology. This study provides the first evidence for a moderately diverse eukaryotic life, at least 1.1 billion years ago in Western Africa. Comparison with coeval worldwide assemblages indicate that a broadly similar microbial biosphere inhabited (generally redox-stratified) oceans, placing better time constraints on early eukaryote palaeogeography and biostratigraphy