Reynolds stresses and mean fields generated by pure waves: applications to shear flows and convection in a rotating shell

A general reformulation of the Reynolds stresses created by two-dimensional waves breaking a translational or a rotational invariance is described. This reformulation emphasizes the importance of a geometrical factor: the slope of the separatrices of the wave flow. Its physical relevance is illustrated by two model systems: waves destabilizing open shear flows; and thermal Rossby waves in spherical shell convection with rotation. In the case of shear-flow waves, a new expression of the Reynolds–Orr amplification mechanism is obtained, and a good understanding of the form of the mean pressure and velocity fields created by weakly nonlinear waves is gained. In the case of thermal Rossby waves, results of a three-dimensional code using no-slip boundary conditions are presented in the nonlinear regime, and compared with those of a two-dimensional quasi-geostrophic model. A semi-quantitative agreement is obtained on the flow amplitudes, but discrepancies are observed concerning the nonlinear frequency shifts. With the quasi-geostrophic model we also revisit a geometrical formula proposed by Zhang to interpret the form of the zonal flow created by the waves, and explore the very low Ekman-number regime. A change in the nature of the wave bifurcation, from supercritical to subcritical, is found

On the stability of some continuous systems subjected to random excitation

Conditions determined for sure stability of continuous systems subjected to random excitatio

On the stability of a column subjected to a time-dependent axial load

Exponential bounds and stability conditions for linear elastic column subjected to time varying axial loa

Proper Motions in the Galactic Bulge: Plaut's Window

A proper motion study of a field of 20' x 20' inside Plaut's low extinction window (l,b)=(0 deg,-8 deg), has been completed. Relative proper motions and photographic BV photometry have been derived for ~21,000 stars reaching to V~20.5 mag, based on the astrometric reduction of 43 photographic plates, spanning over 21 years of epoch difference. Proper motion errors are typically 1 mas/yr and field dependent systematics are below 0.2 mas/yr. Cross-referencing with the 2MASS catalog yielded a sample of ~8,700 stars, from which predominantly disk and bulge subsamples were selected photometrically from the JH color-magnitude diagram. The two samples exhibited different proper-motion distributions, with the disk displaying the expected reflex solar motion as a function of magnitude. Galactic rotation was also detected for stars between ~2 and ~3 kpc from us. The bulge sample, represented by red giants, has an intrinsic proper motion dispersion of (sigma_l,sigma_b)=(3.39, 2.91)+/-(0.11,0.09) mas/yr, which is in good agreement with previous results, and indicates a velocity anisotropy consistent with either rotational broadening or tri-axiality. A mean distance of 6.37^{+0.87}_{-0.77} kpc has been estimated for the bulge sample, based on the observed K magnitude of the horizontal branch red clump. The metallicity [M/H] distribution was also obtained for a subsample of 60 bulge giants stars, based on calibrated photometric indices. The observed [M/H] shows a peak value at [M/H]~-0.1 with an extended metal poor tail and around 30% of the stars with supersolar metallicity. No change in proper motion dispersion was observed as a function of [M/H]. We are currently in the process of obtaining CCD UBVRI photometry for the entire proper-motion sample of ~21,000 stars.Comment: Submitted to AJ April 17th 2007. Accepted June 8th 2007. 45 pages, 14 figure

Quasiparticle properties of a coupled quantum wire electron-phonon system

We study leading-order many-body effects of longitudinal optical (LO) phonons on electronic properties of one-dimensional quantum wire systems. We calculate the quasiparticle properties of a weakly polar one dimensional electron gas in the presence of both electron-phonon and electron-electron interactions. The leading-order dynamical screening approximation (GW approximation) is used to obtain the electron self-energy, the quasiparticle spectral function, and the quasiparticle damping rate in our calculation by treating electrons and phonons on an equal footing. Our theory includes effects (within the random phase approximation) of Fermi statistics, Landau damping, plasmon-phonon mode coupling, phonon renormalization, dynamical screening, and impurity scattering. In general, electron-electron and electron-phonon many-body renormalization effects are found to be nonmultiplicative and nonadditive in our theoretical results for quasiparticle properties.Comment: 21 pages, Revtex, 12 figures enclose

Shallow radar (SHARAD) sounding observations of the Medusae Fossae Formation, Mars

The SHARAD (shallow radar) sounding radar on the Mars Reconnaissance Orbiter detects subsurface reflections in the eastern and western parts of the Medusae Fossae Formation (MFF). The radar waves penetrate up to 580 m of the MFF and detect clear subsurface interfaces in two locations: west MFF between 150 and 155◦ E and east MFF between 209 and 213◦ E. Analysis of SHARAD radargrams suggests that the real part of the permittivity is ∼3.0, which falls within the range of permittivity values inferred from MARSIS data for thicker parts of the MFF. The SHARAD data cannot uniquely determine the composition of the MFF material, but the low permittivity implies that the upper few hundred meters of the MFF material has a high porosity. One possibility is that the MFF is comprised of low-density welded or interlocked pyroclastic deposits that are capable of sustaining the steep-sided yardangs and ridges seen in imagery. The SHARAD surface echo power across the MFF is low relative to typical martian plains, and completely disappears in parts of the east MFF that correspond to the radar-dark Stealth region. These areas are extremely rough at centimeter to meter scales, and the lack of echo power is most likely due to a combination of surface roughness and a low near-surface permittivity that reduces the echo strength from any locally flat regions. There is also no radar evidence for internal layering in any of the SHARAD data for the MFF, despite the fact that tens-of-meters scale layering is apparent in infrared and visible wavelength images of nearby areas. These interfaces may not be detected in SHARAD data if their permittivity contrasts are low, or if the layers are discontinuous. The lack of closely spaced internal radar reflectors suggests that the MFF is not an equatorial analog to the current martian polar deposits, which show clear evidence of multiple internal layers in SHARAD dat

Population health and the economy: Mortality and the Great Recession in Europe

We analyze the evolution of mortality‐based health indicators in 27 European countries before and after the start of the Great Recession. We find that in the countries where the crisis has been particularly severe, mortality reductions in 2007–2010 were considerably bigger than in 2004–2007. Panel models adjusted for space‐invariant and time‐invariant factors show that an increase of 1 percentage point in the national unemployment rate is associated with a reduction of 0.5% (p < .001) in the rate of age‐adjusted mortality. The pattern of mortality oscillating procyclically is found for total and sex‐specific mortality, cause‐specific mortality due to major causes of death, and mortality for ages 30–44 and 75 and over, but not for ages 0–14. Suicides appear increasing when the economy decelerates—countercyclically—but the evidence is weak. Results are robust to using different weights in the regression, applying nonlinear methods for detrending, expanding the sample, and using as business cycle indicator gross domestic product per capita or employment‐to‐population ratios rather than the unemployment rate. We conclude that in the European experience of the past 20 years, recessions, on average, have beneficial short‐term effects on mortality of the adult population.Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/142224/1/hec3495_am.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/142224/2/hec3495.pd

Spectral quantification of nonlinear behaviour of the nearshore seabed and correlations with potential forcings at Duck, N.C., U.S.A

Local bathymetric quasi-periodic patterns of oscillation are identified from monthly profile surveys taken at two shore-perpendicular transects at the USACE field research facility in Duck, North Carolina, USA, spanning 24.5 years and covering the swash and surf zones. The chosen transects are the two furthest (north and south) from the pier located at the study site. Research at Duck has traditionally focused on one or more of these transects as the effects of the pier are least at these locations. The patterns are identified using singular spectrum analysis (SSA). Possible correlations with potential forcing mechanisms are discussed by 1) doing an SSA with same parameter settings to independently identify the quasi-periodic cycles embedded within three potentially linked sequences: monthly wave heights (MWH), monthly mean water levels (MWL) and the large scale atmospheric index known as the North Atlantic Oscillation (NAO) and 2) comparing the patterns within MWH, MWL and NAO to the local bathymetric patterns. The results agree well with previous patterns identified using wavelets and confirm the highly nonstationary behaviour of beach levels at Duck; the discussion of potential correlations with hydrodynamic and atmospheric phenomena is a new contribution. The study is then extended to all measured bathymetric profiles, covering an area of 1100m (alongshore) by 440m (cross-shore), to 1) analyse linear correlations between the bathymetry and the potential forcings using multivariate empirical orthogonal functions (MEOF) and linear correlation analysis and 2) identify which collective quasi-periodic bathymetric patterns are correlated with those within MWH, MWL or NAO, based on a (nonlinear) multichannel singular spectrum analysis (MSSA). (...continued in submitted paper)Comment: 50 pages, 3 tables, 8 figure