Closed-form expressions for particle relative velocities induced by turbulence

In this note we present complete, closed-form expressions for random relative velocities between colliding particles of arbitrary size in nebula turbulence. These results are exact for very small particles (those with stopping times much shorter than the large eddy overturn time) and are also surprisingly accurate in complete generality (that is, also apply for particles with stopping times comparable to, or much longer than, the large eddy overturn time). We note that some previous studies may have adopted previous simple expressions, which we find to be in error regarding the size dependence in the large particle regime.Comment: 8 pages, accepted as Research Note by A&

Limb imaging of the Venus O2 visible nightglow with the Venus Monitoring Camera

We investigated the Venus O2 visible nightglow with imagery from the Venus Monitoring Camera on Venus Express. Drawing from data collected between April 2007 and January 2011, we study the global distribution of this emission, discovered in the late 70s by the Venera 9 and 10 missions. The inferred limb-viewing intensities are on the order of 150 kiloRayleighs at the lower latitudes and seem to drop somewhat towards the poles. The emission is generally stable, although there are episodes when the intensities rise up to 500 kR. We compare a set of Venus Monitoring Camera observations with coincident measurements of the O2 nightglow at 1.27 {\mu}m made with the Visible and Infrared Thermal Imaging Spectrometer, also on Venus Express. From the evidence gathered in this and past works, we suggest a direct correlation between the instantaneous emissions from the two O2 nightglow systems. Possible implications regarding the uncertain origin of the atomic oxygen green line at 557.7 nm are noted.Comment: 7 pages, 3 figure

Pinned Balseiro-Falicov Model of Tunneling and Photoemission in the Cuprates

The smooth evolution of the tunneling gap of Bi_2Sr_2CaCu_2O_8 with doping from a pseudogap state in the underdoped cuprates to a superconducting state at optimal and overdoping, has been interpreted as evidence that the pseudogap must be due to precursor pairing. We suggest an alternative explanation, that the smoothness reflects a hidden SO(N) symmetry near the (pi,0) points of the Brillouin zone (with N = 3, 4, 5, or 6). Because of this symmetry, the pseudogap could actually be due to any of a number of nesting instabilities, including charge or spin density waves or more exotic phases. We present a detailed analysis of this competition for one particular model: the pinned Balseiro-Falicov model of competing charge density wave and (s-wave) superconductivity. We show that most of the anomalous features of both tunneling and photoemission follow naturally from the model, including the smooth crossover, the general shape of the pseudogap phase diagram, the shrinking Fermi surface of the pseudogap phase, and the asymmetry of the tunneling gap away from optimal doping. Below T_c, the sharp peak at Delta_1 and the dip seen in the tunneling and photoemission near 2Delta_1 cannot be described in detail by this model, but we suggest a simple generalization to account for inhomogeneity, which does provide an adequate description. We show that it should be possible, with a combination of photoemission and tunneling, to demonstrate the extent of pinning of the Fermi level to the Van Hove singularity. A preliminary analysis of the data suggests pinning in the underdoped, but not in the overdoped regime.Comment: 18 pages LaTeX, 26 ps. figure

Helicopter tail rotor thrust and main rotor wake coupling in crosswind flight

The tail rotor of a helicopter with a single main rotor configuration can experience a significant reduction in thrust when the aircraft operates in crosswind flight. Brown’s vorticity transport model has been used to simulate a main rotor and tail rotor system translating at a sideslip angle that causes the tail rotor to interact with the main rotor tip vortices as they propagate downstream at the lateral extremities of the wake. The tail rotor is shown to exhibit a distinct directionally dependent mode during which tail rotors that are configured so that the blades travel forward at the top of the disk develop less thrust than tail rotors with the reverse sense of rotation. The range of flight speeds over which this mode exists is shown to vary considerably with the vertical location of the tail rotor. At low flight speeds, the directionally dependent mode occurs because the tail rotor is immersed within not only the downwash from the main rotor but also the rotational flow associated with clusters of largely disorganized vorticity within the main rotor wake. At higher flight speeds, however, the tail rotor is immersed within a coherent supervortex that strongly influences the velocity field surrounding the tail rotor

Electronic susceptibilities in systems with anisotropic Fermi surfaces

The low temperature dependence of the spin and charge susceptibilities of an anisotropic electron system in two dimensions is analyzed. It is shown that the presence of inflection points at the Fermi surface leads, generically, to a $T \log T$ dependence, and a more singular behavior, $\chi \sim T ^{3/4} \log T$, is also possible. Applications to quasi two-dimensional materials are discussed.Comment: 8 pages, 5 figures, revtex 4 styl

Limb observations of the Martian atmosphere with Mars Express’ High Resolution Stereo Camera

Introduction: Good knowledge about the aerosol distribution and compositions is essential for the understanding of thermodynamic processes in the Martian atmosphere, which in turn is important for the understanding of the Martian climate and the altitude of the upper boundary of the atmosphere. The last point is of special interest for spacecraft aerobreaking manoeuvres. The Martian atmosphere often shows horizontal layers of haze up to altitudes of about 80 km. These have been described and analysed e.g. by Jaquin et al., 1986, usingViking Orbiter images and by Montmessin et al., 2006, who used SPICAM stellar occultation data. Both showed seasonal and latitudinal changes in the vertical structure of the aerosol distribution and composition. Apart from SPICAM, the High Resolution Stereo Camera (HRSC) is also on board ESA’s robotic spacecraft Mars Express. HRSC was build and is operated by the German Aerospace Center (Neukum et al. 2004; Jaumann et al. 2007). Mars Express is orbiting Mars in an elliptical orbit, with HRSC scanning the surface of Mars, primarily for geological research. In addition to that, HRSC has been used to sample the planetary limb. We examine the HRSC planetary limb data and analyse the seasonal and latitudinal variations of the maximum altitude of the haze layer and of the occurrence of high altitude detached hazes. We make some comparisons with earlier work. In contrast to the SPICAM instrument, HRSC observes the atmosphere during daytime, which makes it possible to compare night and daytime observations. The HRSC Limb Data: HRSC is a push broom scanner with nine line sensors pointing in different directions to facilitate stereoscopic imaging. Four of the sensors have colour filters at 440 nm, 530 nm, 750 nm and 970 nm, respectively. The five other sensors all have filters centred at 650 nm. These panchromatic filters have a much wider bandpass than the four colour filters. The surface observations which are HRSC’s main purpose, are usually take while the spacecraft is nadirtracking near pericentre. Limb observations, however, are mostly made with a pointing of the spacecraft being inertially fixxed in celestial space. This leaves only a small time window to make observations of the limb during descent or ascent. Therefore, usually only a few of the nine sensors can be used for the limb observation. Due to the motion of the spacecraft, the individual image lines are taken at different geographical locations and altitudes. The position of each image pixel above the limb has to be calculated from the spacecraft positioning information (Scholten, pers. comm.). The typical difference in altitude between two neighbouring pixels is between a couple of dozen metres and 150 m. HRSC has been observing the limb occasionally throughout the mission since 2004. So far the northern hemisphere and especially the north polar region, were particularly well covered (Figure 1 and 2). In Figure 2, we give an overview of the available data, sorted by season (LS) and latitude. The channel in which the observations have been made is colourcoded. Most observations were made with the panchromatic channels. There are also many observations with the blue and green sensors and only a few were made in the red and infra red channels. We find the best data coverage in northern spring in the northern most latitudes. For obvious reasons, we do not have any data during polar nights. For most of our actual analysis we sample the five central pixels of the sensor lines. This allows for minimal horizontal averaging. Analysis: As an example, Fig. 3 shows images and profiles for the blue, nadir, and green channels from orbit 6104. Al three images show a continuously bright limb haze until an altitude of about 20 km. At higher altitudes the limb haze becomes darker and stratified consistent with the limb profiles described by Jacquin et al., 1986. As Mars Express progresses along its orbit, the limb observations are made at different locations above the surface. The locations of the three profiles in Fig. 3 are still in close proximity of each other, in fact they overlap, but none the less they show different vertical aerosol distributions. Beginning above the North Polar cap and going southward, we observe less reflectivity above 20 km and more reflectivity below 20 km, hinting at different compositions or amounts of aerosols. It is not possible to obtain and compare profiles at the same location and at the same time with different sensors, but still, averages of profiles over place and season can provide us with information about typical atmospheric conditions. In Fig. 4 we show spectra from the average profiles at three different latitudinal bands between 70�N–90�N, 30�S–30�N, and 90�S– 70�S, on the left, centre, and right, respectively. The different symbols and colours represent the different altitudes at which the spectra were sampled. The size of the symbol increases with the number of averaged profiles. There are very few observations above the South Polar region (compare Fig. 1). In the North (and South) Polar region there is almost no signal above 30 km altitude, while around the equator the limb haze remains bright until altitudes of about 60 km. At the poles, the spectrum at 10 km is reddish. At higher altitudes the spectrum gets whiter, indicating smaller particles or higher ice content. At the low latitudes the spectra are reddish up to 40 km. At 60 km we see a more or less white spectrum. Figure 5 shows the maximum altitude of the aerosols as seen by HRSC, depending on season. During aphelion (LS � 70�) the maximum altitude of the aerosols that are visible with HRSC is around 40 km. During perihelion (LS � 250�) the maximum altitude is around 70 km. Discussion: Figure 1 and 2 show that there are plenty of visual and near infra red HRSC observations of the Martian limb available. These show aerosol distributions that change with season and latitude (Fig. 3 and 4). The plots in Fig. 4 show the spectra of the average limb profiles at several altitudes for three latitudinal bands. Two important distinctions can be made between the equatorial and the polar regions. First, the altitude at which aerosol occur is higher in the equatorial region and second, the composition of the aerosols at different altitudes is different. While the spectrum is white around 20 km altitude above the north pole, it is red at the low latitudes. The seasonal variations of maximum altitude of the aerosols is in good agreement with Jaquin et al. (1986) and with Montmessin et al. (2006). The similarity between Montmessin’s results and ours is likely to be due to the large annual variation of atmospheric dust load compared to the diurnal cycle. A much closer look at the data, is forseen to analyse the daily variation of aerosols in the Martian atmosphere. The CO2 and waterice aerosols are more likely to change their vertical distribution (above the planetary boundary layer) between day and night than the mineral (dust) aerosols. Spectral information would help to discriminate between these components. HRSC can not provide it, because the observation for the different filters take place at different locations and times (see Fig. 3). An alternative is to fit aerosol models to the inverted profiles. Currently, we are preparing this work. Mars Express’ HRSC limb data present a valuable opportunity to analyse Mars daytime atmospheric dust at a high vertical resolution. This work gives a short overview of the available data and analyses some seasonal and latitudinal properties

Kinematics of electrons near a Van Hove singularity

A two dimensional electronic system, where the Fermi surface is close to a Van Hove singularity, shows a variety of weak coupling instabilities, and it is a convenient model to study the interplay between antiferromagnetism and anisotropic superconductivity. We present a detailed analysis of the kinematics of the electron scattering in this model. The similitudes, and differences, between a standard Renormalization Group approach and previous work based on parquet summations of log$^2$ divergences are analyzed, with emphasis on the underlying physical processes. General properties of the phase diagram are discussed.Comment: 5 pages, 3 postscript figure

Superconducting and pseudogap phases from scaling near a Van Hove singularity

We study the quantum corrections to the Fermi energy of a two-dimensional electron system, showing that it is attracted towards the Van Hove singularity for a certain range of doping levels. The scaling of the Fermi level allows to cure the infrared singularities left in the BCS channel after renormalization of the leading logarithm near the divergent density of states. A phase of d-wave superconductivity arises beyond the point of optimal doping corresponding to the peak of the superconducting instability. For lower doping levels, the condensation of particle-hole pairs due to the nesting of the saddle points takes over, leading to the opening of a gap for quasiparticles in the neighborhood of the singular points.Comment: 4 pages, 6 Postscript figures, the physical discussion of the results has been clarifie

Diffuse Gamma-Ray Emission from Starburst Galaxies and M31

We present a search for high energy gamma-ray emission from 9 nearby starburst galaxies and M31 with the EGRET instrument aboard CGRO. Though the diffuse gamma-ray emission from starburst galaxies was suspected to be detectable, we find no emission from NGC 253, M82 nor from the average of all 9 galaxies. The 2 sigma upper limit for the EGRET flux above 100 MeV for the averaged survey observations is 1.8 x 10-8 ph cm-2 s-1. From a model of the expected radio and gamma-ray emission, we find that the magnetic field in the nuclei of these galaxies is > 25 micro Gauss, and the ratio of proton and electron densities is < 400. The EGRET limits indicate that the rate of massive star formation in the survey galaxies is only about an order of magnitude higher than in the Milky Way. The upper limit to the gamma-ray flux above 100 MeV for M31 is 1.6 x 10-8 ph cm-2 s-1. At the distance of M31, the Milky Way flux would be over twice this value, indicating higher gamma-ray emissivities in our Galaxy. Therefore, since the supernova rate of the Milky Way is higher than in M31, our null detection of M31 supports the theory of the supernova origin of cosmic rays in galaxies.Comment: 17 pages, plus 1 Postscript figure, AAS Latex macros v4.0, accepted for publication in ApJ Main Journa

Deformation of the Fermi surface in the extended Hubbard model

The deformation of the Fermi surface induced by Coulomb interactions is investigated in the t-t'-Hubbard model. The interplay of the local U and extended V interactions is analyzed. It is found that exchange interactions V enhance small anisotropies producing deformations of the Fermi surface which break the point group symmetry of the square lattice at the Van Hove filling. This Pomeranchuck instability competes with ferromagnetism and is suppressed at a critical value of U(V). The interaction V renormalizes the t' parameter to smaller values what favours nesting. It also induces changes on the topology of the Fermi surface which can go from hole to electron-like what may explain recent ARPES experiments.Comment: 5 pages, 4 ps figure