A geometric approach to high resolution TVD schemes

A geometric approach, similar to Van Leer's MUSCL schemes, is used to construct a second-order accurate generalization of Godunov's method for solving scalar conservation laws. By making suitable approximations, a scheme is obtained which is easy to implement and total variation diminishing. The entropy condition is also investigated from the standpoint of the spreading of rarefaction waves. Quantitative information is obtained for Godunov's method on the rate of spreading which explain the kinks in rarefaction waves often observed at the sonic point

Scintillation Caustics in Planetary Occultation Light Curves

We revisit the GSC5249-01240 light curve obtained during its occultation by Saturn's North polar region. In addition to refractive scintillations, the power spectrum of intensity fluctuations shows an enhancement of power between refractive and diffractive regimes. We identify this excess power as due to high amplitude spikes in the light curve and suggest that these spikes are due to caustics associated with ray crossing situations. The flux variation in individual spikes follows the expected caustic behavior, including diffraction fringes which we have observed for the first time in a planetary occultation light curve. The presence of caustics in scintillation light curves require an inner scale cut off to the power spectrum of underlying density fluctuations associated with turbulence. Another possibility is the presence of gravity waves in the atmosphere. While occultation light curves previously showed the existence of refractive scintillations, a combination of small projected stellar size and a low relative velocity during the event have allowed us to identify caustics in this occultation. This has led us to re-examine previous data sets, in which we have also found likely examples of caustics.Comment: 4 pages, 3 figures; ApJL submitte

Coherent Backscattering of Light with Nonlinear Atomic Scatterers

We study coherent backscattering of a monochromatic laser by a dilute gas of cold two-level atoms in the weakly nonlinear regime. The nonlinear response of the atoms results in a modification of both the average field propagation (nonlinear refractive index) and the scattering events. Using a perturbative approach, the nonlinear effects arise from inelastic two-photon scattering processes. We present a detailed diagrammatic derivation of the elastic and inelastic components of the backscattering signal both for scalar and vectorial photons. Especially, we show that the coherent backscattering phenomenon originates in some cases from the interference between three different scattering amplitudes. This is in marked contrast with the linear regime where it is due to the interference between two different scattering amplitudes. In particular we show that, if elastically scattered photons are filtered out from the photo-detection signal, the nonlinear backscattering enhancement factor exceeds the linear barrier two, consistently with a three-amplitude interference effect.Comment: 18 pages, 13 figures, submitted to Phys. Rev.

Studying Migrant Assimilation Through Facebook Interests

Migrants' assimilation is a major challenge for European societies, in part because of the sudden surge of refugees in recent years and in part because of long-term demographic trends. In this paper, we use Facebook's data for advertisers to study the levels of assimilation of Arabic-speaking migrants in Germany, as seen through the interests they express online. Our results indicate a gradient of assimilation along demographic lines, language spoken and country of origin. Given the difficulty to collect timely migration data, in particular for traits related to cultural assimilation, the methods that we develop and the results that we provide open new lines of research that computational social scientists are well-positioned to address.Comment: Accepted as a short paper at Social Informatics 2018 (https://socinfo2018.hse.ru/). Please cite the SocInfo versio

The stationary phase point method for transitional scattering: diffractive radio scintillation for pulsar

The stationary phase point (SPP) method in one-dimensional case is introduced to treat the diffractive scintillation. From weak scattering, where the SPP number N=1, to strong scattering (N$\gg$1), via transitional scattering regime (N$\sim$2,3), we find that the modulation index of intensity experiences the monotonically increasing from 0 to 1 with the scattering strength, characterized by the ratio of Fresnel scale \rf to diffractive scale \rdiff.Comment: Hanas Meeting paper, appear in ChJAA, 2006, 6, Su

Radio Scintillation due to Discontinuities in the Interstellar Plasma Density

We develop the theory of interstellar scintillation as caused by an irregular plasma having a power-law spatial density spectrum with a spectral exponent of 4 corresponding to a medium with abrupt changes in its density. An ``outer scale'' is included in the model representing the typical scale over which the density of the medium remains uniform. Such a spectrum could be used to model plasma shock fronts in supernova remnants or other plasma discontinuities. We investigate and develop equations for the decorrelation bandwidth of diffractive scintillations and the refractive scintillation index and compare our results with pulsar measurements. We consider both a medium concentrated in a thin layer and an extended irregular medium. We conclude that the discontinuity model gives satisfactory agreement for many diffractive measurements, in particular the VLBI meaurements of the structure function exponent between 5/3 and 2. However, it gives less satisfactory agreement for the refractive scintillation index than does the Kolmogorov turbulence spectrum. The comparison suggests that the medium consists of a pervasive background distribution of turbulence embedded with randomly placed discrete plasma structures such as shocks or HII regions. This can be modeled by a composite spectrum following the Kolmogorov form at high wavenumbers and steepening at lower wavenumbers corresponding to the typical (inverse) size of the discrete structures. Such a model can also explain the extreme scattering events. However, lines of sight through the enhanced scattering prevalent at low galactic latitudes are accurately described by the Kolmogorov spectrum in an extended medium and do not appear to have a similar low-wavenumber steepening.Comment: Accpeted for ApJ vol 531, March 200

Dynamic Correlation in Wave Propagation in Random Media

We report time-resolved measurements of the statistics of pulsed transmission through quasi-one-dimensional dielectric media with static disorder. The normalized intensity correlation function with displacement and polarization rotation for an incident pulse of linewidth $\sigma$ at delay time t is a function only of the field correlation function, which is identical to that found for steady-state excitation, and of $\kappa_{\sigma}(t)$, the residual degree of intensity correlation at points at which the field correlation function vanishes. The dynamic probability distribution of normalized intensity depends only upon $\kappa_{\sigma}(t)$. Steady-state statistics are recovered in the limit $\sigma$->0, in which $\kappa_{\sigma=0}$ is the steady-state degree of correlation.Comment: 4 RevTex pages, 4 figure

Ice in the Antarctic polar stratosphere

On six occasions during the 1987 Airborne Antarctic Ozone Experiment, the Polar Stratospheric Cloud (PSC) ice crystals were replicated over the Palmer Peninsula at approximately 70 deg South. The sampling altitude was approximately 60 to 65 thousand feet, the temperature range was -83.5 to -72C and the atmosphere was subsaturated in all cases. The collected crystals were predominantly complete and hollow prismatic columns with maximum dimensions up to 217 microns. Evidence of scavenging of submicron particles was detected on several crystals. While the replicated crystal sizes were larger than anticipated, their relatively low concentration results in a total surface area less than one tenth that of the sampled aerosol particles. The presence of large crystals suggest that PSC ice crystals can play a very important role in stratospheric dehydration processes