A Modified Version of the Waxman Algorithm

The iterative algorithm recently proposed by Waxman for solving eigenvalue problems, which relies on the method of moments, has been modified to improve its convergence considerably without sacrificing its benefits or elegance. The suggested modification is based on methods to calculate low-lying eigenpairs of large bounded hermitian operators or matrices

A New Constraint on the Escape Fraction in Distant Galaxies Using Gamma-ray Burst Afterglow Spectroscopy

We describe a new method to measure the escape fraction fesc of ionizing radiation from distant star-forming galaxies using the afterglow spectra of long-duration gamma-ray bursts (GRBs). Optical spectra of GRB afterglows allow us to evaluate the optical depth of the host ISM, according to the neutral hydrogen column density N(HI) observed along the sightlines toward the star-forming regions where the GRBs are found. Different from previous effort in searching for faint, transmitted Lyman continuum photons, our method is not subject to background subtraction uncertainties and does not require prior knowledge of either the spectral shape of the host galaxy population or the IGM Lya forest absorption along these GRB sightlines. Because most GRBs occur in sub-L_* galaxies, our study also offers the first constraint on fesc for distant low-mass galaxies that dominate the cosmic luminosity density. We have compiled a sample of 27 GRBs at redshift z>2 for which the underlying N(HI) in the host ISM are known. These GRBs together offer a statistical sampling of the integrated optical depth to ionizing photons along random sightlines from star-forming regions in the host galaxies, and allow us to estimate the mean escape fraction averaged over different viewing angles. We find =0.02\pm 0.02 and place a 95% c.l. upper limit <= 0.075 for these hosts. We discuss possible biases of our approach and implications of the result. Finally, we propose to extend this technique for measuring at z~0.2 using spectra of core-collapse supernovae.Comment: Five journal pages, including one figure; ApJL in pres

Class Attendance and Students’ Evaluations of Teaching: Do No-Shows Bias Course Ratings and Rankings?

Background: Many university departments use students’ evaluations of teaching (SET) to compare and rank courses. However, absenteeism from class is often nonrandom and, therefore, SET for different courses might not be comparable. Objective: The present study aims to answer two questions. Are SET positively biased due to absenteeism? Do procedures, which adjust for absenteeism, change course rankings? Research Design: The author discusses the problem from a missing data perspective and present empirical results from regression models to determine which factors are simultaneously associated with students’ class attendance and course ratings. In order to determine the extent of these biases, the author then corrects average ratings for students’ absenteeism and inspect changes in course rankings resulting from this adjustment. Subjects: The author analyzes SET data on the individual level. One or more course ratings are available for each student. Measures: Individual course ratings and absenteeism served as the key outcomes. Results: Absenteeism decreases with rising teaching quality. Furthermore, both factors are systematically related to student and course attributes. Weighting students’ ratings by actual absenteeism leads to mostly small changes in ranks, which follow a power law. Only a few, average courses are disproportionally influenced by the adjustment. Weighting by predicted absenteeism leads to very small changes in ranks. Again, average courses are more strongly affected than courses of very high or low in quality. Conclusions: No-shows bias course ratings and rankings. SET are more appropriate to identify high- and low-quality courses than to determine the exact ranks of average courses

A New Variable Modified Chaplygin Gas Model Interacting with Scalar Field

In this letter we present a new form of the well known Chaplygin gas model by introducing inhomogeneity in the EOS. This model explains $\omega=-1$ crossing. Also we have given a graphical representation of the model using $\{r,s\}$ parameters. We have also considered an interaction of this model with the scalar field by introducing a phenomenological coupling function and have shown that the potential decays with time.Comment: 7 pages, 3 figure

Asymptotic self-similarity breaking at late times in cosmology

We study the late time evolution of a class of exact anisotropic cosmological solutions of Einstein's equations, namely spatially homogeneous cosmologies of Bianchi type VII$_0$ with a perfect fluid source. We show that, in contrast to models of Bianchi type VII$_h$ which are asymptotically self-similar at late times, Bianchi VII$_0$ models undergo a complicated type of self-similarity breaking. This symmetry breaking affects the late time isotropization that occurs in these models in a significant way: if the equation of state parameter $\gamma$ satisfies $\gamma \leq 4/3$ the models isotropize as regards the shear but not as regards the Weyl curvature. Indeed these models exhibit a new dynamical feature that we refer to as Weyl curvature dominance: the Weyl curvature dominates the dynamics at late times. By viewing the evolution from a dynamical systems perspective we show that, despite the special nature of the class of models under consideration, this behaviour has implications for more general models.Comment: 29 page

Resistance of a domain wall in the quasiclassical approach

Starting from a simple microscopic model, we have derived a kinetic equation for the matrix distribution function. We employed this equation to calculate the conductance $G$ in a mesoscopic F'/F/F' structure with a domain wall (DW). In the limit of a small exchange energy $J$ and an abrupt DW, the conductance of the structure is equal to $G_{2d}=4\sigma_{\uparrow}\sigma_{\downarrow }/(\sigma_{\uparrow}+\sigma_{\downarrow})L$. Assuming that the scattering times for electrons with up and down spins are close to each other we show that the account for a finite width of the DW leads to an increase in this conductance. We have also calculated the spatial distribution of the electric field in the F wire. In the opposite limit of large $J$ (adiabatic variation of the magnetization in the DW) the conductance coincides in the main approximation with the conductance of a single domain structure $G_{1d}=(\sigma_{\uparrow}+\sigma_{\downarrow})/L$. The account for rotation of the magnetization in the DW leads to a negative correction to this conductance. Our results differ from the results in papers published earlier.Comment: 11 pages; replaced with revised versio

Analysis of the application of the optical method to the measurements of the water vapor content in the atmosphere - Part 1: Basic concepts of the measurement technique

We retrieved the total content of the atmospheric water vapor (or Integrated Water Vapor, IWV) from extensive sets of photometric data obtained since 1995 at Lindenberg Meteorological Observatory with star and sun photometers. Different methods of determination of the empirical parameters that are necessary for the retrieval are discussed. The instruments were independently calibrated using laboratory measurements made at Pulkovo Observatory with the VKM-100 multi-pass vacuum cell. The empirical parameters were also calculated by the simulation of the atmospheric absorption by water vapor, using the MODRAN-4 program package for different model atmospheres. The results are compared to those presented in the literature, obtained with different instruments and methods of the retrieval. The reliability of the empirical parameters, used for the power approximation that links the water vapor content with the observed absorption, is analyzed. Currently, the total (from measurements, calibration, and calculations) errors yield the standard uncertainty of about 10% in the total column water vapor. We discuss the possibilities for improving the accuracy of calibration to ~1% as indispensable condition in order to make it possible to use data obtained by optical photometry as an independent reference for other methods (GPS, MW-radiometers, lidar, etc).Comment: 28 pages, 8 figures, 3 tables. In submitting to Atmospheric Measurement Technique

Global dynamics of the mixmaster model

The asymptotic behaviour of vacuum Bianchi models of class A near the initial singularity is studied, in an effort to confirm the standard picture arising from heuristic and numerical approaches by mathematical proofs. It is shown that for solutions of types other than VIII and IX the singularity is velocity dominated and that the Kretschmann scalar is unbounded there, except in the explicitly known cases where the spacetime can be smoothly extended through a Cauchy horizon. For types VIII and IX it is shown that there are at most two possibilities for the evolution. When the first possibility is realized, and if the spacetime is not one of the explicitly known solutions which can be smoothly extended through a Cauchy horizon, then there are infinitely many oscillations near the singularity and the Kretschmann scalar is unbounded there. The second possibility remains mysterious and it is left open whether it ever occurs. It is also shown that any finite sequence of distinct points generated by iterating the Belinskii-Khalatnikov-Lifschitz mapping can be realized approximately by a solution of the vacuum Einstein equations of Bianchi type IX.Comment: 16 page

Flux-Induced Vortex in Mesoscopic Superconducting Loops

We predict the existence of a quantum vortex for an unusual situation. We study the order parameter in doubly connected superconducting samples embedded in a uniform magnetic field. For samples with perfect cylindrical symmetry, the order parameter has been known for long and no vortices are present in the linear regime. However, if the sample is not symmetric, there exist ranges of the field for which the order parameter vanishes along a line, parallel to the field. In many respects, the behavior of this line is qualitatively different from that of the vortices encountered in type II superconductivity. For samples with mirror symmetry, this flux-induced vortex appears at the thin side for small fluxes and at the opposite side for large fluxes. We propose direct and indirect experimental methods which could test our predictions.Comment: 6 pages, Latex, 4 figs., uses RevTex, extended to situations far from cylindrical symmetr