751 research outputs found
Angular diameter distances reconsidered in the Newman and Penrose formalism
Using the Newman and Penrose spin coefficient (NP) formalism, we provide a
derivation of the Dyer-Roeder equation for the angular diameter distance in
cosmological space-times. We show that the geodesic deviation equation written
in NP formalism is precisely the Dyer-Roeder equation for a general
Friedman-Robertson-Walker (FRW) space-time, and then we examine the angular
diameter distance to redshift relation in the case that a flat FRW metric is
perturbed by a gravitational potential. We examine the perturbation in the case
that the gravitational potential exhibits the properties of a thin
gravitational lens, demonstrating how the weak lensing shear and convergence
act as source terms for the perturbed Dyer-Roeder equation.Comment: 21 pages, 6 figures, accepted to GR
Null Geodesics and Wave Front Singularities in the Godel Space-time
We explore wave fronts of null geodesics in the Godel metric emitted from
point sources both at, and away from, the origin. For constant time wave fronts
emitted by sources away from the origin, we find cusp ridges as well as blue
sky metamorphoses where spatially disconnected portions of the wave front
appear, connect to the main wave front, and then later break free and vanish.
These blue sky metamorphoses in the constant time wave fronts highlight the
non-causal features of the Godel metric. We introduce a concept of physical
distance along the null geodesics, and show that for wave fronts of constant
physical distance, the reorganization of the points making up the wave front
leads to the removal of cusp ridges
Five is 75: Student Success Perspectives, Status, & Highlights
Bridgewater State University\u27s incoming first-time, full-time freshmen cohorts have included about 1,500 students since 2007. A 5% gain in the overall graduation rate means helping 75 additional students achieve their goals. Many schools have achievement gaps between male and female students, but Bridgewater State University has typically had larger gaps than other institutions in its peer group. In recent years, Bridgewater has been particularly concerned about the graduation and retention rates for men of color. In data presented in this poster, we show that there is strong evidence that the overall performance of men of color has improved significantly, but that gender differences persist in general. Unlike students of color, there have been only very minimal closings in the achievement gaps for low income and first generation students
Accuracy of the thin-lens approximation in strong lensing by smoothly truncated dark matter haloes
The accuracy of mass estimates by gravitational lensing using the thin-lens approximation applied to Navarro–Frenk–White mass models with a soft truncation mechanism recently proposed by Baltz, Marshall and Oguri is studied. The gravitational lens scenario considered is the case of the inference of lens mass from the observation of Einstein rings (strong lensing). It is found that the mass error incurred by the simplifying assumption of thin lenses is below 0.5 per cent. As a byproduct, the optimal tidal radius of the soft truncation mechanism is found to be at most 10 times the virial radius of the mass model
Required Peer-cooperative Learning Improves Retention of STEM Majors
Background: Peer-cooperative learning has been shown in the literature to improve student success in gateway science and mathematics courses. Such studies typically demonstrate the impact of students’ attending peer-led learning sessions on their learning or grades in an individual course. In this article, we examine the effects of introducing a required, comprehensive peer-cooperative learning system across five departments simultaneously at a master’s public university, looking not only at students’ success in supported classes, but also their retention within STEM fields two years hence. Combining institutional demographic data with students’ course grades and retention rates, we compare outcomes between 456 students who took their major’s introductory course in the two years prior to implementation of the program, and 552 students who did so after implementation.
Results: While these two student groups did not significantly differ in either their demographic profile or their SAT scores, the post-implementation group earned significantly higher grades in their introductory courses in each major, due largely to an erasure of the mediating effect of SAT scores on course grades. Further, this increase in introductory course grades was also associated with an increase in the two-year retention rate of students in STEM majors.
Conclusions: This finding is significant as it suggests that implementing comprehensive educational reform using required peer-led cooperative learning may have the proximate effect of mitigating differences in academic preparation (as measured by SAT scores) for students in introductory STEM courses. Furthermore, this increase in success leads to increased retention rates in STEM, expanding the pipeline of students retained in such fields
Spacetime perspective of Schwarzschild lensing
We propose a definition of an exact lens equation without reference to a
background spacetime, and construct the exact lens equation explicitly in the
case of Schwarzschild spacetime. For the Schwarzschild case, we give exact
expressions for the angular-diameter distance to the sources as well as for the
magnification factor and time of arrival of the images. We compare the exact
lens equation with the standard lens equation, derived under the
thin-lens-weak-field assumption (where the light rays are geodesics of the
background with sharp bending in the lens plane, and the gravitational field is
weak), and verify the fact that the standard weak-field thin-lens equation is
inadequate at small impact parameter. We show that the second-order correction
to the weak-field thin-lens equation is inaccurate as well. Finally, we compare
the exact lens equation with the recently proposed strong-field thin-lens
equation, obtained under the assumption of straight paths but without the small
angle approximation, i.e., with allowed large bending angles. We show that the
strong-field thin-lens equation is remarkably accurate, even for lightrays that
take several turns around the lens before reaching the observer.Comment: 22 pages, 6 figures, to appear in Phys. Rev.
Theme Overview: Agriculture and Water Quality in the Cornbelt: Overview of Issues and Approaches
Resource /Energy Economics and Policy, Q25,
Study of errors in strong gravitational lensing
We examine the accuracy of strong gravitational lensing determinations of the
mass of galaxy clusters by comparing the conventional approach with the
numerical integration of the fully relativistic null geodesic equations in the
case of weak gravitational perturbations on Robertson-Walker metrics. In
particular, we study spherically-symmetric, three-dimensional singular
isothermal sphere models and the three-dimensional matter distribution of
Navarro et al. (1997), which are both commonly used in gravitational lensing
studies. In both cases we study two different methods for mass-density
truncation along the line of sight: hard truncation and conventional (no
truncation). We find that the relative error introduced in the total mass by
the thin lens approximation alone is less than 0.3% in the singular isothermal
sphere model, and less than 2% in the model of Navarro et al. (1997). The
removal of hard truncation introduces an additional error of the same order of
magnitude in the best case, and up to an order of magnitude larger in the worst
case studied. Our results ensure that the future generation of precision
cosmology experiments based on lensing studies will not require the removal of
the thin-lens assumption, but they may require a careful handling of
truncation.Comment: accepted to Ap
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