Flat rank of automorphism groups of buildings

The flat rank of a totally disconnected locally compact group G, denoted flat-rk(G), is an invariant of the topological group structure of G. It is defined thanks to a natural distance on the space of compact open subgroups of G. For a topological Kac-Moody group G with Weyl group W, we derive the inequalities: alg-rk(W)\le flat-rk(G)\le rk(|W|\_0). Here, alg-rk(W) is the maximal $\mathbb{Z}$-rank of abelian subgroups of W, and rk(|W|\_0) is the maximal dimension of isometrically embedded flats in the CAT0-realization |W|\_0. We can prove these inequalities under weaker assumptions. We also show that for any integer n \geq 1 there is a topologically simple, compactly generated, locally compact, totally disconnected group G, with flat-rk(G)=n and which is not linear

Effective inertial frame in an atom interferometric test of the equivalence principle

In an ideal test of the equivalence principle, the test masses fall in a common inertial frame. A real experiment is affected by gravity gradients, which introduce systematic errors by coupling to initial kinematic differences between the test masses. We demonstrate a method that reduces the sensitivity of a dual-species atom interferometer to initial kinematics by using a frequency shift of the mirror pulse to create an effective inertial frame for both atomic species. This suppresses the gravity-gradient-induced dependence of the differential phase on initial kinematic differences by a factor of 100 and enables a precise measurement of these differences. We realize a relative precision of $\Delta g / g \approx 6 \times 10^{-11}$ per shot, which improves on the best previous result for a dual-species atom interferometer by more than three orders of magnitude. By suppressing gravity gradient systematic errors to below one part in $10^{13}$, these results pave the way for an atomic test of the equivalence principle at an accuracy comparable with state-of-the-art classical tests.Comment: 5 pages, 4 figure

Linking engagement and performance: The social network analysis perspective

Theories developed by Tinto and Nora identify academic performance, learning gains, and involvement in learning communities as significant facets of student engagement that, in turn, support student persistence. Collaborative learning environments, such as those employed in the Modeling Instruction introductory physics course, provide structure for student engagement by encouraging peer-to-peer interactions. Because of the inherently social nature of collaborative learning, we examine student interactions in the classroom using network analysis. We use centrality---a family of measures that quantify how connected or "central" a particular student is within the classroom network---to study student engagement longitudinally. Bootstrapped linear regression modeling shows that students' centrality predicts future academic performance over and above prior GPA for three out of four centrality measures tested. In particular, we find that closeness centrality explains 28 % more of the variance than prior GPA alone. These results confirm that student engagement in the classroom is critical to supporting academic performance. Furthermore, we find that this relationship for social interactions does not emerge until the second half of the semester, suggesting that classroom community develops over time in a meaningful way

2-D and 3-D Radiation Transfer Models of High-Mass Star Formation

2-D and 3-D radiation transfer models of forming stars generally produce bluer 1-10 micron colors than 1-D models of the same evolutionary state and envelope mass. Therefore, 1-D models of the shortwave radiation will generally estimate a lower envelope mass and later evolutionary state than multidimensional models. 1-D models are probably reasonable for very young sources, or longwave analysis (wavelengths > 100 microns). In our 3-D models of high-mass stars in clumpy molecular clouds, we find no correlation between the depth of the 10 micron silicate feature and the longwave (> 100 micron) SED (which sets the envelope mass), even when the average optical extinction of the envelope is >100 magnitudes. This is in agreement with the observations of Faison et al. (1998) of several UltraCompact HII (UCHII) regions, suggesting that many of these sources are more evolved than embedded protostars. We have calculated a large grid of 2-D models and find substantial overlap between different evolutionary states in the mid-IR color-color diagrams. We have developed a model fitter to work in conjunction with the grid to analyze large datasets. This grid and fitter will be expanded and tested in 2005 and released to the public in 2006.Comment: 10 pages, 8 figures, to appear in the proceedings of IAU Symp 227, Massive Star Birth: A Crossroads of Astrophysics, (Cesaroni R., Churchwell E., Felli M., Walmsley C. editors

Interpreting Spectral Energy Distributions from Young Stellar Objects. I. A grid of 200,000 YSO model SEDs

We present a grid of radiation transfer models of axisymmetric young stellar objects (YSOs), covering a wide range of stellar masses (from 0.1Msun to 50Msun) and evolutionary stages (from the early envelope infall stage to the late disk-only stage). The grid consists of 20,000 YSO models, with spectral energy distributions (SEDs) and polarization spectra computed at ten viewing angles for each model, resulting in a total of 200,000 SEDs. [...]. These models are publicly available on a dedicated WWW server: http://www.astro.wisc.edu/protostars/ . In this paper we summarize the main features of our models, as well as the range of parameters explored. [...]. We examine the dependence of the spectral indices of the model SEDs on envelope accretion rate and disk mass. In addition, we show variations of spectral indices with stellar temperature, disk inner radius, and disk flaring power for a subset of disk-only models. We also examine how changing the wavelength range of data used to calculate spectral indices affects their values. We show sample color-color plots of the entire grid as well as simulated clusters at various distances with typical {\it Spitzer Space Telescope} sensitivities. We find that young embedded sources generally occupy a large region of color-color space due to inclination and stellar temperature effects. Disk sources occupy a smaller region of color-color space, but overlap substantially with the region occupied by embedded sources, especially in the near- and mid-IR. We identify regions in color-color space where our models indicate that only sources at a given evolutionary stage should lie. [...].Comment: 69 pages, 28 figures, Accepted for publication in ApJS. Preprint with full resolution figures available at http://www.astro.wisc.edu/protostars

Fragmentation Instability of Molecular Clouds: Numerical Simulations

We simulate fragmentation and gravitational collapse of cold, magnetized molecular clouds. We explore the nonlinear development of an instability mediated by ambipolar diffusion, in which the collapse rate is intermediate to fast gravitational collapse and slow quasistatic collapse. Initially uniform stable clouds fragment into elongated clumps with masses largely determined by the cloud temperature, but substantially larger than the thermal Jeans mass. The clumps are asymmetric, with significant rotation and vorticity, and lose magnetic flux as they collapse. The clump shapes, intermediate collapse rates, and infall profiles may help explain observations not easily fit by contemporary slow or rapid collapse models.Comment: 25pp, 20 small eps figures, in press ApJ, April 1, 200