Twisted equivariant K-theory, groupoids and proper actions

In this paper we define twisted equivariant K-theory for actions of Lie groupoids. For a Bredon-compatible Lie groupoid, this defines a periodic cohomology theory on the category of finite CW-complexes with equivariant stable projective bundles. A classification of these bundles is shown. We also obtain a completion theorem and apply these results to proper actions of groups.Comment: 26 page

Testing the Hubble Law with the IRAS 1.2 Jy Redshift Survey

We test and reject the claim of Segal et al. (1993) that the correlation of redshifts and flux densities in a complete sample of IRAS galaxies favors a quadratic redshift-distance relation over the linear Hubble law. This is done, in effect, by treating the entire galaxy luminosity function as derived from the 60 micron 1.2 Jy IRAS redshift survey of Fisher et al. (1995) as a distance indicator; equivalently, we compare the flux density distribution of galaxies as a function of redshift with predictions under different redshift-distance cosmologies, under the assumption of a universal luminosity function. This method does not assume a uniform distribution of galaxies in space. We find that this test has rather weak discriminatory power, as argued by Petrosian (1993), and the differences between models are not as stark as one might expect a priori. Even so, we find that the Hubble law is indeed more strongly supported by the analysis than is the quadratic redshift-distance relation. We identify a bias in the the Segal et al. determination of the luminosity function, which could lead one to mistakenly favor the quadratic redshift-distance law. We also present several complementary analyses of the density field of the sample; the galaxy density field is found to be close to homogeneous on large scales if the Hubble law is assumed, while this is not the case with the quadratic redshift-distance relation.Comment: 27 pages Latex (w/figures), ApJ, in press. Uses AAS macros, postscript also available at http://www.astro.princeton.edu/~library/preprints/pop682.ps.g

On a notion of maps between orbifolds, I. function spaces

This is the first of a series of papers which are devoted to a comprehensive theory of maps between orbifolds. In this paper, we define the maps in the more general context of orbispaces, and establish several basic results concerning the topological structure of the space of such maps. In particular, we show that the space of such maps of C^r-class between smooth orbifolds has a natural Banach orbifold structure if the domain of the map is compact, generalizing the corresponding result in the manifold case. Motivations and applications of the theory come from string theory and the theory of pseudoholomorphic curves in symplectic orbifolds.Comment: Final version, 46 pages. Accepted for publication in Communications in Contemporary Mathematics. A preliminary version of this work is under a different title "A homotopy theory of orbispaces", arXiv: math. AT/010202

Numerical Model Studies of the Martian Mesoscale Circulations

Studies concerning mesoscale topographical effects on Martian flows examined low-level jets in the near equatorial latitudes and the dynamical intensification of flow by steep terrain. Continuation of work from previous years included evaluating the dissipation of cold air mass outbreaks due to enhanced sensible heat flux, further sensitivity and scaling evaluations for generalization of the characteristics of Martian mesoscale circulation caused by horizontal sensible heat-flux gradients, and evaluations of the significance that non-uniform surface would have on enhancing the polar CO2 ice sublimation during the spring. The sensitivity of maximum and minimum atmospheric temperatures to changes in wind speed, surface albedo, and deep soil temperature was investigated

Wigner function and Schroedinger equation in phase space representation

We discuss a family of quasi-distributions (s-ordered Wigner functions of Agarwal and Wolf) and its connection to the so called phase space representation of the Schroedinger equation. It turns out that although Wigner functions satisfy the Schroedinger equation in phase space they have completely different interpretation.Comment: 6 page

Decoherence in elastic and polaronic transport via discrete quantum states

Here we study the effect of decoherence on elastic and polaronic transport via discrete quantum states. The calculations are performed with the help of nonperturbative computational scheme, based on the Green's function theory within the framework of polaron transformation (GFT-PT), where the many-body electron-phonon interaction problem is mapped exactly into a single-electron multi-channel scattering problem. In particular, the influence of dephasing and relaxation processes on the shape of the electrical current and shot noise curves is discussed in detail under the linear and nonlinear transport conditions.Comment: 11 pages, 3 figure

NetMod: A Design Tool for Large-Scale Heterogeneous Campus Networks

The Network Modeling Tool (NetMod) uses simple analytical models to provide the designers of large interconnected local area networks with an in-depth analysis of the potential performance of these systems. This tool can be used in either a university, industrial, or governmental campus networking environment consisting of thousands of computer sites. NetMod is implemented with a combination of the easy-to-use Macintosh software packages HyperCard and Excel. The objectives of NetMod, the analytical models, and the user interface are described in detail along with its application to an actual campus-wide network.http://deepblue.lib.umich.edu/bitstream/2027.42/107971/1/citi-tr-90-1.pd

Diffusion, thermalization and optical pumping of YbF molecules in a cold buffer gas cell

We produce YbF molecules with a density of 10^18 m^-3 using laser ablation inside a cryogenically-cooled cell filled with a helium buffer gas. Using absorption imaging and absorption spectroscopy we study the formation, diffusion, thermalization and optical pumping of the molecules. The absorption images show an initial rapid expansion of molecules away from the ablation target followed by a much slower diffusion to the cell walls. We study how the time constant for diffusion depends on the helium density and temperature, and obtain values for the YbF-He diffusion cross-section at two different temperatures. We measure the translational and rotational temperatures of the molecules as a function of time since formation, obtain the characteristic time constant for the molecules to thermalize with the cell walls, and elucidate the process responsible for limiting this thermalization rate. Finally, we make a detailed study of how the absorption of the probe laser saturates as its intensity increases, showing that the saturation intensity is proportional to the helium density. We use this to estimate collision rates and the density of molecules in the cell.Comment: 20 pages, 11 figures, minor revisions following referee suggestion