Multi-Transition Study of M51's Molecular Gas Spiral Arms

Two selected regions in the molecular gas spiral arms in M51 were mapped with the Owens Valley Radio Observatory (OVRO) mm-interferometer in the 12CO(2-1), 13CO(1-0), C18O(1-0), HCN(1-0) and HCO+(1-0) emission lines. The CO data have been combined with the 12CO(1-0) data from Aalto et al. (1999) covering the central 3.5kpc to study the physical properties of the molecular gas. All CO data cubes were short spacing corrected using IRAM 30m (12CO(1-0): NRO 45m) single dish data. A large velocity gradient (LVG) analysis finds that the giant molecular clouds (GMCs) are similar to Galactic GMCs when studied at 180pc (120pc) resolution with an average kinetic temperature of T_kin = 20(16)K and H_2 density of n(H_2) = 120(240)cm^(-3) when assuming virialized clouds (a constant velocity gradient dv/dr. The associated conversion factor between H_2 mass and CO luminosity is close to the Galactic value for most regions analyzed. Our findings suggest that the GMC population in the spiral arms of M51 is similar to those of the Milky Way and therefore the strong star formation occurring in the spiral arms has no strong impact on the molecular gas in the spiral arms. Extinction inferred from the derived H_2 column density is very high (A_V about 15 - 30 mag), about a factor of 5-10 higher than the average value derived toward HII regions. Thus a significant fraction of the ongoing star formation could be hidden inside the dust lanes of the spiral arms. A comparison of MIPS 24um and H_alpha data, however, suggests that this is not the case and most of the GMCs studied here are not (yet) forming stars. We also present low (4.5") resolution OVRO maps of the HCN(1-0) and HCO+(1-0) emission at the location of the brightest 12CO(1-0) peak.Comment: 41 pages, 12 figures, 7 tables; accepted for publication by Ap

A Compact Introduction to a Generalized Extreme Value Theorem

In a short paper published just one year prior to his thesis, Maurice Frechet gives a simple generalization one what we might today call the Extreme value theorem. This generalization is a simple matter of coming up with ``the right definitions in order to make this work. In this mini PSP, we work through Frechet\u27s entire 1.5 page paper to give an extreme value theorem in more general topological spaces, ones which, to use Frechet\u27s newly coined term, are compact

Type II Quantum Computing Algorithm for Computational Fluid Dynamics

An algorithm is presented to simulate fluid dynamics on a three qubit type II quantum computer: a lattice of small quantum computers that communicate classical information. The algorithm presented is called a three qubit factorized quantum lattice gas algorithm. It is modeled after classical lattice gas algorithms which move virtual particles along an imaginary lattice and change the particles’ momentums using collision rules when they meet at a lattice node. Instead of moving particles, the quantum algorithm presented here moves probabilities, which interact via a unitary collision operator. Probabilities are determined using ensemble measurement and are moved with classical communications channels. The lattice node spacing is defined to be a microscopic scale length. A mesoscopic governing equation for the lattice is derived for the most general three qubit collision operator which preserves particle number. In the continuum limit of the lattice, a governing macroscopic partial differential equation—the diffusion equation—is derived for a particular collision operator using a Chapman- Enskog expansion. A numerical simulation of the algorithm is carried out on a conventional desktop computer and compared to the analytic solution of the diffusion equation. The simulation agrees very well with the known solution

The Effects of Estrogen on Dorsal Root Ganglion Neurons

Skin sensation is mediated by dorsal root ganglion (DRG) neurons. Data indicates that skin sensitivity in female rats is estrogen-dependent. Some DRG neurons have estrogen receptors (ERs) which are regulated by estrogen. In these cells, nerve growth factor (NGF) and estrogen receptors colocalize. Regulation of NGF receptors and neuronal sensitivity to NGF may allow estrogen to regulate NGF-dependent genes. The goals of the present study were to determine which DRG neurons express the ER gene and to analyze the effects of long-term estrogen administration on the interrelated expression of tyrosine kinase A (trkA), preprotachykinin (PPT), and 68kD neurofilament (NF) genes and to compare warm thermal withdrawal latencies in these animals. The hypothesis tested by the current study was that estrogen upregulates trkA and by doing so, increases the sensitivity of NGF-receptive neurons to the growth factor. Three groups of ovariectomized (OVX) Sprague-Dawley rats were used: OVX (no replacement), 1X (low dose) and 10X (high dose). The replacement groups received daily Premarin injections. Rats from each group were killed at 56 or 90 days and their lumbar DRGs harvested. ER mRNA localization was done by in situ hybridization. Results showed that ER mRNA was of low abundance, but was evident in smaller neurons. Quantification revealed that both trkA and PPT mRNA was downregulated in both estrogen replacement groups at both time points when compared to the OVX group. TrkA mRNA was localized predominantly in small DRG neurons. PPT mRNA was restricted to small neurons. Estrogen treatment slowed warm thermal plantar withdrawal, but not significantly. Neurofilament mRNA levels were dramatically increased by 56 days of estrogen treatment in a dose-dependent manner in all size populations of DRG neurons. Ninety days of estrogen treatment had a similar effect. These data indicate that estrogen regulates DRG neuronal gene expression. An overlapping population of DRG neurons express the ER, trkA and PPT genes. Estrogen may regulate the trkA and PPT genes by altering NGF sensitivity. Since the ER gene does not appear to be expressed by all DRG neurons, the effect of estrogen on neurofilament gene expression must involve alternative mechanisms

The Cantor Set Before Cantor

A special construction used in both analysis and topology today is known as the Cantor set. Cantor used this set in a paper in the 1880s. Yet it appeared as early as 1875 in a paper by the Irish mathematician Henry John Stephen Smith (1826 - 1883). Smith, who is best known for the Smith normal form of a matrix, was a professor at Oxford who made great contributions in matrix theory and number theory. In this project, we will explore parts of a paper he wrote titled On the Integration of Discontinuous Functions

Topology From Analysis

Topology is often described as having no notion of distance, but a notion of nearness. How can such a thing be possible? Isn\u27t this just a distinction without a difference? In this project, we will discover the notion of nearness without distance by studying the work of Georg Cantor and a problem he was investigating involving Fourier series. We will see that it is the relationship of points to each other, and not their distances per se, that is a proper view. We will see the roots of topology organically springing from analysis