The Generalized Ricci Flow for 3D Manifolds with One Killing Vector

We consider 3D flow equations inspired by the renormalization group (RG) equations of string theory with a three dimensional target space. By modifying the flow equations to include a U(1) gauge field, and adding carefully chosen De Turck terms, we are able to extend recent 2D results of Bakas to the case of a 3D Riemannian metric with one Killing vector. In particular, we show that the RG flow with De Turck terms can be reduced to two equations: the continual Toda flow solved by Bakas, plus its linearizaton. We find exact solutions which flow to homogeneous but not always isotropic geometries

Geophysical characteristics and crustal structure of greenstone terranes: Canadian Shield

Geophysical studies in the Canadian Shield have provided some insights into the tectonic setting of greenstone belts. Greenstone belts are not rooted in deep crustal structures. Geophysical techniques consistently indicate that greenstones are restricted to the uppermost 10 km or so of crust and are underlain by geophysically normal crust. Gravity models suggest that granitic elements are similarly restricted, although magnetic modelling suggests possible downward extension to the intermediate discontinuity around approx. 18 km. Seismic evidence demonstrates that steeply-dipping structure, which can be associated with the belts in the upper crust, is not present in the lower crust. Horizontal intermediate discontinuities mapped under adjacent greenstone and granitic components are not noticeably disrupted in the boundary zone. Geophysical evidence points to the presence of discontinuities between greenhouse-granite and adjacent metasedimentary erranes. Measured stratigraphic thicknesses of greenstone belts are often twice or more the vertical thicknesses determined from gravity modelling. Explantations advanced for the discrepancy include stratigraphy repeated by thrust faulting and/or listric normal faulting, mechanisms which are consistent with certain aspects of conceptual models of greenstone development. Where repetition is not a factor the gravity evidence points to removal of the root zones of greenstone belts. For one region, this has been attributed to magmatic stopping during resurgent caldera activity

Circles in the Sky: Finding Topology with the Microwave Background Radiation

If the universe is finite and smaller than the distance to the surface of last scatter, then the signature of the topology of the universe is writ large on the microwave background sky. We show that the microwave background will be identified at the intersections of the surface of last scattering as seen by different ``copies'' of the observer. Since the surface of last scattering is a two-sphere, these intersections will be circles, regardless of the background geometry or topology. We therefore propose a statistic that is sensitive to all small, locally homogeneous topologies. Here, small means that the distance to the surface of last scatter is smaller than the ``topology scale'' of the universe.Comment: 14 pages, 10 figures, IOP format. This paper is a direct descendant of gr-qc/9602039. To appear in a special proceedings issue of Class. Quant. Grav. covering the Cleveland Topology & Cosmology Worksho

Hormonal Regulation of Glucocorticoid Inactivation and Reactivation in aT3-1 and LßT2 Gonadotroph Cells

The regulation of reproductive function by glucocorticoids occurs at all levels of the hypothalamo-pituitary-gonadal axis. Within the pituitary, glucocorticoids have been shown to directly alter gene expression in gonadotrophs, indicating that these cell types are sensitive to regulation by the glucocorticoid receptor. Whilst the major glucocorticoid metabolising enzymes, 11β-hydroxysteroid dehydrogenase (11βHSD; HSD11B1 and HSD11B2), have been described in human pituitary adenomas, the activity of these enzymes within different pituitary cell types has not been reported. Radiometric conversion assays were performed in αT3-1, LβT2 (gonadotrophs), AtT-20 (corticotrophs) and GH3 (somatolactotrophs) anterior pituitary cell lines, using tritiated cortisol, corticosterone, cortisone or 11-dehydrocorticosterone as substrates. The net oxidation of cortisol/corticosterone and net reduction of cortisone/11-dehydrocorticosterone were significantly higher in the two gonadotroph cells lines compared with the AtT-20 and GH3 cells after 4 h. Whilst these enzyme activities remained the same in αT3-1 and LβT2 cells over a 24 h period, there was a significant increase in glucocorticoid metabolism in both AtT-20 and GH3 cells over this same period, suggesting cell-type specific activity of the 11βHSD enzyme(s). Stimulation of both gonadotroph cell lines with either 100 nM GnRH or PACAP (known physiological regulators of gonadotrophs) resulted in significantly increased 11β-dehydrogenase (11βDH) and 11-ketosteroid reductase (11KSR) activities, over both 4 and 24 h. These data reveal that gonadotroph 11βHSD enzyme activity can act to regulate local glucocorticoid availability to mediate the influence of the HPA axis on gonadotroph function

Quadri-tilings of the plane

We introduce {\em quadri-tilings} and show that they are in bijection with dimer models on a {\em family} of graphs $\{R^*\}$ arising from rhombus tilings. Using two height functions, we interpret a sub-family of all quadri-tilings, called {\em triangular quadri-tilings}, as an interface model in dimension 2+2. Assigning "critical" weights to edges of $R^*$, we prove an explicit expression, only depending on the local geometry of the graph $R^*$, for the minimal free energy per fundamental domain Gibbs measure; this solves a conjecture of \cite{Kenyon1}. We also show that when edges of $R^*$ are asymptotically far apart, the probability of their occurrence only depends on this set of edges. Finally, we give an expression for a Gibbs measure on the set of {\em all} triangular quadri-tilings whose marginals are the above Gibbs measures, and conjecture it to be that of minimal free energy per fundamental domain.Comment: Revised version, minor changes. 30 pages, 13 figure

Measuring Topological Chaos

The orbits of fluid particles in two dimensions effectively act as topological obstacles to material lines. A spacetime plot of the orbits of such particles can be regarded as a braid whose properties reflect the underlying dynamics. For a chaotic flow, the braid generated by the motion of three or more fluid particles is computed. A ``braiding exponent'' is then defined to characterize the complexity of the braid. This exponent is proportional to the usual Lyapunov exponent of the flow, associated with separation of nearby trajectories. Measuring chaos in this manner has several advantages, especially from the experimental viewpoint, since neither nearby trajectories nor derivatives of the velocity field are needed.Comment: 4 pages, 6 figures. RevTeX 4 with PSFrag macro

Soft phonons and structural phase transitions in La1.875_{1.875}Ba0.125_{0.125}CuO4_{4}

Soft phonon behavior associated with a structural phase transition from the low-temperature-orthorhombic (LTO) phase ($Bmab$ symmetry) to the low-temperature-tetragonal (LTT) phase ($P4_{2}/ncm$ symmetry) was investigated in La$_{1.875}$Ba$_{0.125}$CuO$_{4}$ using neutron scattering. As temperature decreases, the TO-mode at $Z$-point softens and approaches to zero energy around $T_{\rm d2}=62$ K, where the LTO -- LTT transition occurs. Below $T_{\rm d2}$, the phonon hardens quite rapidly and it's energy almost saturates below 50 K. At $T_{\rm d2}$, the energy dispersion of the soft phonon along in-plane direction significantly changes while the dispersion along out-of-plane direction is almost temperature independent. Coexistence between the LTO phase and the LTT phase, seen in both the soft phonon spectra and the peak profiles of Bragg reflection, is discussed in context of the order of structural phase transitions.Comment: 6 pages, 8 figure

Black Holes in Three Dimensional Topological Gravity

We investigate the black hole solution to (2+1)-dimensional gravity coupled to topological matter, with a vanishing cosmological constant. We calculate the total energy, angular momentum and entropy of the black hole in this model and compare with results obtained in Einstein gravity. We find that the theory with topological matter reverses the identification of energy and angular momentum with the parameters in the metric, compared with general relativity, and that the entropy is determined by the circumference of the inner rather than the outer horizon. We speculate that this results from the contribution of the topological matter fields to the conserved currents. We also briefly discuss two new possible (2+1)-dimensional black holes.Comment: 14 pages, LateX, UNB Tech. Rep. 94-03, UCD- 94-3

Physical Conditions in the Narrow-Line Region of M51

We have investigated the physical conditions in the narrow-line region (NLR) of M51 using long-slit spectra obtained with the Space Telescope Imaging Spectrograph (STIS) aboard the Hubble Space Telescope (HST) and 3.6 cm radio continuum observations obtained with the Very Large Array (VLA). Emission-line diagnostics were employed for nine NLR clouds, which extend 2.5" (102 pc) from the nucleus, to examine the electron density, temperature, and ionization state of the NLR gas. The emission-line ratios are consistent with those typically found in Seyfert nuclei and indicate that within the inner near-nuclear region (r ~< 1") the ionization decreases with increasing radius. Upper-limits to the [O III] electron temperature (T ~< 11,000 K) for the inner NLR clouds indicate that photoionization is the dominant ionization mechanism close to the nucleus. The emission-line fluxes for most of the NLR clouds can be reproduced reasonably well by simple photoionization models using a central power-law continuum source and supersolar nitrogen abundances. Shock+precursor models, however, provide a better fit to the observed fluxes of an NLR cloud ~2.5" south of the nucleus that is identified with the extra-nuclear cloud (XNC). The large [O III] electron temperature of this cloud (T = 24,000 K) further suggests the presence of shocks. This cloud is straddled by two radio knots and lies near the location where a weak radio jet, ~2.5" (102pc) in extent, connects the near-nuclear radio emission with a diffuse lobe structure spanning \~4" (163 pc). It is plausible that this cloud represents the location where the radio jet impinges on the disk ISM.Comment: 25 pages, 26 figures (9 color), 7 tables. Accepted for publication in the Astrophysical Journa