Time-dependent Circulation Flows: Iron Enrichment in Cooling Flows with Heated Return Flows

We describe a new type of dynamical model for hot gas in galaxy groups and clusters in which gas moves simultaneously in both radial directions. Circulation flows are consistent with (1) the failure to observe cooling gas in X-ray spectra, (2) multiphase gas observed near the centers of these flows and (3) the accumulation of iron in the hot gas from Type Ia supernovae in the central galaxy. Dense inflowing gas cools, producing a positive central temperature gradient, as in normal cooling flows. Bubbles of hot, buoyant gas flow outward. Circulation flows eventually cool catastrophically if the outward flowing gas transports mass but no heat; to maintain the circulation both mass and energy must be supplied to the inflowing gas over a large volume, extending to the cooling radius. The rapid radial recirculation of gas produces a flat central core in the gas iron abundance, similar to many observations. We believe the circulation flows described here are the first gasdynamic, long-term evolutionary models that are in good agreement with all essential features observed in the hot gas: little or no gas cools as required by XMM spectra, the gas temperature increases outward near the center, and the gaseous iron abundance is about solar near the center and decreases outward.Comment: 17 pages (emulateapj5) with 6 figures; accepted by The Astrophysical Journa

Compound transfer matrices: Constructive and destructive interference

Scattering from a compound barrier, one composed of a number of distinct non-overlapping sub-barriers, has a number of interesting and subtle mathematical features. If one is scattering classical particles, where the wave aspects of the particle can be ignored, the transmission probability of the compound barrier is simply given by the product of the transmission probabilities of the individual sub-barriers. In contrast if one is scattering waves (whether we are dealing with either purely classical waves or quantum Schrodinger wavefunctions) each sub-barrier contributes phase information (as well as a transmission probability), and these phases can lead to either constructive or destructive interference, with the transmission probability oscillating between nontrivial upper and lower bounds. In this article we shall study these upper and lower bounds in some detail, and also derive bounds on the closely related process of quantum excitation (particle production) via parametric resonance.Comment: V1: 28 pages. V2: 21 pages. Presentation significantly streamlined and shortened. This version accepted for publication in the Journal of Mathematical Physic

Analytic calculation of energies and wave functions of the quartic and pure quartic oscillators

Ground state energies and wave functions of quartic and pure quartic oscillators are calculated by first casting the Schr\"{o}dinger equation into a nonlinear Riccati form and then solving that nonlinear equation analytically in the first iteration of the quasilinearization method (QLM). In the QLM the nonlinear differential equation is solved by approximating the nonlinear terms by a sequence of linear expressions. The QLM is iterative but not perturbative and gives stable solutions to nonlinear problems without depending on the existence of a smallness parameter. Our explicit analytic results are then compared with exact numerical and also with WKB solutions and it is found that our ground state wave functions, using a range of small to large coupling constants, yield a precision of between 0.1 and 1 percent and are more accurate than WKB solutions by two to three orders of magnitude. In addition, our QLM wave functions are devoid of unphysical turning point singularities and thus allow one to make analytical estimates of how variation of the oscillator parameters affects physical systems that can be described by the quartic and pure quartic oscillators.Comment: 8 pages, 12 figures, 1 tabl

Relativistic Charged Spheres II: Regularity and Stability

We present new results concerning the existence of static, electrically charged, perfect fluid spheres that have a regular interior and are arbitrarily close to a maximally charged black-hole state. These configurations are described by exact solutions of Einstein's field equations. A family of these solutions had already be found (de Felice et al., 1995) but here we generalize that result to cases with different charge distribution within the spheres and show, in an appropriate parameter space, that the set of such physically reasonable solutions has a non zero measure. We also perform a perturbation analysis and identify the solutions which are stable against adiabatic radial perturbations. We then suggest that the stable configurations can be considered as classic models of charged particles. Finally our results are used to show that a conjecture of Kristiansson et al. (1998) is incorrect.Comment: revtex, 13 pages. five EPS figures. Accepted by CQ

Heating Cooling Flows with Weak Shock Waves

The discovery of extended, approximately spherical weak shock waves in the hot intercluster gas in Perseus and Virgo has precipitated the notion that these waves may be the primary heating process that explains why so little gas cools to low temperatures. This type of heating has received additional support from recent gasdynamical models. We show here that outward propagating, dissipating waves deposit most of their energy near the center of the cluster atmosphere. Consequently, if the gas is heated by (intermittent) weak shocks for several Gyrs, the gas within 30-50 kpc is heated to temperatures that far exceed observed values. This heating can be avoided if dissipating shocks are sufficiently infrequent or weak so as not to be the primary source of global heating. Local PV and viscous heating associated with newly formed X-ray cavities are likely to be small, which is consistent with the low gas temperatures generally observed near the centers of groups and clusters where the cavities are located.Comment: 14 pages; Accepted by Ap

Maximizing Neumann fundamental tones of triangles

We prove sharp isoperimetric inequalities for Neumann eigenvalues of the Laplacian on triangular domains. The first nonzero Neumann eigenvalue is shown to be maximal for the equilateral triangle among all triangles of given perimeter, and hence among all triangles of given area. Similar results are proved for the harmonic and arithmetic means of the first two nonzero eigenvalues

Organization of the double-stranded RNA-activated protein kinase DAI and virus-associated VA RNAI in adenovirus-2-infected HeLa cells

We have examined the cellular distribution of the double-stranded RNA-activated protein kinase DAI in adenovirus 2 (Ad2)-infected and uninfected HeLa cells. In uninfected cells DAI was found to be concentrated in the cytoplasm. In addition, DAI was localized in the nucleoli and diffusely distributed throughout the nucleoplasm. Cells treated with alpha-interferon displayed a similar pattern of distribution for DAI. When RNA polymerase I activity was inhibited by the drug actinomycin D, nucleoli segregated and DAI was found to colocalize with the dense fibrillar region of the nucleoli. During mitosis, the distribution of DAI paralleled that of rRNA. In adenovirus-infected cells the localization of DAI was similar to that in uninfected interphase cells. VA RNAI was detected in Ad2-infected cells by 10-14 hours post-infection as fine dots in the nucleoplasm. By 18-24 hours post-infection, VA RNAI appeared in bigger and more abundant dots in the nucleoplasm and the cytoplasm was intensively labeled. Transient expression of the VA RNAI gene in uninfected cells resulted in a similar localization of the RNA. Our results are consistent with a role for DAI and VA RNAI in protein synthesis and suggest that DAI may play an early role in ribosome biogenesis in the nucleolus in addition to its cytoplasmic role in translation

A non-linear Oscillator with quasi-Harmonic behaviour: two- and nn-dimensional Oscillators

A nonlinear two-dimensional system is studied by making use of both the Lagrangian and the Hamiltonian formalisms. The present model is obtained as a two-dimensional version of a one-dimensional oscillator previously studied at the classical and also at the quantum level. First, it is proved that it is a super-integrable system, and then the nonlinear equations are solved and the solutions are explicitly obtained. All the bounded motions are quasiperiodic oscillations and the unbounded (scattering) motions are represented by hyperbolic functions. In the second part the system is generalized to the case of $n$ degrees of freedom. Finally, the relation of this nonlinear system with the harmonic oscillator on spaces of constant curvature, two-dimensional sphere $S^2$ and hyperbolic plane $H^2$, is discussed.Comment: 30 pages, 4 figures, submitted to Nonlinearit

Herschel PACS Observations and Modeling of Debris Disks in the Tucana-Horologium Association

We present Herschel PACS photometry of seventeen B- to M-type stars in the 30 Myr-old Tucana-Horologium Association. This work is part of the Herschel Open Time Key Programme "Gas in Protoplanetary Systems" (GASPS). Six of the seventeen targets were found to have infrared excesses significantly greater than the expected stellar IR fluxes, including a previously unknown disk around HD30051. These six debris disks were fitted with single-temperature blackbody models to estimate the temperatures and abundances of the dust in the systems. For the five stars that show excess emission in the Herschel PACS photometry and also have Spitzer IRS spectra, we fit the data with models of optically thin debris disks with realistic grain properties in order to better estimate the disk parameters. The model is determined by a set of six parameters: surface density index, grain size distribution index, minimum and maximum grain sizes, and the inner and outer radii of the disk. The best fitting parameters give us constraints on the geometry of the dust in these systems, as well as lower limits to the total dust masses. The HD105 disk was further constrained by fitting marginally resolved PACS 70 micron imaging.Comment: 15 pages, 7 figures, Accepted to Ap