Properties of the series solution for Painlevé I

We present some observations on the asymptotic behaviour of the coefficients in the Laurent series expansion of solutions of the first Painlevé equation. For the general solution, explicit recursive formulae for the Taylor expansion of the tau-function around a zero are given, which are natural extensions of analogous formulae for the elliptic sigma function, as given by Weierstrass. Numerical and exact results on the symmetric solution which is singular at the origin are also presented

Uso do método de graus-dia para estimar a data de diferenciação da panícula de grupos de cultivares de arroz irrigado no Rio Grande do Sul.

bitstream/item/33519/1/documento-126.pd

The Evolution of the Galaxy Sizes in the NTT Deep Field: a Comparison with CDM Models

The sizes of the field galaxies with I<25 have been measured in the NTT Deep Field. Intrinsic sizes have been obtained after deconvolution of the PSF with a multigaussian method. The reliability of the method has been tested using both simulated data and HST observations of the same field. The distribution of the half light radii is peaked at r_{hl} 0.3 arcsec, in good agreement with that derived from HST images at the same magnitude. An approximate morphological classification has been obtained using the asymmetry and concentration parameters. The intrinsic sizes of the galaxies are shown as a function of their redshifts and absolute magnitudes using photometric redshifts derived from the multicolor catalog. While the brighter galaxies with morphological parameters typical of the normal spirals show a flat distribution in the range r_{d}=1-6 kpc, the fainter population at 0.4<z<0.8 dominates at small sizes. To explore the significance of this behaviour, an analytical rendition of the standard CDM model for the disc size evolution has been computed. The model showing the best fit to the local luminosity function and the Tully-Fisher relation is able to reproduce at intermediate redshifts a size distribution in general agreement with the observations, although it tends to underestimate the number of galaxies fainter than M_B~ -19 with disk sizes r_d~ 1-2 kpc.Comment: 16 pages, 11 figures, ApJ in press, Dec 199

Permutable entire functions satisfying algebraic differential equations

It is shown that if two transcendental entire functions permute, and if one of them satisfies an algebraic differential equation, then so does the other one.Comment: 5 page

The Effects of Gas Dynamics, Cooling, Star Formation, and Numerical Resolution in Simulations of Cluster Formation

We present the analysis of a suite of simulations of a Virgo mass galaxy cluster. Undertaken within the framework of standard cold dark matter cosmology, these simulations were performed at differing resolutions and with increasingly complex physical processes, with the goal of identifying the effects of each on the evolution of the cluster. We focus on the cluster at the present epoch and examine properties including the radial distributions of density, temperature, entropy and velocity. We also map `observable' projected properties such as the surface mass density, X-ray surface brightness and SZ signature. We identify significant differences between the simulations, which highlights the need for caution when comparing numerical simulations to observations of galaxy clusters. While resolution affects the inner density profile in dark matter simulations, the addition of a gaseous component, especially one that cools and forms stars, affects the entire cluster. We conclude that both resolution and included physical processes play an important role in simulating the formation and evolution of galaxy clusters. Therefore, physical inferences drawn from simulations that do not include a gaseous component that can cool and form stars present a poor representation of reality. (Abridged)Comment: Accepted for publication in the Astrophysical Journal. Several changes from previous version, including new materia

Correlations Between Central Massive Objects And Their Host Galaxies: From Bulgeless Spirals to Ellipticals

Recent observations by Ferrarese et al. (2006) and Wehner et al. (2006) reveal that a majority of galaxies contain a central massive object (CMO), either a supermassive black hole (SMBH) or a compact stellar nucleus, regardless of the galaxy mass or morphological type, and that there is a tight relation between the masses of CMOs and those of the host galaxies. Several recent studies show that feedback from black holes can successfully explain the \msigma correlation in massive elliptical galaxies that contain SMBHs. However, puzzles remain in spirals or dwarf spheroids that do not appear to have black holes but instead harbor a compact central stellar cluster. Here we use three-dimensional, smoothed particle hydrodynamics simulations of isolated galaxies to study the formation and evolution of CMOs in bulgeless disk galaxies, and simulations of merging galaxies to study the transition of the CMO--host mass relation from late-type bulgeless spirals to early-type ellipticals. Our results suggest that the observed correlations may be established primarily by the depletion of gas in the central region by accretion and star-formation, and may hold for all galaxy types. A systematic search for CMOs in the nuclei of bulgeless disk galaxies would offer a test of this conclusion. (Abridged)Comment: 11 pages, 8 figures, accepted to Ap

Gravitational Collapse in Turbulent Molecular Clouds. I. Gasdynamical Turbulence

Observed molecular clouds often appear to have very low star formation efficiencies and lifetimes an order of magnitude longer than their free-fall times. Their support is attributed to the random supersonic motions observed in them. We study the support of molecular clouds against gravitational collapse by supersonic, gas dynamical turbulence using direct numerical simulation. Computations with two different algorithms are compared: a particle-based, Lagrangian method (SPH), and a grid-based, Eulerian, second-order method (ZEUS). The effects of both algorithm and resolution can be studied with this method. We find that, under typical molecular cloud conditions, global collapse can indeed be prevented, but density enhancements caused by strong shocks nevertheless become gravitationally unstable and collapse into dense cores and, presumably, stars. The occurance and efficiency of local collapse decreases as the driving wave length decreases and the driving strength increases. It appears that local collapse can only be prevented entirely with unrealistically short wave length driving, but observed core formation rates can be reproduced with more realistic driving. At high collapse rates, cores are formed on short time scales in coherent structures with high efficiency, while at low collapse rates they are scattered randomly throughout the region and exhibit considerable age spread. We suggest that this naturally explains the observed distinction between isolated and clustered star formation.Comment: Minor revisions in response to referee, thirteen figures, accepted to Astrophys.

Aircraft engine with inter-turbine engine frame supported counter rotating low pressure turbine rotors

An aircraft gas turbine engine assembly includes an inter-turbine frame axially located between high and low pressure turbines. Low pressure turbine has counter rotating low pressure inner and outer rotors with low pressure inner and outer shafts which are at least in part rotatably disposed co-axially within a high pressure rotor. Inter-turbine frame includes radially spaced apart radially outer first and inner second structural rings disposed co-axially about a centerline and connected by a plurality of circumferentially spaced apart struts. Forward and aft sump members having forward and aft central bores are fixedly joined to axially spaced apart forward and aft portions of the inter-turbine frame. Low pressure inner and outer rotors are rotatably supported by a second turbine frame bearing mounted in aft central bore of aft sump member. A mount for connecting the engine to an aircraft is located on first structural ring

Semi-Analytical Models for the Formation of Disk Galaxies: I. Constraints from the Tully-Fisher Relation

We present new semi-analytical models for the formation of disk galaxies with the purpose of investigating the origin of the near-infrared Tully-Fisher (TF) relation. The models assume that disks are formed by cooling of the baryons inside dark halos with realistic density profiles, and that the baryons conserve their specific angular momentum. Only gas with densities above the critical density given by Toomre's stability criterion is considered eligible for star formation, and a simple recipe for supernovae feedback is included. We emphasize the importance of extracting the proper luminosity and velocity measures from the models, something that has often been ignored in the past. The observed K-band TF relation has a slope that is steeper than simple predictions based on dynamical arguments suggest. Taking the stability related star formation threshold densities into account steepens the TF relation, decreases its scatter, and yields gas mass fractions that are in excellent agreement with observations. In order for the TF slope to be as steep as observed, further physics are required. We argue that the characteristics of the observed near-infrared TF relation do not reflect systematic variations in stellar populations, or cosmological initial conditions, but are governed by feedback. Finally we show that our models provide a natural explanation for the small amount of scatter that makes the TF relation useful as a cosmological distance indicator.Comment: 20 pages, 10 figures. Accepted for publication in Ap