Self-gravitating Newtonian disks revisited

Recent analytic results concerning stationary, self-gravitating fluids in Newtonian theory are discussed. We give a theorem that forbids infinitely extended fluids, depending on the assumed equation of state and the rotation law. This part extends previous results that have been obtained for static configurations. The second part discusses a Sobolev bound on the mass of the fluid and a rigorous Jeans-type inequality that is valid in the stationary case.Comment: A talk given at the Spanish Relativity Meeting in Portugal 2012. To appear in Progress in Mathematical Relativity, Gravitation and Cosmology, Proceedings of the Spanish Relativity Meeting ERE2012, University of Minho, Guimaraes, Portugal, 3-7 September 2012, Springer Proceedings in Mathematics & Statistics, Vol. 6

Geometry of Keplerian disk systems and bounds on masses of their components

We investigate accreting disk systems with polytropic gas in Keplerian motion. Numerical data and partial analytic results show that the self-gravitation of the disk speeds up its rotation -- its rotational frequency is larger than that given by the well known strictly Keplerian formula that takes into account the central mass only. Thus determination of central mass in systems with massive disks requires great care -- the strictly Keplerian formula yields only an upper bound. The effect of self-gravity depends on geometric aspects of disk configurations. Disk systems with a small (circa $10^{-4}$) ratio of the innermost radius to the outermost disk radius have the central mass close to the upper limit, but if this ratio is of the order of unity then the central mass can be smaller by many orders of magnitude from this bound.Comment: 20 pages, 10 figure

Investigation of low-cost fabrication of ablative heat shields

The fabrication, testing, and evaluation of materials and techniques employed in the fabrication of ablative heat shield panels are described. Results of this effort show projected reductions in labor man-hours for dielectric curing of panels when compared to panels molded in a steam-heated press. In addition, panels were fabricated with more than one density within the cross-section. These dual-density panels show significant weight and cost reduction potentials

Computation of forces in strongly nonlinear magnetic fields using higher-order eggshell algorithm

A novel version of the eggshell-based procedure for numerical computation of magnetic forces and torques acting on ferromagnetic bodies in highly nonlinear magnetic fields is presented. The procedure works with a fully adaptive higher-order finite element method developed for years in our research group, that is implemented in own code Agros2D and library Hermes. The power of the methodology and both codes is demonstrated on the solution of two typical examples: computation of the static characteristic of a magnetic actuator and torque characteristic of a flux-switched permanent-magnet machine. The results obtained are compared with data calculated by several other available codes

Theorem on the proportionality of inertial and gravitational masses in classical mechanics

We considered the problem of the proportionality of inertial and gravitational masses in classical mechanics. We found that the kinetic energy of a material mass point m in a circular motion with a constant angular velocity around another material point M depends only on its gravitational mass. This fact, together with the known result that the straight line is a circumference with an infinite radius, allowed us to prove the proportionality between the inertial and gravitational masses.Comment: ReVTeX file, 10p

On the stability of self-gravitating accreting flows

Analytic methods show stability of the stationary accretion of test fluids but they are inconclusive in the case of self-gravitating stationary flows. We investigate numerically stability of those stationary flows onto compact objects that are transonic and rich in gas. In all studied examples solutions appear stable. Numerical investigation suggests also that the analogy between sonic and event horizons holds for small perturbations of compact support but fails in the case of finite perturbations.Comment: 10 pages, accepted for publication in PR

FMEA and FTA Analyses of the Adhesive Joining Process using Electrically Conductive Adhesives

This paper introduces a formulation of appropriate risk estimation methods that can be used for improving of processes in the electronics area. Two risk assessment methods have been chosen with regard to the specifics of adhesive joining based on electrically conductive adhesives. The paper provides a combination of a failure mode and effect analysis (FMEA) and fault tree analysis (FTA) for optimizing of the joining process. Typical features and failures of the process are identified. Critical operations are found and actions for avoiding failures in these actions are proposed. A fault treehas been applied to the process in order to get more precise information about the steps and operations in the process, and the relations between these operations. The fault tree identifies potential failures of the process. Then the effects of the failures have been estimated by the failure mode and effect analysis method. All major differences between failure mode and effect analysis and fault tree analysis are defined and there is a discussion about how to use the two techniquescomplement each other and achieve more efficient results

Accretion and Structure of Radiating Disks

We studied a steadily accreting, geometrically thick disk model that selfconsistently takes into account selfgravitation of the polytropic gas, its interaction with the radiation and the mass accretion rate. The accreting mass is injected inward in the vicinity of the central $z=0$ plane, where also radiation is assumed to be created. The rest of the disk remains approximately stationary. Only conservation laws are employed and the gas-radiation interaction in the bulk of the disk is described in the thin-gas approximation. We demonstrate that this scheme is numerically viable and yields a structure of the bulk that is influenced by the radiation and (indirectly) by the prescribed mass accretion rate. The obtained disk configurations are typical for environments in Active Galactic Nuclei (AGN), with the central mass of the order of 10^7 M_{\astrosun} to 10^8 M_{\astrosun}, quasi-Keplerian rotation curves, disk masses ranging from about 10^6 M_{\astrosun} to 10^7 M_{\astrosun}, and the luminosity ranging from 10^6 L_{\astrosun} to 10^9 L_{\astrosun}. These luminosities are much lower than the corresponding Eddington limit.Comment: Changes according to the version accepted by Astronomy & Astrophysic