9,098 research outputs found
Convergence Analysis and Error Estimates for a Second Order Accurate Finite Element Method for the Cahn-Hilliard-Navier-Stokes System
In this paper, we present a novel second order in time mixed finite element
scheme for the Cahn-Hilliard-Navier-Stokes equations with matched densities.
The scheme combines a standard second order Crank-Nicholson method for the
Navier-Stokes equations and a modification to the Crank-Nicholson method for
the Cahn-Hilliard equation. In particular, a second order Adams-Bashforth
extrapolation and a trapezoidal rule are included to help preserve the energy
stability natural to the Cahn-Hilliard equation. We show that our scheme is
unconditionally energy stable with respect to a modification of the continuous
free energy of the PDE system. Specifically, the discrete phase variable is
shown to be bounded in and the discrete
chemical potential bounded in , for any time
and space step sizes, in two and three dimensions, and for any finite final
time . We subsequently prove that these variables along with the fluid
velocity converge with optimal rates in the appropriate energy norms in both
two and three dimensions.Comment: 33 pages. arXiv admin note: text overlap with arXiv:1411.524
Saturated hydrocarbon polymeric binder for advanced solid propellant and hybrid solid grains Quarterly report no. 3, 1 May - 31 Jul. 1966
Saturated hydrocarbon polymeric binder for advanced solid propellant and hybrid solid grain
Saturated hydrocarbon polymeric binder for advanced solid propellant and hybrid solid grains Quarterly report no. 2, 1 Feb. - 30 Apr. 1966
Synthesis and analysis of ethylene-neohexene copolymers with other non ketene-imine group free radicals for solid and hybrid grain propellant saturated hydrocarbon binder progra
Polychart contour plotter enables data extrapolation from multiple plotting charts
A polychart contour plotter is used to reduce the data from all 19 antenna pattern charts to a one-chart form
The Detectability of AGN Cavities in Cooling-Flow Clusters
Chandra X-ray Observatory has revealed X-ray cavities in many nearby cooling
flow clusters. The cavities trace feedback from the central active galactic
nulceus (AGN) on the intracluster medium (ICM), an important ingredient in
stabilizing cooling flows and in the process of galaxy formation and evolution.
But, the prevalence and duty cycle of such AGN outbursts is not well
understood. To this end, we study how the cooling is balanced by the cavity
heating for a complete sample of clusters (the Brightest 55 clusters of
galaxies, hereafter B55). In the B55, we found 33 cooling flow clusters, 20 of
which have detected X-ray bubbles in their ICM. Among the remaining 13, all
except Ophiuchus could have significant cavity power yet remain undetected in
existing images. This implies that the duty cycle of AGN outbursts with
significant heating potential in cooling flow clusters is at least 60 % and
could approach 100 %, but deeper data is required to constrain this further.Comment: 4 pages, 2 figures; to appear in the proceedings of "The Monsters'
Fiery Breath", Madison, Wisconsin 1-5 June 2009, Eds. Sebastian Heinz & Eric
Wilcots; added annotation to the figur
X-ray Supercavities in the Hydra A Cluster and the Outburst History of the Central Galaxy's Active Nucleus
A 227 ksec Chandra Observatory X-ray image of the hot plasma in the Hydra A
cluster has revealed an extensive cavity system. The system was created by a
continuous outflow or a series of bursts from the nucleus of the central galaxy
over the past 200-500 Myr. The cavities have displaced 10% of the plasma within
a 300 kpc radius of the central galaxy, creating a swiss-cheese-like topology
in the hot gas. The surface brightness decrements are consistent with empty
cavities oriented within 40 degrees of the plane of the sky. The outflow has
deposited upward of 10^61 erg into the cluster gas, most of which was propelled
beyond the inner ~100 kpc cooling region. The supermassive black hole has
accreted at a rate of approximately 0.1-0.25 solar masses per year over this
time frame, which is a small fraction of the Eddington rate of a ~10^9 solar
mass black hole, but is dramatically larger than the Bondi rate. Given the
previous evidence for a circumnuclear disk of cold gas in Hydra A, these
results are consistent with the AGN being powered primarily by infalling cold
gas. The cavity system is shadowed perfectly by 330 MHz radio emission. Such
low frequency synchrotron emission may be an excellent proxy for X-ray cavities
and thus the total energy liberated by the supermassive black hole.Comment: 8 pages, 3 figures; Submitted to ApJ, revised per referee's
suggestion
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