Effective Q Criterion for Disk Stability in an External Potential

The standard Q criterion (with Q > 1) describes the stability against local, axisymmetric perturbations in a disk supported by rotation and random motion. Most astrophysical disks, however, are under the influence of an external gravitational potential, which can significantly affect their stability. A typical example is a galactic disk embedded in a dark matter halo. Here, we do a linear perturbation analysis for a disk in an external potential and obtain a generalized dispersion relation and the effective stability criterion. An external potential, such as that due to the dark matter halo concentric with the disk, contributes to the unperturbed rotational field and significantly increases its stability. We obtain the values for the effective Q parameter for the Milky Way and for a low surface brightness galaxy, UGC 7321. We find that in each case the stellar disk by itself is barely stable and it is the dark matter halo that stabilizes the disk against local, axisymmetric gravitational instabilities. Thus, the dark matter halo is necessary to ensure local disk stability. This result has been largely missed so far because in practice the Q parameter for a galactic disk is obtained using the observed rotational field that already includes the effect of the halo

EFFECTIVE Q CRITERION FOR DISK STABILITY IN AN EXTERNAL POTENTIAL

standard Q criterion (with Q > 1) describes the stability against local, axisymmetric perturbations in a disk supported by rotation and random motion. Most astrophysical disks, however, are under the influence of an external gravitational potential, which can significantly affect their stability. A typical example is a galactic disk embedded in a dark matter halo. Here, we do a linear perturbation analysis for a disk in an external potential and obtain a generalized dispersion relation and the effective stability criterion. An external potential, such as that due to the dark matter halo concentric with the disk, contributes to the unperturbed rotational field and significantly increases its stability. We obtain the values for the effective Q parameter for the Milky Way and for a low surface brightness galaxy, UGC 7321. We find that in each case the stellar disk by itself is barely stable and it is the dark matter halo that stabilizes the disk against local, axisymmetric gravitational instabilities. Thus, the dark matter halo is necessary to ensure local disk stability. This result has been largely missed so far because in practice the Q parameter for a galactic disk is obtained using the observed rotational field that already includes the effect of the halo.

Mixed Mode Analysis of Obliquely Oriented Edge Cracked Semicircular Disk Under Compression

A new mixed-mode compression fracture specimen, obliquely oriented edge cracked semicircular disk (OECSD) is analyzed by extending pure opening mode configuration of edge cracked semicircular disk (ECSD) under Hertzian compression. Photoelastic experiments are conducted on two different specimens of OECSD of same size and different crack lengths and inclinations. Finite element method (FEM) is used to solve a number of cases of the problem varying crack length and crack inclination. FE results show a good match with experiments. Inclination of edge crack in OECSD can be so made as to obtain any mode-mixity ratio between zero and one and beyond for any crack length. The new specimen can be used for fracture testing under compression more conveniently than the existing ones in several ways.

Medieval pulse of great earthquakes in the central Himalaya: Viewing past activities on the frontal thrust

The Himalaya has experienced three great earthquakes during the last century1934 Nepal-Bihar, 1950 Upper Assam, and arguably the 1905 Kangra. Focus here is on the central Himalayan segment between the 1905 and the 1934 ruptures, where previous studies have identified a great earthquake between thirteenth and sixteenth centuries. Historical data suggest damaging earthquakes in A.D. 1255, 1344, 1505, 1803, and 1833, although their sources and magnitudes remain debated. We present new evidence for a great earthquake from a trench across the base of a 13m high scarp near Ramnagar at the Himalayan Frontal Thrust. The section exposed four south verging fault strands and a backthrust offsetting a broad spectrum of lithounits, including colluvial deposits. Age data suggest that the last great earthquake in the central Himalaya most likely occurred between A.D. 1259 and 1433. While evidence for this rupture is unmistakable, the stratigraphic clues imply an earlier event, which can most tentatively be placed between A.D. 1050 and 1250. The postulated existence of this earlier event, however, requires further validation. If the two-earthquake scenario is realistic, then the successive ruptures may have occurred in close intervals and were sourced on adjacent segments that overlapped at the trench site. Rupture(s) identified in the trench closely correlate with two damaging earthquakes of 1255 and 1344 reported from Nepal. The present study suggests that the frontal thrust in central Himalaya may have remained seismically inactive during the last similar to 700years. Considering this long elapsed time, a great earthquake may be due in the region.

5.4-MHz single-crystal silicon wine glass mode disk resonator with quality factor of 2 million

This paper reports the design and electrical characterization of a micromechanical disk resonator fabricated in single crystal silicon using a foundry SOI micromachining process. The microresonator has been selectively excited in the radial extensional and the wine glass modes by reversing the polarity of the DC bias voltage applied on selected drive electrodes around the resonant structure. The quality factor of the resonator vibrating in the radial contour mode was 8000 at a resonant frequency of 6.34 MHz at pressure below 10 mTorr vacuum. The highest measured quality factor of the resonator in the wine glass resonant mode was 1.9 × 106 using a DC bias voltage of 20 V at about the same pressure in vacuum; the resonant frequency was 5.43 MHz and the lowest motional resistance measured was approximately 17 kΩ using a DC bias voltage of 60 V applied across 2.7 μm actuation gaps. This corresponds to a resonant frequency-quality factor (f-Q) product of 1.02 × 1013, among the highest reported for single crystal silicon microresonators, and on par with the best quartz crystal resonators. The quality factor for the wine glass mode in air was approximately 10,000. © 2009 Elsevier B.V. All rights reserved.

Transmission Electron Microscopy Characterization of Laser Welding Cast Ni-Based Superalloy K418 Turbo Disk And Alloy Steel 42Crmo Shaft

Microstructure characterization is important for controlling the quality of laser welding. In the present work, a detailed microstructure characterization by transmission electron microscopy was carried out on the laser welding cast Ni-based superalloy K418 turbo disk and alloy steel 42CrMo shaft and an unambiguous identification of phases in the weldment was accomplished. It was found that there are gamma-FeCrNiC austenite solid solution dendrites as the matrix, (Nb, Ti) C type MC carbides, fine and dispersed Ni-3 Al gamma' phase as well as Laves particles in the interdendritic region of the seam zone. A brief discussion was given for their existence based on both kinetic and thermodynamic principles. (c) 2007 Elsevier B.V. All rights reserved.

Research on laser welding of cast Ni-based superalloy K418 turbo disk and alloy steel 42CrMo shaft

Exploratory experiments of laser welding cast Ni-based superalloy K418 turbo disk and alloy steel 42CrMo shaft were conducted. Microstructure of the welded seam was characterized by optical microscopy (OM), scanning electron microscopy (SEM), X-ray diffraction (XRD), energy-dispersive spectrometer (EDS). Mechanical properties of the welded seam were evaluated by microhardness and tensile strength testing. The corresponding mechanisms were discussed in detail. Results showed that the laser-welded seam had non-equilibrium solidified microstructures consisting of FeCr0.29Ni0.16C0.06 austenite solid solution dendrites as the dominant and some fine and dispersed Ni3Al gamma' phase and Laves particles as well as little amount of MC short stick or particle-like carbides distributed in the interdendritic regions. The average microhardness of the welded seam was relatively uniform and lower than that of the base metal due to partial dissolution and suppression of the strengthening phase gamma' to some extent. About 88.5% tensile strength of the base metal was achieved in the welded joint because of a non-full penetration welding and the fracture mechanism was a mixture of ductility and brittleness. The existence of some Laves particles in the welded seam also facilitated the initiation and propagation of the microcracks and microvoids and hence, the detrimental effects of the tensile strength of the welded joint. The present results stimulate further investigation on this field. (c) 2006 Elsevier B.V. All rights reserved.