The effect of planetary migration on the corotation resonance

The migration of a planet through a gaseous disc causes the locations of their resonant interactions to drift and can alter the torques exerted between the planet and the disc. We analyse the time-dependent dynamics of a non-coorbital corotation resonance under these circumstances. The ratio of the resonant torque in a steady state to the value given by Goldreich & Tremaine (1979) depends essentially on two dimensionless quantities: a dimensionless turbulent diffusion time-scale and a dimensionless radial drift speed. When the drift speed is comparable to the libration speed and the viscosity is small, the torque can become much larger than the unsaturated value in the absence of migration, but is still proportional to the large-scale vortensity gradient in the disc. Fluid that is trapped in the resonance and drifts with it acquires a vortensity anomaly relative to its surroundings. If the anomaly is limited by viscous diffusion in a steady state, the resulting torque is inversely proportional to the viscosity, although a long time may be required to achieve this state. A further, viscosity-independent, contribution to the torque comes from fluid that streams through the resonant region. In other cases, torque oscillations occur before the steady value is achieved. We discuss the significance of these results for the evolution of eccentricity in protoplanetary systems. We also describe the possible application of these findings to the coorbital region and the concept of runaway (or type III) migration. [Abridged]Comment: 15 pages, 6 figures, to be published in MNRA

Numerical nonlinear inelastic analysis of stiffened shells of revolution. Volume 3: Engineer's program manual for STARS-2P digital computer program

Engineering programming information is presented for the STARS-2P (shell theory automated for rotational structures-2P (plasticity)) digital computer program, and FORTRAN 4 was used in writing the various subroutines. The execution of this program requires the use of thirteen temporary storage units. The program was initially written and debugged on the IBM 370-165 computer and converted to the UNIVAC 1108 computer, where it utilizes approximately 60,000 words of core. Only basic FORTRAN library routines are required by the program: sine, cosine, absolute value, and square root

The evolution of a warped disc around a Kerr black hole

We consider the evolution of a warped disc around a Kerr black hole, under conditions such that the warp propagates in a wavelike manner. This occurs when the dimensionless effective viscosity, alpha, that damps the warp is less than the characteristic angular semi-thickness, H/R, of the disc. We adopt linearized equations that are valid for warps of sufficiently small amplitude in a Newtonian disc, but also account for the apsidal and nodal precession that occur in the Kerr metric. Through analytical and time-dependent studies, we confirm the results of Demianski & Ivanov, and of Ivanov & Illarionov, that such a disc takes on a characteristic warped shape. The inner part of the disc is not necessarily aligned with the equator of the hole, even in the presence of dissipation. We draw attention to the fact that this might have important implications for the directionality of jets emanating from discs around rotating black holes.Comment: 8 pages, 6 figures, to be published in MNRA

Instability of an accretion disk with a magnetically driven wind

We present a linear analysis of the stability of accretion disks in which angular momentum is removed by the magnetic torque exerted by a centrifugally driven wind. The effects of the dependence of the wind torque on field strength and inclination, the sub-Keplerian rotation due to magnetic forces, and the compression of the disk by the field are included. A WKB dispersion relation is derived for the stability problem. We find that the disk is always unstable if the wind torque is strong. At lower wind torques instability also occurs provided the rotation is close to Keplerian. The growth time scale of the instability can be as short as the orbital time scale. The instability is mainly the result of the sensitivity of the mass flux to changes in the inclination of the field at the disk surface. Magnetic diffusion in the disk stabilizes if the wind torque is small.Comment: Submitted to A&

What is a Church by Law Established?

This paper examines one narrow question which is raised tangentially by virtue of the Constitution Act 1867, section 93 and the Constitution Act 1982, section 29 as interpreted by the Supreme Court of Canada in the Reference Re An Act to Amend the Education Act: what is an established church? It argues that when a single church alone enjoys constitutionally entrenched state support for its schools to the exclusion of all other religious groups, the real legal question is not about the legal protection of that church as a religious minority, especially when the recipient of state support is the largest and most powerful religious group in Ontario and Canada. Rather, the real legal question is whether or not such exclusive support amounts to legal establishment of that privileged religious group. To determine the nature of establishment in legal theory, the author examines church establishments in England and Scotland, and in Canada prior to 1867, and concludes that the status of the Roman Catholic Church in Ontario today is probably that of a quasi-established church

Flannery O\u27Connor

The entire body or Flannery O\u27Connor\u27s published fiction can be found in two volumes, One, a Signet paperback called Three by Flannery O\u27Connor, contains her two novels and first short story collection, The other is the posthumous volume of short stories, Everything that Rises Must Converge. Miss O\u27Connor\u27s work has already been subjected to much critical analysis and will undoubtedly be subjected to a great deal more before there is substantial agreement on just what it is that she is saying. The purpose of this study is to consider her attitude toward her art; to examine her philosophy as a Christian writer; to analyze her use of allegory and symbolism, principally in her novels; and to compare briefly her work to that of one other modern author, Nathanael West, and one traditional author, Nathaniel Hawthorne

Development of a scanning electron mirror microscope

Scanning electron mirrors microscope design and developmen