Compact objects in general relativity: From Buchdahl stars to quasiblack holes

A Buchdahl star is a highly compact star for which the boundary radius [Formula: see text] obeys [Formula: see text], where [Formula: see text] is the gravitational radius of the star itself. A quasiblack hole is a maximum compact star, or more generically a maximum compact object, for which the boundary radius [Formula: see text] obeys [Formula: see text]. Quasiblack holes are objects on the verge of becoming black holes. Continued gravitational collapse ends in black holes and has to be handled with the Oppenheimer–Snyder formalism. Quasistatic contraction ends in a quasiblack hole and should be treated with appropriate techniques. Quasiblack holes, not black holes, are the real descendants of Mitchell and Laplace dark stars. Quasiblack holes have many interesting properties. We develop the concept of a quasiblack hole, give several examples of such an object, define what it is, draw its Carter–Penrose diagram, study its pressure properties, obtain its mass formula, derive the entropy of a nonextremal quasiblack hole and through an extremal quasiblack hole give a solution to the puzzling entropy of extremal black holes.

Production Decline Behavior Analysis of a Vertical Well with a Natural Water Influx/Waterflood

The production decline type curves are considered as a robust technique to interpret the production data and obtain the flow parameters, the original gas in place, etc. However, most of the previous models have focused on the primary depletion with a closed boundary, rather than on the secondary depletion with a water influx/waterflood. Therefore, in this study, a transient flow model considering the water influx/waterflood is developed. Subsequently, the functions of the production decline type curves for a vertical well with a water influx/waterflood are derived based on the material balance equation. In other words, the theory of Blasingame production decline analysis is extended to the water influx/waterflood reservoir. Further advanced Blasingame production decline type curves for a vertical well in water influx/waterflood reservoirs are generated. Compared with Blasingame type curves without a water influx/waterflood, the behavior of the ones presented in this study is quite different at the boundary. Thereafter, the effects of the relevant parameters, including the dimensionless maximum water influx, the dimensionless beginning time of the water influx, and the dimensionless external boundary radius, are studied on type curves. Finally, Blasingame type curves for a vertical well in water influx/waterflood reservoirs are verified through a field case study. This work provides very meaningful references for reservoir engineers working on the evaluation of the water influx and the estimation of the beginning time of the water influx by matching the developed type curves with the actual field data.

The role of three-body stability in tidally interacting globular clusters

The role of stability in the general three-body problem is investigated with regard to the tidal radius of a globular cluster (GC) in a galactic potential. This proceedings is a summary of two papers which outline the stability method (Kennedy 2014a) and compare the predicted stability boundary radius to observations of velocity dispersion profiles in Milky Way GCs (Kennedy 2014b).

Fractal Analysis and Fractography: What Can we Learn that’s New?

The tenets of fractography are well known. The principles of fractal geometry have been applied to fracture surfaces for several decades. How these two fields can be used in a synergistic manner eludes many. The key element in discovering that a fracture surface is fractal is that the features we observe with the naked or aided eye also occur at the atomic scale! Thus, we should be able to interpret the mirror, mist and hackle boundaries in terms of atomic bond breaking. I will present a consistent hypothesis for relating the bond breaking process at the atomic scale to the features we all observe on the fracture surface of materials. I suggest these can be related through one equation: 2 = E a0 D*, where  is the fracture energy, E is the elastic modulus, a0 is a characteristic dimension related to the structure of the material, and D* is the fractal dimensional increment. In turn, D* = c/r1 for which c is the crack size and r1 is the mirror mist boundary radius. Thus, the energy expended in fracture at the atomic scale is encoded on the fracture surface features we observe. The novel combination of fractography, fracture mechanics and fractal geometry can be combined to create a powerful tool for forensic analysis, research investigations and production analyses.

THE CHARACTERISTIC BOUNDARY RADII OF ATOMS

The characteristic boundary radius of an atom has been defined as the distance from the classical turning point of electronic motion to the nucleus of the atom. With the ab initio method, the atomic boundary radii for elements from H through Xe are calculated. For the atoms in the same group, the radii defined in this way are of good linear relationship with the empirical radii commonly accepted, such as the van der Waals and covalent atomic radii determined by experimental data.

On generalized-vortex boundary layers

We define a generalized vortex to have azimuthal velocity proportional to a power of radiusr−n. The properties of the steady laminar boundary layer generated by such a vortex over a fixed coaxial disk of radiusaare examined. Though the boundary-layer thickness is zero a t the edge of the disk, reversals of the radial component of velocity u must occur, so that an extra boundary condition is needed at any interior boundary radiusrEto make the structure unique. Numerical integrations of the unsteady governing equations were carried out forn= − 1, 0, ½ and 1. Whenn= 0 and − 1 solutions of the self-similar equations are known for an infinite disk. Assuming terminal similarity to fix the boundary conditions atr=rEwhenur> 0, a consistent solution was found which agrees with those of the self-similar equations whenrEis small. However, ifn= ½ and 1, no similarity solutions are known, although the terminal structure forn= 1 was deduced earlier by the present authors. From the numerical integration forn= ½, we are able to deduce the limit structure forr→ 0 by using a combination of analytic and numerical techniques with the proviso of a consistent self-similar form asrE→ 0. The structure is then analogous to a ladder consisting of an infinite number of regions where viscosity may be neglected, each separated by much thinner viscous transitional regions playing the role of the rungs. This structure appears to be characteristic of all generalized vortices for which 0.1217 <n< 1.

An Exploratory Study of Stress Concentrations in Thermal Shock Fields

Exploratory investigations were performed on the effect of stress concentrations upon the stresses generated in a free elastic plane space by thermal shock applied to the boundary. The emphasis was on a search for a general upper bound to the stresses induced in a plane space of arbitrary shape by a temperature change T0 applied to the boundary of the space. Theory indicates that, when a thermal shock penetrates into a plane elastic space a distance less than half the local boundary radius of curvature, then αET0 would be the magnitude of the upper bound and the stress field would be confined to a boundary layer. In order to obtain the reported results it was necessary to obtain temperature and fringe pattern data within 10 sec from initiation of thermal shock. The experimental program to accomplish this result is reported in detail.