Strong-field tidal distortions of rotating black holes: II. Horizon dynamics from eccentric and inclined orbits

In a previous paper, we developed tools for studying the horizon geometry of a Kerr black hole that is tidally distorted by a binary companion using techniques that require large mass ratios but can be applied to any bound orbit and allow for arbitrary black hole spin. We now apply these tools to generic Kerr black hole orbits. This allows us to investigate horizon dynamics: the tidal field perturbing the horizon's geometry varies over a generic orbit, with significant variations for eccentric orbits. Many of the features of the horizon's behavior found previously carry over to the dynamical case in a natural way. In particular, we find significant offsets between the applied tide and the horizon's response. This leads to bulging in the horizon's geometry which can lag or lead the orbit, depending upon the hole's rotation and the orbit's geometry. An interesting and apparently new feature we find are small-amplitude, high-frequency oscillations in the horizon's response. We have not been able to identify a mechanism for producing these oscillations, but find that they appear most clearly when rapidly rotating black holes are distorted by very strong-field orbits.Comment: 24 pages, 15 figures. Final accepted version, to appear in Phys. Rev.

Strong-field tidal distortions of rotating black holes: III. Embeddings in hyperbolic 3-space

In previous work, we developed tools for quantifying the tidal distortion of a black hole's event horizon due to an orbiting companion. These tools use techniques which require large mass ratios (companion mass $\mu$ much smaller than black hole mass $M$), but can be used for arbitrary bound orbits, and for any black hole spin. We also showed how to visualize these distorted black holes by embedding their horizons in a global Euclidean 3-space, ${\mathbb{E}}^3$. Such visualizations illustrate interesting and important information about horizon dynamics. Unfortunately, we could not visualize black holes with spin parameter $a_* > \sqrt{3}/2 \approx 0.866$: such holes cannot be globally embedded into ${\mathbb{E}}^3$. In this paper, we overcome this difficulty by showing how to embed the horizons of tidally distorted Kerr black holes in a hyperbolic 3-space, ${\mathbb{H}}^3$. We use black hole perturbation theory to compute the Gaussian curvatures of tidally distorted event horizons, from which we build a two-dimensional metric of their distorted horizons. We develop a numerical method for embedding the tidally distorted horizons in ${\mathbb{H}}^3$. As an application, we give a sequence of embeddings into ${\mathbb{H}}^3$ of a tidally interacting black hole with spin $a_*=0.9999$. A small amplitude, high frequency oscillation seen in previous work shows up particularly clearly in these embeddings.Comment: 10 pages, 6 figure

LIVESTOCK FUTURES MARKETS AND RATIONAL PRICE FORMATION: EVIDENCE FOR LIVE CATTLE AND LIVE HOGS

The efficiency of livestock futures markets continues to receive attention, particularly with regard to their forward pricing or forecasting ability. The purpose of this paper is to present a more general theory that encompasses the forward pricing concept. It is argued that futures contract prices for competitively produced nonstorable commodities, such as live cattle and live hogs, follow a rational formation process. Futures contract prices reflect expected market conditions when contracts are sufficiently close to the delivery month that the supply of the underlying commodity cannot be changed. However, prior to the period when future supplies are relatively fixed, futures contract prices should adjust to reflect the competitive equilibrium, where output price equals average costs of production. Presented evidence suggests that live cattle and live hog futures markets support the rational price formation hypothesis: prices for distant contracts reflect average costs of feeding. Implications for risk management strategies are considered.Demand and Price Analysis, Livestock Production/Industries,

Black Symposium Correspondence between Stephen Hughes and Rhody McCoy on Participating in Symposium on Black America

A letter from University faculty member Stephen Hughes, written on January 8, 1969 to Rhody McCoy, Unit Administrator of Ocean Hill-Brownsville Demonstration School District in Brooklyn New York, to participate in the Symposium on Black America. Rhody McCoy responded on January 15, 1969 accepting the invitation to speak at the Symposium. After the Symposium Stephen Hughes wrote to Rhody McCoy on February 24, 1969 to give thanks for participating in the Symposium and included a check of payment. The last page is a poster created to showcase Rhody McCoy\u27s talk at the University on Monday February 17 at Eight PM in 137 Bennett Hall continuing the series of the Symposium on Black America

Black Symposium_Correspondence between Stephen Hughes and Rhody McCoy on Participating in Symposium on Black America

A letter from University faculty member Stephen Hughes, written on January 8, 1969 to Rhody McCoy, Unit Administrator of Ocean Hill-Brownsville Demonstration School District in Brooklyn New York, to participate in the Symposium on Black America. Rhody McCoy responded on January 15, 1969 accepting the invitation to speak at the Symposium. After the Symposium Stephen Hughes wrote to Rhody McCoy on February 24, 1969 to give thanks for participating in the Symposium and included a check of payment. The last page is a poster created to showcase Rhody McCoy\u27s talk at the University on Monday February 17 at Eight PM in 137 Bennett Hall continuing the series of the Symposium on Black America.https://digitalcommons.library.umaine.edu/racial_justice/1015/thumbnail.jp

Strong-field tidal distortions of rotating black holes: Formalism and results for circular, equatorial orbits

Tidal coupling between members of a compact binary system can have an interesting and important influence on that binary's dynamical inspiral. Tidal coupling also distorts the binary's members, changing them (at lowest order) from spheres to ellipsoids. At least in the limit of fluid bodies and Newtonian gravity, there are simple connections between the geometry of the distorted ellipsoid and the impact of tides on the orbit's evolution. In this paper, we develop tools for investigating tidal distortions of rapidly rotating black holes using techniques that are good for strong-field, fast-motion binary orbits. We use black hole perturbation theory, so our results assume extreme mass ratios. We develop tools to compute the distortion to a black hole's curvature for any spin parameter, and for tidal fields arising from any bound orbit, in the frequency domain. We also develop tools to visualize the horizon's distortion for black hole spin $a/M \le \sqrt{3}/2$ (leaving the more complicated $a/M > \sqrt{3}/2$ case to a future analysis). We then study how a Kerr black hole's event horizon is distorted by a small body in a circular, equatorial orbit. We find that the connection between the geometry of tidal distortion and the orbit's evolution is not as simple as in the Newtonian limit.Comment: 37 pages, 8 figures. Accepted for publication to Physical Review D. This version corrects a number of typographical errors found when reviewing the page proof

Dynamics of face and annular seals with two-phase flow

A detailed study was made of face and annular seals under conditions where boiling, i.e., phase change of the leaking fluid, occurs within the seal. Many seals operate in this mode because of flashing due to pressure drop and/or heat input from frictional heating. Some of the distinctive behavior characteristics of two phase seals are discussed, particularly their axial stability. The main conclusions are that seals with two phase flow may be unstable if improperly balanced. Detailed theoretical analyses of low (laminar) and high (turbulent) leakage seals are presented along with computer codes, parametric studies, and in particular a simplified PC based code that allows for rapid performance prediction: calculations of stiffness coefficients, temperature and pressure distributions, and leakage rates for parallel and coned face seals. A simplified combined computer code for the performance prediction over the laminar and turbulent ranges of a two phase flow is described and documented. The analyses, results, and computer codes are summarized

Deployable Aeroshell Flexible Thermal Protection System Testing

Deployable aeroshells offer the promise of achieving larger aeroshell surface areas for entry vehicles than otherwise attainable without deployment. With the larger surface area comes the ability to decelerate high-mass entry vehicles at relatively low ballistic coefficients. However, for an aeroshell to perform even at the low ballistic coefficients attainable with deployable aeroshells, a flexible thermal protection system (TPS) is required that is capable of surviving reasonably high heat flux and durable enough to survive the rigors of construction handling, high density packing, deployment, aerodynamic loading and aerothermal heating. The Program for the Advancement of Inflatable Decelerators for Atmospheric Entry (PAIDAE) is tasked with developing the technologies required to increase the technology readiness level (TRL) of inflatable deployable aeroshells, and one of several of the technologies PAIDAE is developing for use on inflatable aeroshells is flexible TPS. Several flexible TPS layups were designed, based on commercially available materials, and tested in NASA Langley Research Center's 8 Foot High Temperature Tunnel (8ft HTT). The TPS layups were designed for, and tested at three different conditions that are representative of conditions seen in entry simulation analyses of inflatable aeroshell concepts. Two conditions were produced in a single run with a sting-mounted dual wedge test fixture. The dual wedge test fixture had one row of sample mounting locations (forward) at about half the running length of the top surface of the wedge. At about two thirds of the running length of the wedge, a second test surface drafted up at five degrees relative to the first test surface established the remaining running length of the wedge test fixture. A second row of sample mounting locations (aft) was positioned in the middle of the running length of the second test surface. Once the desired flow conditions were established in the test section the dual wedge test fixture, oriented at 5 degrees angle of attack down, was injected into the flow. In this configuration the aft sample mounting location was subjected to roughly twice the heat flux and surface pressure of the forward mounting location. The tunnel was run at two different conditions for the test series: 1) 'Low Pressure', and 2) 'High Pressure'. At 'Low Pressure' conditions the TPS layups were tested at 6W/cm2 and 11W/cm2 while at 'High Pressure' conditions the TPS layups were tested at 11W/cm2 and 20W/cm2. This paper details the test configuration of the TPS samples in the 8Ft HTT, the sample holder assembly, TPS sample layup construction, sample instrumentation, results from this testing, as well as lessons learned

Thermal Analysis and Testing of Candidate Materials for PAIDAE Inflatable Aeroshell

The Program to Advance Inflatable-Decelerators for Atmospheric Entry (PAIDAE) is a NASA project tasked with developing and evaluating viable inflatable-decelerator aeroshell geometries and materials. Thermal analysis of material layups supporting an inflatable aeroshell was completed in order to identify expected material response, failure times, and to establish an experimental test matrix to keep barrier layer materials from reaching critical temperature limits during thermal soak. Material layups were then tested in the 8- foot High Temperature Tunnel (8'HTT), where they were subjected to hypersonic aerothermal heating conditions, similar to those expected for a Mars entry. This paper presents a broad overview of the thermal analysis supporting multiple materials, and layup configurations tested in the 8'HTT at flight conditions similar to those that would be experienced during Mars entry trajectories. Direct comparison of TPS samples tested in the 8'HTT verify that the thermal model accurately predicted temperature profiles when there are up to four materials in the test layup. As the number of material layers in each test layup increase (greater than 4), the accuracy of the prediction decreases significantly. The inaccuracy of the model predictions for layups with more than four material layers is believed to be a result of the contact resistance values used throughout the model being inaccurate. In addition, the harsh environment of the 8'HTT, including hot gas penetrating through the material layers, could also be a contributing factor

Educational Needs of Southern Forest Landowners

South-central United States forest landowners were surveyed to determine their forestry-related educational needs and appropriate methods for promoting effective programs covering desired topics. The majority of respondents had not participated in past educational programs because they were unaware of their existence. Therefore, forestry professionals and university Extension personnel should inform and encourage nonindustrial private forest (NIPF) landowners to take advantage of available opportunities. They should also use tax rolls to develop forest landowner databases. Once developed, newsletters, pamphlets, brochures, or letters should be mailed to increase forest landowner knowledge and awareness of forestry-related educational programs and activities