A Brief History of Curvature

The trace of the stress-energy tensor of the cosmological fluid, proportional to the Ricci scalar curvature in general relativity, is determined on cosmic scales for times ranging from the inflationary epoch to the present day in the expanding Universe. The post-inflationary epoch and the thermal history of the relativistic fluid, in particular the QCD transition from asymptotic freedom to confinement and the electroweak phase transition, leave significant imprints on the scalar curvature. These imprints can be of either sign and are orders of magnitude larger than the values that would be obtained by naively extrapolating the pressureless matter of the present epoch back into the radiation-dominated epoch.Comment: 13 pages, 8 figure

Micarta Propellers III : General Description of the Design

The design of propellers made of Micarta is discussed. The advantages of the material are noted, especially as compared with wood. The design changes necessitated by the use of Micarta are discussed with reference to the hub boss, the narrowing of the blade tips, the thinning of the blades, the angles of the leading and trailing edges, and the adjustment of the pitch. Results of flight tests show that the Micarta propeller gave a top speed of 2 miles per hour more than the wooden propeller while turning about 120 r.p.m slower, with about the same rate of climb. At top speed, the Micarta propeller shows an improvement of about 7 percent in fuel economy, although the plane is flying 2 miles per hour faster

Micarta propellers IV : technical methods of design

A description is given of the methods used in design of Micarta propellers. The most direct method for working out the design of a Micarta propeller is to start with the diameter and blade angles of a wooden propeller suited for a particular installation and then to apply one of the plan forms suitable for Micarta propellers. This allows one to obtain the corresponding blade widths and to then use these angles and blade widths for an aerodynamic analysis

Micarta propellers I : materials

Here, values for tension, compression edgewise of laminations, and transverse flatwise of laminations are given for Micarta made with various kinds of sheet material. The corresponding values for white oak are given for comparison. It was found by destructive and service tests that Micarta made with a good grade of cotton duck will give satisfactory service with most designs. In propellers having detachable blades, it is desirable that the root of the blade be of a small cross section to decrease the weight of the metal hub. Here the use of the special fabric or wood veneer offers advantages due to greater tensile strength. These materials, especially the wood veneer, produce stiffer blades than duck. This is also a value in controllable and reversible pitch designs where it is desirable that the plan form of the blades be symmetrical

Towards a future singularity?

We discuss whether the future extrapolation of the present cosmological state may lead to a singularity even in case of "conventional" (negative) pressure of the dark energy field, namely $w=p/\rho \geq -1$. The discussion is based on an often neglected aspect of scalar-tensor models of gravity: the fact that different test particles may follow the geodesics of different metric frames, and the need for a frame-independent regularization of curvature singularities.Comment: 8 pages. Essay written for the "2004 Awards for Essays on Gravitation" (Gravity Research Foundation, Wellesley Hills, MA, USA), and selected for "Honorable Mention

Formation of Black Holes from Collapsed Cosmic String Loops

The fraction of cosmic string loops which collapse to form black holes is estimated using a set of realistic loops generated by loop fragmentation. The smallest radius sphere into which each cosmic string loop may fit is obtained by monitoring the loop through one period of oscillation. For a loop with invariant length $L$ which contracts to within a sphere of radius $R$, the minimum mass-per-unit length $\mu_{\rm min}$ necessary for the cosmic string loop to form a black hole according to the hoop conjecture is $\mu_{\rm min} = R /(2 G L)$. Analyzing $25,576$ loops, we obtain the empirical estimate $f_{\rm BH} = 10^{4.9\pm 0.2} (G\mu)^{4.1 \pm 0.1}$ for the fraction of cosmic string loops which collapse to form black holes as a function of the mass-per-unit length $\mu$ in the range $10^{-3} \lesssim G\mu \lesssim 3 \times 10^{-2}$. We use this power law to extrapolate to $G\mu \sim 10^{-6}$, obtaining the fraction $f_{\rm BH}$ of physically interesting cosmic string loops which collapse to form black holes within one oscillation period of formation. Comparing this fraction with the observational bounds on a population of evaporating black holes, we obtain the limit $G\mu \le 3.1 (\pm 0.7) \times 10^{-6}$ on the cosmic string mass-per-unit-length. This limit is consistent with all other observational bounds.Comment: uuencoded, compressed postscript; 20 pages including 7 figure