Acceleration radiation, transition probabilities, and trans-Planckian physics

An important question in the derivation of the acceleration radiation, which also arises in Hawking's derivation of black hole radiance, is the need to invoke trans-Planckian physics for the quantum field that originates the created quanta. We point out that this issue can be further clarified by reconsidering the analysis in terms of particle detectors, transition probabilities, and local two-point functions. By writing down separate expressions for the spontaneous- and induced-transition probabilities of a uniformly accelerated detector, we show that the bulk of the effect comes from the natural (non trans-Planckian) scale of the problem, which largely diminishes the importance of the trans-Planckian sector. This is so, at least, when trans-Planckian physics is defined in a Lorentz invariant way. This analysis also suggests how to define and estimate the role of trans-Planckian physics in the Hawking effect itself.Comment: 19 page

Phosphorus-containing imide resins

Bis- and tris-imides derived from tris (m-aminophenyl) phosphine oxides by reaction with maleic anhydride or its derivatives, and addition polymers of such imides, including a variant in which a mono-imide is condensed with a dianhydride and the product is treated with a further quantity of maleic anhydride. Such monomers or their oligomes may be used to impregnate fibers and fabrics which when cured, are flame resistant. Also an improved method of producing tris (m-aminophenyl) phosphine oxides from the nitro analogues by reduction with hydrazine hydrate using palladized charcoal or Raney nickel as the catalyst is described

Elastomer-modified phosphorus-containing imide resins

Phosphine oxide-containing polyimide resins modified by elastomers, are disclosed which have improved mechanical properties. These products are particularly useful in the production of fiber or fabric-reinforced composites or laminates

Phosphorus-containing bisimide resins

The production of fire-resistant resins particularly useful for making laminates with inorganic fibers such as graphite fibers is discussed. The resins are by (1) condensation of an ethylenically unsaturated cyclic anhydride with a bis(diaminophenyl) phosphine oxide, and (2) by addition polymerization of the bisimide so obtained. Up to about 50%, on a molar basis, of benzophenonetetracarboxylic acid anhydride can be substituted for some of the cyclic anhydride to alter the properties of the products. Graphite cloth laminates made with these resins show 800 C char yields greater than 70% by weight in nitrogen. Limiting oxygen indexes of more than 100% are determined for these resins

The H\alpha\ surface brightness - radius relation: a robust statistical distance indicator for planetary nebulae

Measuring the distances to Galactic planetary nebulae (PNe) has been an intractable problem for many decades. We have now established a robust optical statistical distance indicator, the H$\alpha$ surface brightness- radius or S-r relation, which addresses this problem. We developed this relation from a critically evaluated sample of primary calibrating PNe. The robust nature of the method results from our revised calibrating distances with significantly reduced systematic uncertainties, and the recent availability of high-quality data, including updated nebular diameters and integrated H$\alpha$ fluxes. The S-r technique is simple in its application, requiring only an angular size, an integrated H\alpha\ flux, and the reddening to the PN. From these quantities, an intrinsic radius is calculated, which when combined with the angular size, yields the distance directly. Furthermore, we have found that optically thick PNe tend to populate the upper bound of the trend, while optically-thin PNe fall along the lower boundary in the S-r plane. This enables sub-trends to be developed which offer even better precision in the determination of distances, as good as 18 per cent in the case of optically-thin, high-excitation PNe. This is significantly better than any previous statistical indicator. We use this technique to create a catalogue of statistical distances for over 1100 Galactic PNe, the largest such compilation in the literature to date. Finally, in an appendix, we investigate both a set of transitional PNe and a range of PN mimics in the S-r plane, to demonstrate its use as a diagnostic tool. Interestingly, stellar ejecta around massive stars plot on a tight locus in S-r space with the potential to act as a separate distance indicator for these objects.Comment: 49 pages, 17 tables, 8 figures. Published in MNRAS; supplementary tables are included at end of this manuscrip

Phosphorus-containing imide resins

Cured polymers of bis and tris-imides derived from tris(m-aminophenyl) phosphine oxides by reaction with maleic anhydride or its derivatives, and addition polymers of such imides, including a variant in which a monoimide is condensed with a dianhydride and the product is treated with a further quantity of maleic anhydride prior to curing are disclosed and claimed. Such polymers are flame resistant. Also disclosed are an improved method of producing tris(m-aminophenyl) phosphine oxides from the nitro analogues by reduction with hydrazine hydrate using palladized charcoal or Raney nickel as the catalyst and fiber reinforced cured resin composites

Inflation, Renormalization, and CMB Anisotropies

In single-field, slow-roll inflationary models, scalar and tensorial (Gaussian) perturbations are both characterized by a zero mean and a non-zero variance. In position space, the corresponding variance of those fields diverges in the ultraviolet. The requirement of a finite variance in position space forces its regularization via quantum field renormalization in an expanding universe. This has an important impact on the predicted scalar and tensorial power spectra for wavelengths that today are at observable scales. In particular, we find a non-trivial change in the consistency condition that relates the tensor-to-scalar ratio "r" to the spectral indices. For instance, an exact scale-invariant tensorial power spectrum, n_t=0, is now compatible with a non-zero ratio r= 0.12 +/- 0.06, which is forbidden by the standard prediction (r=-8n_t). Forthcoming observations of the influence of relic gravitational waves on the CMB will offer a non-trivial test of the new predictions.Comment: 4 pages, jpconf.cls, to appear in the Proceedings of Spanish Relativity Meeting 2009 (ERE 09), Bilbao (Spain

Performance of computer-optimized tapered-roller bearings to 2.4 million DN

The performance of 120.65 mm bore high speed design tapered roller bearings was investigated at shaft speeds to 20,000 rpm under combined thrust and radial load. The test bearing design was computer optimized for high speed operation. Temperature distribution and bearing heat generation were determined as a function of shaft speed, radial and thrust loads, lubricant flow rates, and lubricant inlet temperature. The roller bearing operated successfully at shaft speeds up to 20,000 rpm under heavy thrust and radial loads. Cup cooling was effective in decreasing the high cup temperatures to levels equal to the cone temperature

Lubrication of optimized-design tapered-roller bearings to 2.4 million DN

The performance of 120.65 mm (4.75 in.) bore high speed design, tapered roller bearings was investigated at shaft speeds to 20,000 rpm (2.4 million DN) under combined thrust and radial load. The test bearing design was computer optimized for high speed operation. Temperature distribution bearing heat generation were determined as a function of shaft speed, radial and thrust loads, lubricant flow rates, and lubricant inlet temperature. The high speed design, tapered roller bearing operated successfully at shaft speeds up to 20,000 rpm under heavy thrust and radial loads. Bearing temperatures and heat generation with the high speed design bearing were significantly less than those of a modified standard bearing tested previously. Cup cooling was effective in decreasing the high cup temperatures to levels equal to the cone temperature

Endurance tests with large-bore tapered-roller bearings to 2.2 million DN

Endurance life tests were run with standard design and optimized high-speed design 120.65-mm-(4.750-in.-) bore tapered-roller bearings at shaft speeds of 12,500 and 18,500 rpm, respectively. Standard design bearings of vacuum melted AISI 4320 and CBS-1000M, and high-speed design bearings of CBS-1000M and through-hardened AISI M-50 were run under heavy combined radial and thrust load until fatigue failure or until a preset cutoff time of 1100 hours was reached. Standard design bearings made from CBS 1000M material ran to a 10 percent life approximately six times rated catalog life. Twelve identical bearings of AISI 4320 material ran to ten times rated catalog life without failure. Cracking and fracture of the cones of AISI M-50 high-speed design bearings occurred at 18,500 rpm due to high tensile hoop stresses. Four CBS 1000M high-speed design bearings ran to twenty-four times rated catalog life without any spalling, cracking or fracture failures