Partial inner product spaces: Some categorical aspects

We make explicit in terms of categories a number of statements from the theory of partial inner product spaces (PIP spaces) and operators on them. In particular, we construct sheaves and cosheaves of operators on certain PIP spaces of practical interest.Comment: 21 page

Fully representable and *-semisimple topological partial *-algebras

We continue our study of topological partial *-algebras, focusing our attention to *-semisimple partial *-algebras, that is, those that possess a {multiplication core} and sufficiently many *-representations. We discuss the respective roles of invariant positive sesquilinear (ips) forms and representable continuous linear functionals and focus on the case where the two notions are completely interchangeable (fully representable partial *-algebras) with the scope of characterizing a *-semisimple partial *-algebra. Finally we describe various notions of bounded elements in such a partial *-algebra, in particular, those defined in terms of a positive cone (order bounded elements). The outcome is that, for an appropriate order relation, one recovers the \M-bounded elements introduced in previous works.Comment: 26 pages, Studia Mathematica (2012) to appea

Synthesis and analysis of jet fuels from shale oil and coal syncrudes

The technical problems involved in converting a significant portion of a barrel of either a shale oil or coal syncrude into a suitable aviation turbine fuel were studied. TOSCO shale oil, H-Coal and COED coal syncrudes were the starting materials. They were processed by distillation and hydrocracking to produce two levels of yield (20 and 40 weight percent) of material having a distillation range of approximately 422 to 561 K (300 F to 550 F). The full distillation range 311 to 616 K (100 F to 650 F) materials were hydrotreated to meet two sets of specifications (20 and 40 volume percent aromatics, 13.5 and 12.75 weight percent H, 0.2 and 0.5 weight percent S, and 0.1 and 0.2 weight percent N). The hydrotreated materials were distilled to meet given end point and volatility requirements. The syntheses were carried out in laboratory and pilot plant equipment scaled to produce thirty-two 0.0757 cu m (2-gal)samples of jet fuel of varying defined specifications. Detailed analyses for physical and chemical properties were made on the crude starting materials and on the products

From bare interactions, low--energy constants and unitary gas to nuclear density functionals without free parameters: application to neutron matter

We further progress along the line of Ref. [Phys. Rev. {\bf A 94}, 043614 (2016)] where a functional for Fermi systems with anomalously large $s$-wave scattering length $a_s$ was proposed that has no free parameters. The functional is designed to correctly reproduce the unitary limit in Fermi gases together with the leading-order contributions in the s- and p-wave channels at low density. The functional is shown to be predictive up to densities $\sim0.01$ fm$^{-3}$ that is much higher densities compared to the Lee-Yang functional, valid for $\rho < 10^{-6}$ fm$^{-3}$. The form of the functional retained in this work is further motivated. It is shown that the new functional corresponds to an expansion of the energy in $(a_s k_F)$ and $(r_e k_F)$ to all orders, where $r_e$ is the effective range and $k_F$ is the Fermi momentum. One conclusion from the present work is that, except in the extremely low--density regime, nuclear systems can be treated perturbatively in $-(a_s k_F)^{-1}$ with respect to the unitary limit. Starting from the functional, we introduce density--dependent scales and show that scales associated to the bare interaction are strongly renormalized by medium effects. As a consequence, some of the scales at play around saturation are dominated by the unitary gas properties and not directly to low-energy constants. For instance, we show that the scale in the s-wave channel around saturation is proportional to the so-called Bertsch parameter $\xi_0$ and becomes independent of $a_s$. We also point out that these scales are of the same order of magnitude than those empirically obtained in the Skyrme energy density functional. We finally propose a slight modification of the functional such that it becomes accurate up to the saturation density $\rho\simeq 0.16$ fm$^{-3}$

Fuels characterization studies

Current analytical techniques used in the characterization of broadened properties fuels are briefly described. Included are liquid chromatography, gas chromatography, and nuclear magnetic resonance spectroscopy. High performance liquid chromatographic ground-type methods development is being approached from several directions, including aromatic fraction standards development and the elimination of standards through removal or partial removal of the alkene and aromatic fractions or through the use of whole fuel refractive index values. More sensitive methods for alkene determinations using an ultraviolet-visible detector are also being pursued. Some of the more successful gas chromatographic physical property determinations for petroleum derived fuels are the distillation curve (simulated distillation), heat of combustion, hydrogen content, API gravity, viscosity, flash point, and (to a lesser extent) freezing point

Exact phase shifts for atom interferometry

In the case of an external Hamiltonian at most quadratic in position and momentum operators, we use the ABCD formulation of atom optics to establish an exact analytical phase shift expression for atom interferometers with arbitrary spatial or temporal beam splitter configurations. This result is expressed in terms of coordinates and momenta of the wave packet centers at the interaction vertices only

Tunneling study of cavity grade Nb: possible magnetic scattering at the surface

Tunneling spectroscopy was performed on Nb pieces prepared by the same processes used to etch and clean superconducting radio frequency (SRF) cavities. Air exposed, electropolished Nb exhibited a surface superconducting gap delta=1.55 meV, characteristic of clean, bulk Nb. However the tunneling density of states (DOS) was broadened significantly. The Nb pieces treated with the same mild baking used to improve the Q-slope in SRF cavities, reveal a sharper DOS. Good fits to the DOS were obtained using Shiba theory, suggesting that magnetic scattering of quasiparticles is the origin of the gapless surface superconductivity and a heretofore unrecognized contributor to the Q-slope problem of Nb SRF cavities.Comment: 3 pages, 3 figure

Improved Mean-Field Scheme for the Hubbard Model

Ground state energies and on-site density-density correlations are calculated for the 1-D Hubbard model using a linear combination of the Hubbard projection operators. The mean-field coefficients in the resulting linearized Equations of Motion (EOM) depend on both one-particle static expectation values as well as static two-particle correlations. To test the model, the one particle expectation values are determined self-consistently while using Lanczos determined values for the two particle correlation terms. Ground state energies and on-site density-density correlations are then compared as a function of $U$ to the corresponding Lanczos values on a 12 site Hubbard chain for 1/2 and 5/12 fillings. To further demonstrate the validity of the technique, the static correlation functions are also calculated using a similar EOM approach, which ignores the effective vertex corrections for this problem, and compares those results as well for a 1/2 filled chain. These results show marked improvement over standard mean-field techniques.Comment: 10 pages, 3 figures, text and figures as one postscript file -- does not need to be "TeX-ed". LA-UR-94-294

The theory of quantum levitators

We develop a unified theory for clocks and gravimeters using the interferences of multiple atomic waves put in levitation by traveling light pulses. Inspired by optical methods, we exhibit a propagation invariant, which enables to derive analytically the wave function of the sample scattering on the light pulse sequence. A complete characterization of the device sensitivity with respect to frequency or to acceleration measurements is obtained. These results agree with previous numerical simulations and confirm the conjecture of sensitivity improvement through multiple atomic wave interferences. A realistic experimental implementation for such clock architecture is discussed.Comment: 11 pages, 6 Figures. Minor typos corrected. Final versio