Comparison of one-dimensional and quasi-one-dimensional Hubbard models from the variational two-electron reduced-density-matrix method

Minimizing the energy of an $N$-electron system as a functional of a two-electron reduced density matrix (2-RDM), constrained by necessary $N$-representability conditions (conditions for the 2-RDM to represent an ensemble $N$-electron quantum system), yields a rigorous lower bound to the ground-state energy in contrast to variational wavefunction methods. We characterize the performance of two sets of approximate constraints, (2,2)-positivity (DQG) and approximate (2,3)-positivity (DQGT) conditions, at capturing correlation in one-dimensional and quasi-one-dimensional (ladder) Hubbard models. We find that, while both the DQG and DQGT conditions capture both the weak and strong correlation limits, the more stringent DQGT conditions improve the ground-state energies, the natural occupation numbers, the pair correlation function, the effective hopping, and the connected (cumulant) part of the 2-RDM. We observe that the DQGT conditions are effective at capturing strong electron correlation effects in both one- and quasi-one-dimensional lattices for both half filling and less-than-half filling

Stellar Motions in the Polar Ring Galaxy NGC 4650A

We present the first measurement of the stellar kinematics in the polar ring of NGC 4650A. There is well defined rotation, with the stars and gas rotating in the same direction, and with similar amplitude. The gaseous and stellar kinematics suggest an approximately flat rotation curve, providing further support for the hypothesis that the polar material resides in a disk rather than in a ring. The kinematics of the emission line gas at and near the center of the S0 suggests that the polar disk lacks a central hole. We have not detected evidence for two, equal mass, counterrotating stellar polar streams, as is predicted in the resonance levitation model proposed by Tremaine & Yu. A merger seems the most likely explanation for the structure and kinematics of NGC 4650A.Comment: 4 pages, accepted for publication in ApJ Letter

Stationary Points of Scalar Fields Coupled to Gravity

We investigate the dynamics of gravity coupled to a scalar field using a non-canonical form of the kinetic term. It is shown that its singular point represents an attractor for classical solutions and the stationary value of the field may occur distant from the minimum of the potential. In this paper properties of universes with such stationary states are considered. We reveal that such state can be responsible for modern dark energy density.Comment: H. Kroger, invited talk, FFP6, Udine (2004), revised version with corrected author lis

Nucleation and growth of rolling contact failure of 440C bearing steel

A 'two-body' elasto-plastic finite element model of 2-dimensional rolling and rolling-plus-sliding was developed to treat the effect of surface irregularities. The model consists of a smooth cylinder in contact with a semi-infinite half-space that is either smooth or fitted with one of 0.4 microns deep or 7 microns deep groove, or a 0.4 microns high ridge-like asperity. The model incorporates elastic-linear-kinematic hardening-plastic (ELKP) and non-linear-kinematic hardening-plastic (NLKP) material constitutive relations appropriate for hardened bearing steel and the 440C grade. The calculated contact pressure distribution is Hertzian for smooth body contact, and it displays intense, stationary, pressure spikes superposed on the Hertzian pressure for contact with the grooved and ridged surface. The results obtained for the 0.4 microns deep groove compare well with those reported by Elsharkawy and Hamrock for an EHD lubricated contact. The effect of translating the counterface on the half space as opposed to indenting the half space with the counter face with no translation is studied. The stress and strain values near the surface are found to be similar for the two cases, whereas they are significantly different in the subsurface. It is seen that when tiny shoulders are introduced at the edge of the groove in the finite element model, the incremental plasticity and residual stresses are significantly higher in the vicinity of the right shoulder (rolling direction is from left to right) than at the left shoulder. This may explain the experimental observation that the spall nucleation occurs at the exit end of the artificially planted indents. Pure rolling calculations are compared with rolling + sliding calculations. For a coefficient of friction, mu = 0.1, the effect of friction is found to be small. Efforts were made to identify the material constitutive relations which best describe the deformation characteristics of the bearing steels in the initial few cycles. Elastic-linear-kinematic hardening-plastic (ELKP) material constitutive relations produce less net plastic deformation in the initial stages for a given stress, than seen in experiments. A new set of constitutive relations: non-linear-kinematic hardening-plastic (NLKP) was used. This material model produces more plasticity than the ELKP model and shows promise for treating the net distortions in the early stages. Techniques for performing experimental measurements that can be compared with the finite element calculations were devised. The measurements are being performed on 9mm-diameter, 440C steel cylindrical rolling elements in contact with 12.5 mm-diameter, 52100 steel balls in a 3-ball-rod fatigue test machine operating at 3600 RPM. Artificial, 7 microns deep, indents were inserted on the running track of the cylindrical rolling elements and profilometer measurements of these indents made, before and after the rolling. These preliminary measurements show that the indents are substantially deformed plastically in the process of rolling. The deformations of the groove calculated with the finite element model are comparable to those measured experimentally

The Stellar and Gas Kinematics of Several Irregular Galaxies

We present long-slit spectra of three irregular galaxies from which we determinethe stellar kinematics in two of the galaxies (NGC 1156 and NGC 4449) and ionized-gas kinematics in all three (including NGC 2366). We compare this to the optical morphology and to the HI kinematics of the galaxies. In the ionized gas, we see a linear velocity gradient in all three galaxies. In NGC 1156 we also detect a weak linear velocity gradient in the stars of (5+/-1/sin i) km/s/kpc to a radius of 1.6 kpc. The stars and gas are rotating about the same axis, but this is different from the major axis of the stellar bar which dominates the optical light of the galaxy. In NGC 4449 we do not detect organized rotation of the stars and place an upper limit of (3/sin i) km/s/kpc to a radius of 1.2 kpc. For NGC 4449, which has signs of a past interaction with another galaxy, we develop a model to fit the observed kinematics of the stars and gas. In this model the stellar component is in a rotating disk seen nearly face-on while the gas is in a tilted disk with orbits whose planes precess in the gravitational potential. This model reproduces the apparent counter-rotation of the inner gas of the galaxy. The peculiar orbits of the gas are presumed due to acquisition of gas in the past interaction.Comment: To be published in ApJ, November 20, 200

Spitzer reveals what's behind Orion's Bar

We present Spitzer Space Telescope observations of 11 regions SE of the Bright Bar in the Orion Nebula, along a radial from the exciting star theta1OriC, extending from 2.6 to 12.1'. Our Cycle 5 programme obtained deep spectra with matching IRS short-high (SH) and long-high (LH) aperture grid patterns. Most previous IR missions observed only the inner few arcmin. Orion is the benchmark for studies of the ISM particularly for elemental abundances. Spitzer observations provide a unique perspective on the Ne and S abundances by virtue of observing the dominant ionization states of Ne (Ne+, Ne++) and S (S++, S3+) in Orion and H II regions in general. The Ne/H abundance ratio is especially well determined, with a value of (1.01+/-0.08)E-4. We obtained corresponding new ground-based spectra at CTIO. These optical data are used to estimate the electron temperature, electron density, optical extinction, and the S+/S++ ratio at each of our Spitzer positions. That permits an adjustment for the total gas-phase S abundance because no S+ line is observed by Spitzer. The gas-phase S/H abundance ratio is (7.68+/-0.30)E-6. The Ne/S abundance ratio may be determined even when the weaker hydrogen line, H(7-6) here, is not measured. The mean value, adjusted for the optical S+/S++ ratio, is Ne/S = 13.0+/-0.6. We derive the electron density versus distance from theta1OriC for [S III] and [S II]. Both distributions are for the most part decreasing with increasing distance. A dramatic find is the presence of high-ionization Ne++ all the way to the outer optical boundary ~12' from theta1OriC. This IR result is robust, whereas the optical evidence from observations of high-ionization species (e.g. O++) at the outer optical boundary suffers uncertainty because of scattering of emission from the much brighter inner Huygens Region.Comment: 60 pages, 16 figures, 10 tables. MNRAS accepte

Clinical impact of double protease inhibitor boosting with Lopinavir/Ritonavir and Amprenavir as part of salvage antiretroviral therapy

Purpose: Double protease inhibitor (PI) boosting is being explored as a new strategy in salvage antiretroviral (ARV) therapy. However, if a negative drug interaction leads to decreased drug levels of either or both PIs, double PI boosting could lead to decreased virologic response. A negative drug interaction has been described between amprenavir (APV) and lopinavir/ritonavir (LPV/r). This observational cohort study assessed the virologic impact of the addition of APV to a salvage ARV regimen, which also contains LPV/r, compared to a regimen containing LPV/r alone. Method: Patients initiated on a salvage ARV regimen that included LPV/r obtained from the expanded access program in Toronto, Canada, were evaluated. APV (600-1,200 mg bid) was added at the discretion of the treating physician. Results: Using multivariate Cox proportional hazards models, we found that the addition of APV to a LPV/r-containing salvage regimen was not significantly associated with time to virologic suppression (< 50 copies/mL; adjusted hazard ratio [HR] = 0.75, p = .12) or with time to virologic rebound (adjusted HR = 1.46, p = .34). Those patients who received higher doses of APV had an increased chance of virologic suppression (p = .03). In a subset of 27 patients, the median LPV Ctrough was significantly lower in patients receiving APV (p = .04), and the median APV Ctrough was reduced compared to reported controls. Conclusion: Our data do not support an additional benefit in virologic reduction of double boosting with APV and LPV/r relative to LPV/r alone in salvage ARV therapy. Our study's limitations include its retrospective nature and the imbalance between the two groups potentially confounding the results. Although these factors were adjusted for in the multivariate analysis, a prospective randomized controlled trial is warranted to confirm our findings

Mechanisms of rolling contact spalling

The results of a study aimed at analyzing the mechanical material interactions responsible for rolling contact spalling of the 440 C steel, high pressure oxygen turbopump bearings are presented. A coupled temperature displacement finite element analysis of the effects of friction heating under the contact is presented. The contact is modelled as a stationary, heat generating, 2 dimensional indent in an elastic perfectly plastic half-space with heat fluxes up to 8.6 x 10000 KW/m sq comparable to those generated in the bearing. Local temperatures in excess of 1000 C are treated. The calculations reveal high levels of residual tension after the contact is unloaded and cools. Efforts to promote Mode 2/Mode 3 fatigue crack growth under cyclic torsion in hardened 440 C steel are described. Spalls produced on 440 C steel by a 3 ball/rod rolling contact testing machine were studied with scanning microscopy. The shapes of the cyclic, stress strain hysteresis loops displayed by hardened 440 C steel in cyclic torsion at room temperature are defined for the plastic strain amplitudes encountered in rolling/sliding contact. Results of these analyses are discussed in detail