Electronic instabilities of a Hubbard model approached as a large array of coupled chains: competition between d-wave superconductivity and pseudogap phase

We study the electronic instabilities in a 2D Hubbard model where one of the dimensions has a finite width, so that it can be considered as a large array of coupled chains. The finite transverse size of the system gives rise to a discrete string of Fermi points, with respective electron fields that, due to their mutual interaction, acquire anomalous scaling dimensions depending on the point of the string. Using bosonization methods, we show that the anomalous scaling dimensions vanish when the number of coupled chains goes to infinity, implying the Fermi liquid behavior of a 2D system in that limit. However, when the Fermi level is at the Van Hove singularity arising from the saddle points of the 2D dispersion, backscattering and Cooper-pair scattering lead to the breakdown of the metallic behavior at low energies. These interactions are taken into account through their renormalization group scaling, studying in turn their influence on the nonperturbative bosonization of the model. We show that, at a certain low-energy scale, the anomalous electron dimension diverges at the Fermi points closer to the saddle points of the 2D dispersion. The d-wave superconducting correlations become also large at low energies, but their growth is cut off as the suppression of fermion excitations takes place first, extending progressively along the Fermi points towards the diagonals of the 2D Brillouin zone. We stress that this effect arises from the vanishing of the charge stiffness at the Fermi points, characterizing a critical behavior that is well captured within our nonperturbative approach.Comment: 13 pages, 7 figure

Refined a posteriori error estimation for classical and pressure-robust Stokes finite element methods

Recent works showed that pressure-robust modifications of mixed finite element methods for the Stokes equations outperform their standard versions in many cases. This is achieved by divergence-free reconstruction operators and results in pressure independent velocity error estimates which are robust with respect to small viscosities. In this paper we develop a posteriori error control which reflects this robustness. The main difficulty lies in the volume contribution of the standard residual-based approach that includes the $L^2$-norm of the right-hand side. However, the velocity is only steered by the divergence-free part of this source term. An efficient error estimator must approximate this divergence-free part in a proper manner, otherwise it can be dominated by the pressure error. To overcome this difficulty a novel approach is suggested that uses arguments from the stream function and vorticity formulation of the Navier--Stokes equations. The novel error estimators only take the $\mathrm{curl}$ of the right-hand side into account and so lead to provably reliable, efficient and pressure-independent upper bounds in case of a pressure-robust method in particular in pressure-dominant situations. This is also confirmed by some numerical examples with the novel pressure-robust modifications of the Taylor--Hood and mini finite element methods

Development of dynamic calibration methods for POGO pressure transducers

Two dynamic pressure sources are described for the calibration of pogo pressure transducers used to measure oscillatory pressures generated in the propulsion system of the space shuttle. Rotation of a mercury-filled tube in a vertical plane at frequencies below 5 Hz generates sinusoidal pressures up to 48 kPa, peak-to-peak; vibrating the same mercury-filled tube sinusoidally in the vertical plane extends the frequency response from 5 Hz to 100 Hz at pressures up to 140 kPa, peak-to-peak. The sinusoidal pressure fluctuations can be generated by both methods in the presence of high pressures (bias) up to 55 MPa. Calibration procedures are given in detail for the use of both sources. The dynamic performance of selected transducers was evaluated using these procedures; the results of these calibrations are presented. Calibrations made with the two sources near 5 Hz agree to within 3% of each other

A dynamic pressure source for the calibration of pressure transducers

A dynamic pressure source is described for producing sinusoidally varying pressures of up to 34 kPa zero to peak, over the frequency range of approximately 50 Hz to 2 kHz. The source is intended for the dynamic calibration of pressure transducers. The transducer to be calibrated is mounted near the base of the thick walled aluminum tube forming the vessel so that the pressure sensitive element is in contact with the liquid in the tube. A section of the tube is filled with small steel balls to damp the motion of the 10-St dimethyl siloxane working fluid in order to extend the useful frquency range to higher frequencies than would be provided by an undamped system. The dynamic response of six transducers provided by the sponsor was evaluated using the pressure sources; the results of these calibrations are given

Magneto-Roton Modes of the Ultra Quantum Crystal: Numerical Study

The Field Induced Spin Density Wave phases observed in quasi-one-dimensional conductors of the Bechgaard salts family under magnetic field exhibit both Spin Density Wave order and a Quantized Hall Effect, which may exhibit sign reversals. The original nature of the condensed phases is evidenced by the collective mode spectrum. Besides the Goldstone modes, a quasi periodic structure of Magneto-Roton modes, predicted to exist for a monotonic sequence of Hall Quantum numbers, is confirmed, and a second mode is shown to exist within the single particle gap. We present numerical estimates of the Magneto-Roton mode energies in a generic case of the monotonic sequence. The mass anisotropy of the collective mode is calculated. We show how differently the MR spectrum evolves with magnetic field at low and high fields. The collective mode spectrum should have specific features, in the sign reversed "Ribault Phase", as compared to modes of the majority sign phases. We investigate numerically the collective mode in the Ribault Phase.Comment: this paper incorporates material contained in a previous cond-mat preprint cond-mat/9709210, but cannot be described as a replaced version, because it contains a significant amount of new material dealing with the instability line and with the topic of Ribault Phases. It contains 13 figures (.ps files

Optical Signature Analysis of Tumbling Rocket Bodies via Laboratory Measurements

The NASA Orbital Debris Program Office has acquired telescopic lightcurve data on massive intact objects, specifically spent rocket bodies, in order to ascertain tumble rates in support of the Active Debris Removal (ADR) task to help remediate the LEO environment. Rotation rates are needed to plan and develop proximity operations for potential future ADR operations. To better characterize and model optical data acquired from ground-based telescopes, the Optical Measurements Center (OMC) at NASA/JSC emulates illumination conditions in space using equipment and techniques that parallel telescopic observations and source-target-sensor orientations. The OMC employs a 75-watt Xenon arc lamp as a solar simulator, an SBIG CCD camera with standard Johnson/Bessel filters, and a robotic arm to simulate an object's position and rotation. The light source is mounted on a rotary arm, allowing access any phase angle between 0 -- 360 degrees. The OMC does not attempt to replicate the rotation rates, but focuses on how an object is rotating as seen from multiple phase angles. The two targets studied are scaled (1:48), SL-8 Cosmos 3M second stages. The first target is painted in the standard government "gray" scheme and the second target is primary white, as used for commercial missions. This paper summarizes results of the two scaled rocket bodies, each rotated about two primary axes: (a) a spin-stabilized rotation and (b) an end-over-end rotation. The two rotation states are being investigated as a basis for possible spin states of rocket bodies, beginning with simple spin states about the two primary axes. The data will be used to create a database of potential spin states for future works to convolve with more complex spin states. The optical signatures will be presented for specific phase angles for each rocket body and shown in conjunction with acquired optical data from multiple telescope sources