GAUGE INVARIANT FORMULATION OF THE BARDEEN-COOPERSCHRIEFFER THEORY OF SUPERCONDUCTIVITY
Gauge invariant formulation of the bardeen-cooper- schrieffer theory of superconductivity
GAUGE INVARIANCE↗
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Gravitational matter-antimatter asymmetry and four-dimensional Yang-Mills gauge symmetry
A formulation of gravity based on the maximum four-dimensional Yang-Mills gauge symmetry is studied. The theory predicts that the gravitational force inside matter (fermions) is different from that inside antimatter. This difference could lead to the cosmic separation of matter and antimatter in the evolution of the universe. Moreover, a new gravitational long-range spin-force between two fermions is predicted, in addition to the usual Newtonian force. The geometrical foundation of such a gravitational theory is the Riemann-Cartan geometry, in which there is a torsion. The results of the theory for weak fields are consistent with previous experiments.
Hsu, J. P.↗
Simple intuitive models of programming
It is hypothesized that mathematical models of the programming process can be formulated to gauge the sensitivities of that process to various given parameters, and that such models can be calibrated on an empirical basis and used as guides toward maximizing productivity, documentation quality, and programming reliability. Three oversimplified models are presented as illustrations.
Tausworthe, R. C.↗
On lattice chiral gauge theories
The Smit-Swift-Aoki formulation of a lattice chiral gauge theory is presented. In this formulation the Wilson and other non invariant terms in the action are made gauge invariant by the coupling with a nonlinear auxilary scalar field, omega. It is shown that omega decouples from the physical states only if appropriate parameters are tuned so as to satisfy a set of BRST identities. In addition, explicit ghost fields are necessary to ensure decoupling. These theories can give rise to the correct continuum limit. Similar considerations apply to schemes with mirror fermions. Simpler cases with a global chiral symmetry are discussed and it is shown that the theory becomes free at decoupling. Recent numerical simulations agree with those considerations.
Maiani, L.↗
Superconducting axisymmetric finite elements based on a gauged potential variational principle. Part 1: Formulation
The present work is part of a research program for the numerical simulation of electromagnetic (EM) fields within conventional Ginzburg-Landau (GL) superconductors. The final goal of this research is to formulate, develop and validate finite element (FE) models that can accurately capture electromagnetic thermal and material phase changes in a superconductor. The formulations presented here are for a time-independent Ginzburg-Landau superconductor and are derived from a potential-based variational principle. We develop an appropriate variational formulation of time-independent supercontivity for the general three-dimensional case and specialize it to the one-dimensional case. Also developed are expressions for the material-dependent parameters alpha and beta of GL theory and their dependence upon the temperature T. The one-dimensional formulation is then discretized for finite element purposes and the first variation of these equations is obtained. The resultant Euler equations contain nonlinear terms in the primary variables. To solve these equations, an incremental-iterative solution method is used. Expressions for the internal force vector, external force vector, loading vector and tangent stiffness matrix are therefore developed for use with the solution procedure.
Schuler, James J.↗
Cross-Effects in Microgravity Flows
Film growth by chemical/physical vapor deposition is a process of considerable interest in microgravity experiments. The absence of natural convection should allow better control of film growth processes but, in highly non-isothermal ampoules, thermal slip (creep) can become a matter of significant concern. The reported research is a theoretical and experimental investigation of the flow of gas/vapor mixtures under non-continuum conditions. The Boltzmann equation has been solved for a monatomic gas under non-condensing conditions and the various phenomenological coefficients have been computed. Computations for realistic potentials as well as for velocity and creep slip have been completed and the creep slip has been found to be dependent on the type of gas confirming the accuracy of previous variational results. The variational technique has been extended and planar flows calculated via the Burnett solutions. Velocity, diffusion and creep slips have been computed for gas mixtures and previously unknown dependencies of the creep slip on the mixture properties have been observed. Also for gas mixtures, an integral representation of the linearized Boltzmann operator has been developed for use in numerical and variational calculations for all intermolecular force laws. Two, two-bulb capillary systems have been designed, built and tested for the measurements of cross-flows; one of glass for isothermal measurements and one of stainless steel for non-isothermal measurements. Extensive data have been collected for Ar-He and N2-He mixtures at a variety of pressures and mole ratios. Viscosity, velocity slip coefficients and tangential momentum accommodation coefficients have been obtained from measurements with a spinning rotor gauge via a new theory that has been formulated for the spinning rotor gauge in the slip regime. The FIDAP fluid dynamics code has been applied to condensing flows in ampoules in the continuum regime and agreement obtained with the earlier work of Duval.
Loyalka, Sudarshan K.↗
Miniature high temperature plug-type heat flux gauges
The objective is to describe continuing efforts to develop methods for measuring surface heat flux, gauge active surface temperature, and heat transfer coefficient quantities. The methodology involves inventing a procedure for fabricating improved plug-type heat flux gauges and also for formulating inverse heat conduction models and calculation procedures. These models and procedures are required for making indirect measurements of these quantities from direct temperature measurements at gauge interior locations. Measurements of these quantities were made in a turbine blade thermal cycling tester (TBT) located at MSFC. The TBT partially simulates the turbopump turbine environment in the Space Shuttle Main Engine. After the TBT test, experiments were performed in an arc lamp to analyze gauge quality.
Liebert, Curt H.↗
Miniature high temperature plug-type heat flux gauges
The objective is to describe continuing efforts to develop methods for measuring surface heat flux, gauge active surface temperature, and heat transfer coefficient quantities. The methodology involves inventing a procedure for fabricating improved plug-type heat flux gauges and also for formulating inverse heat conduction models and calculation procedures. These models and procedures are required for making indirect measurements of these quantities from direct temperature measurements at gauge interior locations. Measurements of these quantities were made in a turbine blade thermal cycling tester (TBT) located at MSFC. The TBT partially simulates the turbopump turbine environment in the Space Shuttle Main Engine. After the TBT test, experiments were performed in an arc lamp to analyze gauge quality.
Liebert, Curt H.↗
An Efficient Inverse Finite Element Method for Shape and Stress Sensing of Laminated Composite and Sandwich Plates and Shells
The inverse Finite Element Method (iFEM) is a revolutionary methodology for real-time reconstruction of full-field structural displacements and stresses in structures that are instrumented with strain sensors. This inverse problem is commonly referred to as shape and stress sensing, which is well-recognized as an enabling technology for structural health monitoring systems. In this study, an improved iFEM formulation is proposed for shape and stress sensing of laminated composite and sandwich plates and shells. The formulation includes the kinematics of a shear deformation plate theory known as Refined Zigzag Theory (RZT) as its baseline. The present iFEM formulation is based upon the minimization of a weighted-least-squares functional that uses the complete set of section strains of RZT. The improved iFEM methodology is applicable for shape and stress sensing of thin and moderately thick plate and shell structures involving a relatively small number of strain gauges. The main advantage of the current formulation is that highly accurate through-the-thickness distributions of displacements, strains, and stresses are attainable using an element based on simple C0-continuous displacement interpolation functions. A three-node inverseshell element, named i3-RZT, is developed. Two example problems are examined in detail: (1) a simply supported rectangular laminated composite plate and (2) a wedge structure with a hole near one of the clamped ends. For both problems, the experimental strain data are generated numerically by the direct finite element analysis using high-fidelity discretizations. These strains are then regarded as the experimental strains obtained from surface mounted strain gauges or embedded fiber Bragg grating (FBG) sensors. The numerical results demonstrate the superior capability and potential applicability of the i3- RZT/iFEM methodology for performing accurate shape and stress sensing of complex composite structures.
Kefal, Adnan↗
Origin of gauge invariance in string theory
A first quantization of the space-time embedding Chi exp mu and the world-sheet metric rho of the open bosonic string. The world-sheet metric rho decouples from S-matrix elements in 26 dimensions. This formulation of the theory naturally includes 26-dimensional gauge transformations. The gauge invariance of S-matrix elements is a direct consequence of the decoupling of rho. Second quantization leads to a string field Phi(Chi exp mu, rho) with a gauge-covariant equation of motion.
Horowitz, G. T.↗
Development and Design of a Zero-G Liquid Quantity Gauge for a Solar Thermal Vehicle
The development and design of a cryogenic liquid quantity gauge for zero-g applications is described. The gauge, named the Compression Mass Gauge (CMG), operates on the principle of slightly changing the volume of the tank by an oscillating bellows. The resulting pressure change is measured and used to predict the volume of vapor in the tank, from which the volume of liquid is computed. For each gauging instance, pressures are measured for several different bellows frequencies to enable minor real-gas effects to be quantified and thereby to obtain a gauging accuracy of +/- 1% of tank volume. Southwest Research Institute (Tm) and NASA-GRC (Glenn Research Center) have developed several previous breadboard and engineering development gauges and tested them in cryogenic hydrogen and nitrogen to establish the gauge capabilities, to resolve several design issues, and to formulate data processing algorithms. The CMG has been selected by NASA's Future X program for a flight demonstration on the USAF (United States Air Force) / Boeing Solar Thermal Vehicle Space Experiment (SOTVSE). This paper reviews the design trade studies needed to satisfy the SOTVSE limitations on CMG power, volume, and mass, and describes the mechanical design of the CMG.
Dodge, Franklin T.↗
Purely cubic action for string field theory
It is shown that Witten's (1986) open-bosonic-string field-theory action and a closed-string analog can be written as a purely cubic interaction term. The conventional form of the action arises by expansion around particular solutions of the classical equations of motion. The explicit background dependence of the conventional action via the Becchi-Rouet-Stora-Tyutin operator is eliminated in the cubic formulation. A closed-form expression is found for the full nonlinear gauge-transformation law.
Horowitz, G. T.↗
SRM Internal Flow Tests and Computational Fluid Dynamic Analysis: RSRM Full Scale Motor Analyses - Volume 2
The purpose of the RSRM Nozzle Slag Ejection Precursor Test is to investigate the effect that slag ejection from the RSRM nozzle has on the chamber pressure and trust of the SRB's. In past firings of the Reusable Solid Rocket Motor (RSRM) both static test and flight motors have shown small pressure perturbations occurring primarily between 65 and 80 seconds. A joint NASA/Thiokol team investigation concluded that the cause of the pressure perturbations was the periodic ingestion and ejection of molten aluminum oxide slag from the cavity around the submerged nozzle nose which tends to trap and collect individual aluminum oxide droplets from the approach flow. The conclusions of the team were supported by numerous data and observations from special tests including high speed photographic films, real time radiography, plume calorimeters, accelerometers, strain gauges, nozzle TVC system force gauges, and motor pressure and thrust data. A simplistic slag ballistics model was formulated to relate a given pressure perturbation to a required slag quantity. Also, a cold flow model using air and water was developed to provide data on the relationship between the slag flow rate and the chamber pressure increase. Both the motor and the cold flow model exhibited low frequency oscillations in conjunction with periods of slag ejection. Motor and model frequencies were related to scaling parameters. The data indicate that there is a periodicity to the slag entrainment and ejection phenomena which is possibly related to organized oscillations from instabilities in the dividing streamline shear layer which impinges on the underneath surface of the nozzle.
Source record↗
Effects of Slag Ejection on Solid Rocket Motor Performance
In past firings of the Reusable Solid Rocket Motor (RSRM) both static test and flight motors have shown small pressure perturbations occurring primarily between 65 and 80 seconds. A joint NASA/Thiokol team investigation concluded that the cause of the pressure perturbations was the periodic ingestion and ejection of molten aluminum oxide slag from the cavity around the submerged nozzle nose which tends to trap and collect individual aluminum oxide droplets from the approach flow. The conclusions of the team were supported by numerous data and observations from special tests including high speed photographic films, real time radiography, plume calorimeters, accelerometers, strain gauges, nozzle TVC system force gauges, and motor pressure and thrust data. A simplistic slag ballistics model was formulated to relate a given pressure perturbation to a required slag quantity. Also, a cold flow model using air and water was developed to provide data on the relationship between the slag flow rate and the chamber pressure increase. Both the motor and the cold flow model exhibited low frequency oscillations in conjunction with periods of slag ejection. Motor and model frequencies were related to scaling parameters. The data indicate that there is a periodicity to the slag entrainment and ejection phenomena which is possibly related to organized oscillations from instabilities in the dividing streamline shear layer which impinges on the underneath surface of the nozzle.
Whitesides, R. Harold↗
Improved Fermion Hamiltonians for Quantum Simulations
Constructing improved hamiltonians for gauge theories coupled to fermonic matter will be important for improving continuum limit extrapolations of quantum computations. In this talk we will present a formulation for simulating ASQTAD fermions for lattice computation and provide fault tolerant resource costs in terms of primitive group operations. We additionally show that the scaling of energies with respect to the lattice spacing are better than for the unimproved Hamiltonian for toy models.
Quantum Algorithms↗
Improved Fermion Hamiltonians for Quantum Simulations
Constructing improved hamiltonians for gauge theories coupled to fermonic matter will be important for improving continuum limit extrapolations of quantum computations. In this talk we will present a formulation for simulating ASQTAD fermions for lattice computation and provide fault tolerant resource costs in terms of primitive group operations. We additionally show that the scaling of energies with respect to the lattice spacing are better than for the unimproved Hamiltonian for toy models.
Erik Joseph Gustafson↗
Improved Fermion Hamiltonians for Quantum Simulations
Constructing improved hamiltonians for gauge theories coupled to fermonic matter will be important for improving continuum limit extrapolations of quantum computations. In this talk we will present a formulation for simulating ASQTAD fermions for lattice computation and provide fault tolerant resource costs in terms of primitive group operations. We additionally show that the scaling of energies with respect to the lattice spacing are better than for the unimproved Hamiltonian for toy models.
Erik Gustafson↗
Nanocomposite Strain Gauges Having Small TCRs
Ceramic strain gauges in which the strain-sensitive electrically conductive strips made from nanocomposites of noble metal and indium tin oxide (ITO) are being developed for use in gas turbine engines and other power-generation systems in which gas temperatures can exceed 1,500 F (about 816 C). In general, strain gauges exhibit spurious thermally induced components of response denoted apparent strain. When temperature varies, a strain-gauge material that has a nonzero temperature coefficient of resistance (TCR) exhibits an undesired change in electrical resistance that can be mistaken for the change in resistance caused by a change in strain. It would be desirable to formulate straingauge materials having TCRs as small as possible so as to minimize apparent strain. Most metals exhibit positive TCRs, while most semiconductors, including ITO, exhibit negative TCRs. The present development is based on the idea of using the negative TCR of ITO to counter the positive TCRs of noble metals and of obtaining the benefit of the ability of both ITO and noble metals to endure high temperatures. The noble metal used in this development thus far has been platinum. Combinatorial libraries of many ceramic strain gauges containing nanocomposites of various proportions of ITO and platinum were fabricated by reactive co-sputtering from ITO and platinum targets onto alumina- and zirconia-based substrates mounted at various positions between the targets.
Gregory, Otto↗