Gauge Constants Research Articles

Role of shift constant in Energy Shifted SAV for Hamiltonian Systems

In recent years, considerable work has been devoted to the design of energy-stable numerical methods, a class of geometrical integration technique in which the discrete energy or pseudo-energy remains conserved. This property finds practical applications in systems for which the energy is bounded from below since the growth of the solutions is then itself bounded, yielding a form of stability. Such a property may be further exploited to transform the energy overall into a quadratic form, representing the core of recent numerical techniques such as the invariant energy quadratization (IEQ) and the scalar auxiliary variable (SAV) approaches. These methods have been applied to a large class of problems due to their remarkable efficiency. Yet, several aspects of such techniques have seen little investigation. In this work, the role of the “shift” constant in the expression of the potential energy in Hamiltonian systems is investigated. This is a positive gauge constant that may be used to augment the expression of the energy. Since Hamilton’s equations are given in terms of gradients of the Hamiltonian, such a constant has no influence on the resulting dynamics in the continuous system. However, empirical evidence has suggested that the convergence properties of the associated SAV approaches are affected by the magnitude of the shift factor. In this work, the behaviour of the relative global error of SAV schemes in the cases of the harmonic and Duffing oscillators is numerically investigated. The results reveal an optimal shift factor that increases the convergence rate. Using the optimal shift factor, the proposed method displays variable order accuracy ranging from second to twelfth order.

Planck length in classical and quantum Hamiltonian formulations of general relativity

The physical meaning of the Planck length (ell _{P}) is investigated in the framework of the unconstrained synchronous variational formulation of classical general relativity (GR). This theoretical setting permits the establishment of manifestly-covariant Lagrangian and Hamiltonian theories for the Einstein field equations of the continuum gravitational field. It is shown that such a formulation is distinguished by the existence of a novel variational contribution expressed by an infinite series summation of suitable 4-scalar terms in which the coupling coefficients are even powers of the Planck length. However, the requirement of realization of a classical GR Hamiltonian theory places stringent constraints on the admissible Planck-length power terms to be retained. In fact, excluding the trivial gauge constant, it is proved that only the Oleft( ell _{P}^{0}right) contribution of the series is ultimately permitted, namely the unique one which is independent of ell _{P}. Therefore, the Planck length is effectively not allowed to appear at the classical level for consistency with the Hamiltonian principle. This places important consequences on the mathematical establishment of the corresponding canonical quantum gravity theory, which is then found to be correct through Oleft( ell _{P}^{2}right) . Additional implications concern the physical significance of related quantum momenta and their meaning in the semi-classical limit, as well as the role of the Planck length in the same quantum-gravity realm.

Dynamical chiral magnetic current and instability in Weyl semimetals

Weyl semimetals realize massless relativistic fermions with two Weyl nodes separated in energy and momentum space, whose low-energy physics is described by Dirac fermions with an axial gauge constant. Here, we study their electromagnetic linear responses based on the effective field theory and on the chiral kinetic theory. Although the static chiral magnetic effect is canceled by the Chern-Simons current under the Pauli-Villars regularization, a dynamical magnetic field is found capable of driving an electric current along its direction, with the total transported charge being independent of temperature and chemical potential for a uniform field. We also incorporate dissipation in the relaxation-time approximation and study collective excitations coupled with Maxwell electromagnetic fields when Weyl node populations deviate from equilibrium. Their dispersion relations at low frequency and long wavelength are determined only by electric, chiral magnetic, and anomalous Hall conductivities, which predict unstable modes leading to anisotropic generation of electromagnetic waves oriented to the direction of Weyl node separation.

High-Speed Railway Intruding Object Image Generating with Generative Adversarial Networks.

Foreign object intrusion is a great threat to high-speed railway safety operations. Accurate foreign object intrusion detection is particularly important. As a result of the lack of intruding foreign object samples during the operational period, artificially generated ones will greatly benefit the development of the detection methods. In this paper, we propose a novel method to generate railway intruding object images based on an improved conditional deep convolutional generative adversarial network (C-DCGAN). It consists of a generator and multi-scale discriminators. Loss function is also improved so as to generate samples with a high quality and authenticity. The generator is extracted in order to generate foreign object images from input semantic labels. We synthesize the generated objects to the railway scene. To make the generated objects more similar to real objects, on scale in different positions of a railway scene, a scale estimation algorithm based on the gauge constant is proposed. The experimental results on the railway intruding object dataset show that the proposed C-DCGAN model outperforms several state-of-the-art methods and achieves a higher quality (the pixel-wise accuracy, mean intersection-over-union (mIoU), and mean average precision (mAP) are 80.46%, 0.65, and 0.69, respectively) and diversity (the Fréchet-Inception Distance (FID) score is 26.87) of generated samples. The mIoU of the real-generated pedestrian pairs reaches 0.85, and indicates a higher scale of accuracy for the generated intruding objects in the railway scene.

Effect of the tank car thickness on the nonlinear dynamics of railroad vehicles

The expression of the centrifugal forces resulting from a flexible body negotiating a curve differs significantly from the expression of the centrifugal forces used in rigid body dynamics. In rigid body railroad vehicle dynamics, the balance speed does not depend on the body inertia; it depends on the vehicle speed, super elevation, track gauge, and gravity constant. This is not, however, the case when the structural flexibility is considered. In this paper, a general multibody system (MBS) approach that accounts for the nonlinear dynamic coupling between the wheel–rail contact forces and the tank car structural flexibility is used to examine the effect of increasing the tank car thickness on the nonlinear dynamics of railroad vehicles. The flexible tank cars are modelled in this investigation using the nonlinear finite element (FE) floating frame of reference (FFR) formulation. The tank car FE model is integrated with a computational railroad vehicle algorithm in which a three-dimensional elastic contact formulation is used to describe the rail–wheel interaction in order to allow for wheel–rail separations. A complete expression for the centrifugal and Coriolis forces is used with triangular shell finite elements to develop the tank car models with different thicknesses. The effect of the coupling between different modes of displacements is examined by comparing the results of the simulations of the flexible and rigid tank car models. A parametric study is performed in order to explain the effect of the thickness increase on the tank car natural frequencies. Furthermore, the effect of increasing the tank car thickness on the critical speed as well as on the nonlinear dynamics of the railroad vehicle during curve negotiation is examined. The FE/FFR formulation allows for accurately capturing the effect of the change of the tank car thickness on the centrifugal and Coriolis inertia forces that define the balance speed during curve negotiations. The analysis presented in this paper shows that there is a strong dynamic coupling between different modes of displacements of the tank car, the plate thickness, and the wheel–rail contact parameters. The effect of increasing the tank car thickness on the wheel wear is also examined in this paper.

Electromagnetic structure of W ± bosons in the e – e + → W + W – reaction

A model-independent analysis of anomalous gauge coupling constants of W ± bosons is presented and the corresponding restrictions on them and on the electromagnetic characteristics of W ± bosons following from the experiments on measuring the $ {e^{+} }{e^{-} } \to {W^{+} }{W^{-} } \to \left( {{{e} \left/ {{\mu, \bar{v}}} \right.}} \right) \oplus \left( {q,\bar{q}} \right) $ process on the e + e − International Linear Collider are obtained. The method of obtaining the model-independent restrictions on the anomalous gauge constants is based on the use of the polarization scattering cross sections for different initial and final polarization states.

Bogoliubov compensation principle in the electro-weak interaction: value of the gauge constant, muon g-2 anomaly, predictions for Tevatron and LHC

We apply the Bogoliubov compensation principle to the gauge electro-weak interaction to demonstrate the spontaneous generation of an anomalous three-boson gauge invariant effective interaction. The non-trivial solution of the compensation equations uniquely defines the values of the parameters of the theory and the form factor of the anomalous interaction. The contribution of this interaction to the running EW coupling, α ew(p 2), gives its observable value α ew(M 2 )=0.0374, in satisfactory agreement to the experiment. The anomalous three-boson interaction gives a natural explanation of the well-known discrepancy in the muon g−2. The implications for EW studies at Tevatron and LHC are briefly discussed.

MIRROR WORLD WITH BROKEN MIRROR PARITY, E6 UNIFICATION AND COSMOLOGY

In the present paper we develop a concept of parallel ordinary (O) and mirror (M) worlds. We have shown that in the case of a broken mirror parity (MP), the evolutions of fine structure constants in the O- and M-worlds are not identical. It is assumed that E6-unification inspired by superstring theory restores the broken MP at the scale ~ 1018 GeV , what unavoidably leads to the different E6-breakdowns at this scale: E6 → SO (10) × U (1)Z — in the O-world, and E′6 → SU (6)′ × SU (2)′Z — in the M-world. Considering only asymptotically free theories, we have presented the running of all the inverse gauge constants [Formula: see text] in the one-loop approximation. Then a "quintessence" scenario suggested in Refs. 56–61 is discussed for our model of accelerating universe. Such a scenario is related with an axion ("acceleron") of a new gauge group SU (2)′Z which has a coupling constant gZ extremely growing at the scale ΛZ ~ 10-3 eV .

Quark Masses in Terms of Gauge Constants and Cabibbo Angle

Fritzsch type of mass matrices for the 2×2 case and appropriate Lagrangians enable the choice of Yukawa constants of the Lagrangians in terms of the gauge constants. The mass matrices for the four quarks are shown to be proportional to V L . The Cabibbo angle is computed to be 13∘36′.

Calibration stability of hot cathode ionization gauges: A discussion of the importance of electron path length and gauge constant

The ion current, i+, in an ionization gauge is given by the equation i+=Ki−P where K is a gas dependent gauge constant, i− is the electron current, and P is the pressure. Values of K for nitrogen for gauges designed for use at ultrahigh vacuum and extreme high vacuum range from 10/Torr to 106/Torr. It is important to know whether calibration stability is sacrificed when K, and the electron path length are large. Using a simple model, the electron path length is estimated as a function of the probability, β, that an electron will make another pass through the ionizing region. An equation is obtained for K as a function of β. The fractional change in K, ΔK/K, is zero for those gauges where the electrons make a single pass, but is increasingly larger for higher sensitivity gauges with greater probabilities of multiple passes. As an example, assume that the probability of the next pass changes by 1%, then the change in sensitivity is 1.5% for a B-A with K=25/Torr, and 9% for a gauge with K=102/Torr.

Particle spectrum in the modified nonminimal supersymmetric standard model in the strong Yukawa coupling regime

A theoretical analysis of solutions of renormalization group equations in the minimal supersymmetric standard model, which lead to a quasi-fixed point has shown that the mass of the lightest Higgs boson in these models does not exceed 94 ± 5 GeV. This implies that a considerable part of the parameter space in the minimal supersymmetric model is in fact eliminated by existing LEPII experimental data. In the nonminimal supersymmetric standard model the upper bound on the mass of the lightest Higgs boson reaches its maximum in the strong Yukawa coupling regime when the Yukawa constants are substantially greater than the gauge constants on the grand unification scale. In the present paper the particle spectrum is studied using the simplest modification of the nonminimal supersymmetric standard model which gives a self-consistent solution in this region of parameter space. This model can give m h ∼ 125 GeV even for comparatively low values of β ≥ 1.9. The spectrum of Higgs bosons and neutralinos is analyzed using the method of diagonalizing mass matrices proposed earlier. In this model the mass of the lightest Higgs boson does not exceed 130.5 ± 3.5 GeV.

583 Scaling-up Heat-balance Sap Flow Sensors for the High Flow Rates of Mature Grape Vines

Management strategies like “deficit irrigation” in wine grapes require accurate, reliable information on vine water use, making direct measurements of vine transpiration highly desirable. The heat-balance sap flow method has the advantages of being non-invasive and requiring no other calibration beyond a zero-flow set. Potential violations of the method's assumptions were dealt with and the heat balance method successfully applied to mature grape vines under conditions of extremely high sap flow. Greenhouse studies suggested that vines transpire at night, up to 9.5% of the total 24-h water loss, thus violating the zero-flow assumption for setting the gauge constant. Using a predetermined gauge constant caused smaller errors than using daily, pre-dawn constants set in situ. The steady-state assumption was violated only in early and late hours of the day, and the inclusion of a term to account for the change in heat stored by the stem only marginally improved daily estimates of water use. The assumption of radially uniform temperature across the heated stem segment is violated at very high flows (e.g., >700 g·h–1), but can be corrected for by using wider heaters and adjusting the placement of thermocouples. For a mature, potted vine in the greenhouse, the maximum absolute error in cumulative daytime water use between a sap gauge and a precision load cell was about –10%, with the gauge almost exclusively underestimating water loss. A custom-built, 20-gauge system was run continuously in the field for 90 days. Vine-to-vine variability in water use was not accounted for by normalizing sap flow by leaf area, suggesting that it is critical to include in any field study the largest number of gauges that are technically feasible.

Ocean tides in the Asian semienclosed seas from TOPEX/POSEIDON

The eight leading ocean tides (M2, S2, N2, K2, K1, O1, P1, and Q1) have been mapped in Asian semienclosed seas by inverting combined sets of tide gauge harmonic constants and a reduced set of TOPEX/POSEIDON satellite altimeter data. The tidal maps are given on a 0.5°×0.5° grid with their formal error estimates. Numerical experiments conducted in the South China Sea have shown the inverse solutions to be quite insensitive to changes in the parameters of the a priori covariance functions for both the tidal signals and data residual errors. Once the various parameters of the inversion scheme are fixed, the algorithm is applied to the Sea of Okhotsk, the Sea of Japan, the “East China” Sea (including the Bo Hai and Yellow Seas) and the Indonesian Seas. A set of tide gauge constants, not used in our solutions, is then used for comparison. Though these accuracy estimates may be biased because of the uneven stations coverage, we conclude that the inversion of only 21 cycles of TOPEX/POSEIDON data leads to solutions with an accuracy comparable to the Schwiderski (1980b, c) semiempirical model and the Cartwright and Ray (1990) model derived from Geosat altimetry.

Plots of gauge constant vs pressure for analyzing cold-cathode gauge calibration data

Gauge current vs pressure calibrations of inverted magnetron cold-cathode ionization gauges were made over the pressure range 10 −10 to 10 −4 torr. For pressures greater than 10 −6 torr a spinning rotor gauge (SRG) was used as the pressure reference. At lower pressures the reference was an extractor gauge which had been calibrated against the SRG in the overlap region. In addition to the usual log-log plots of current vs pressure used to fit the cold-cathode gauge equation I ga = K' P rmn , it was found useful to make plots of the gauge constant, K', vs P. Such plots are more sensitive to scatter in the data due to poor measurement techniques or to discontinuities in the gauge characteristic curve. Examples of K' vs P plots are given for two inverted magnetron cold-cathode gauges. The value of K' for two grouped nitrogen calibrations of a prototype gauge with a 2.2 kG magnetic field was constant within ±4.5% from 10 −8 to 10 −4 torr.

A mechanism for setting the scale for gauge coupling constants

The author identifies the spin connection of four-dimensional spacetime with a subgroup of a simple gauge group G. The remaining subgroups of G are the usual internal symmetry groups. Using the work of Weinberg (1983) to relate gauge constants to the circumferences of compact spaces and identifying the known spin of elementary particles with the eigenvalues of the spin connection allows us to set the scale of G. The author can then calculate the remaining gauge coupling constants numerically. The author shows how this mechanism works for the sample calculation where G is SU4, the spin connection is the usual SU2*SU2 and the internal gauge symmetry is U1. The author finds the electromagnetic fine-structure constant to be approximately 1/100.

General consideration of electronic transitions in many-electron atoms and ions

The relativistic electric multipole transition operators are considered, not specifying the gauge condition of the electromagnetic field potential. The nonrelativistic limit of the relativistic expressions obtained is found. The relativistic corrections to various forms of the electric dipole transition operators are investigated. The electric multipole transition operator contains an arbitrary parameter, the gauge constant, dependence on which can serve as one of the criteria for the accuracy of the wavefunctions used. Calculated examples of the theory, starting with the general expressions found, are presented. The methods described and the formulae presented allow the authors to investigate in an effective way the electric multipole transitions for atoms and their isoelectronic sequences, including very highly ionised atoms.

Effect of contributions from bending in evaluation of axial strain in rods with circular cross-section

Contributions from bending to the evaluated axial strain in an elastic rod are commonly suppressed by forming half the sum of measured surface strains at diametrically opposite positions. A simple method is presented which gives a useful estimation of the bending suppression (the ratio of the bending strain to the absolute value of the evaluated axial strain when a rod is subject to bending only) from (i) optically measured mis-positioning, and (ii) estimated differences between the gauge constants for the two strain gauges. Good agreement is obtained with results obtained from strain measurements on a rod loaded in bending.

The microdetermination of H 2O, CO 2, and SO 2 in glass using a 1280°C microscope vacuum heating stage, cryopumping, and vapor pressure measurements from 77 to 273 K

A new microscope vacuum heating stage and gas analyzer has been developed for measurement of H 2O, CO 2, SO 2, and noncondensable gas (H 2, CO, N 2, Ar, CH 4, etc.) evolved from samples, particularly natural glass, at temperatures up to 1280°C. The gas evolved upon heating to 1280δC is collected in a liquid nitrogen cold trap. Gas components are identified by the characteristic vapor pressure and temperature ranges over which solid and vapor are in equilibrium during sublimation of individual components. The masses of CO 2, SO 2, and H 2O derived from samples and blanks are calculated using the ideal gas law, the molecular weights of the components, and the gauge constant (i.e. the ratio of the number of moles of a gas to its partial pressure in the constant volume). Results obtained by repeated determinations of H 2O, CO 2, and SO 2 evolved from a submarine basaltic glass from Kilauea volcano, Hawaii, (average sample mass = 3 × 10 −3 g) gave probable errors for the determinations of H 2O (0.23%), CO 2 (0.025%), and S (0.071%) equal to 4, 10, and 8% respectively, of the concentrations. Determinations of H 2O in smaller samples of H 2O-poor basaltic pumice show a linear proportionality (0.063%) between the measured H 2O and the sample mass over the range 0.1 × 10 −6 to 1.7 × 10 −6 g H 2O. Comparisons of H 2O determinations by this technique with those obtained by Penfield, gas chromatic, microcoulometric, and vacuum fusion techniques used elsewhere show reasonably good agreement. Determinations of SO 2 by this technique agree reasonably well X-ray fluorescence and electron microprobe determinations of sulfur. Determinations of CO 2 by the present technique are reproducible but cannot be compared directly to measurements made in other labs because of differences in samples analyzed. The principle advantages of this analytical technique are the very small sample required, the simultaneous determination of H 2O, CO 2, SO 2 and noncondensable gas, the avoidance of calibration procedures dependent on chemical standards, and the visual observations that can be made during sample outgassing.

Simple pressure gauge for uranium hexafluoride

A sensitive detector and pressure gauge for uranium hexafluoride in high-vacuum systems is described. Negative surface ionization of UF(6) occurs on ribbon filaments operated at temperatures too low for electron emission to be significant. The ion current measured on a cylindrical collector surrounding the filament assembly varies regularly with UF(6) pressure below 10(-3) Torr. Different filament materials are considered, including rhenium, thoriated tungsten, and platinum. Rhenium is found to be the most satisfactory material for operation of diode emitters as a pressure gauge. Gauge constants (in A Torr(-1)) are derived from comparing negative surface ionization currents with the response of a capacitance manometer and are shown to be independent of temperature within a reasonable operating range. The effects of exposing the rhenium filament to various gases is considered, and it is shown that brief exposure to acetylene substantially improves the operating characteristics of the gauge.

A numerical solution of a model for a superconductor field problem

A model of a magnetic field problem occurring in connection with Josephson junction devices is derived, and numerical solutions are obtained. The model is of mathematical interest, because the magnetic vector potential satisfies inhomogeneous Helmholtz equations in part of the region, i.e., the superconductors, and the Laplace equation elsewhere. Moreover, the inhomogeneities are the gauge constants for the potential, which are different for each superconductor, and their magnitudes are proportional to the currents flowing in the superconductors. These constants are directly related to the self and mutual inductances of the superconducting elements in the device. The numerical solution is obtained by the iterative use of a fast Poisson solver. Chebyshev acceleration is used to reduce the number of iterations required to obtain a solution. A typical problem involves solving 100,000 simultaneous equations, which the algorithm used with this model does in 20 iterations, requiring three minutes of CPU time on an IBM YM/370/168. Excellent agreement is obtained between calculated and observed values for the inductances.