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We compute the proper real-time interaction potential between a static quark and antiquark in classical lattice gauge theory at finite temperature. Our central result is the determination of the screened real-part of this potential, and we reconfirm the presence of an imaginary part. The real part is intimately related to the back-reaction of the static sources onto the gauge fields, incorporated via Gauss's law. Differences in the treatment of static sources in quantum and classical lattice gauge theory are discussed., 24 pages, 10 figures, supplementary material: 2 Mathematica scripts, source code available on Zenodo

In this paper, we show that a simple generalization of the holographic axion model can realize spontaneous breaking of translational symmetry by considering a special gauge-axion higher derivative term. The finite real part and imaginary part of the stress tensor imply that the dual boundary system is a viscoelastic solid. By calculating quasi-normal modes and making a comparison with predictions from the elasticity theory, we verify the existence of phonons and pseudo-phonons, where the latter is realized by introducing a weak explicit breaking of translational symmetry, in the transverse channel. Finally, we discuss how the phonon dynamics affects the charge transport., v3: 29 pages, 11 figures, matching the version published in JHEP

Angular measurements lie on the circumference of a circle and have different characteristics than standard scalar measurements. For applications involving angular data, treating the measured values...

The Yang-Mills equations generalize Maxwell's equations to nonabelian gauge groups, and a quantity analogous to charge is locally conserved by the nonlinear time evolution. Christiansen and Winther observed that, in the nonabelian case, the Galerkin method with Lie algebra-valued finite element differential forms appears to conserve charge globally but not locally, not even in a weak sense. We introduce a new hybridization of this method, give an alternative expression for the numerical charge in terms of the hybrid variables, and show that a local, per-element charge conservation law automatically holds., Comment: New section on nonzero current, new tables and figures for numerical experiments, and expanded introduction. 27 pages, 2 figures, 1 table

Approaches to a non-perturbative formulation of chiral gauge theories on the lattice regulator through a gauge non-invariant approach is discussed. Non-perturbative gauge fixing of Abelian and non-Abelian gauge theories are also discussed in this context.

For a high-speed rail vehicle with gauge-changeable wheelsets, wheel/rail interactions and vehicle dynamics were numerically and experimentally studied within 600 km/h. Matching among four treads, ...

The Lagrange formalism is developed for Bateman oscillators, which include both damped and amplified systems, and a novel method to derive the Caldirola-Kanai and null Lagrangians is presented. For the null Lagrangians, corresponding gauge functions are obtained. It is shown that the gauge functions can be used to convert the undriven Bateman oscillators into the driven ones. Applications of the obtained results to quantizatation of the Bateman oscillators are briefly discussed., Comment: 10 pages

In this paper, we introduce extended b -gauge spaces and the extended family of generalized extended pseudo- b -distances. Moreover, we define the sequential completeness and construct the Caristi-type G -contractions in the framework of extended b -gauge spaces. Furthermore, we develop periodic and fixed point results in this new setting endowed with a graph. The obtained results of this paper not only generalize but also unify and improve the existing results in the corresponding literature.

In a previous manuscript, we addressed the possibility of generating a reflection in a region of spacetime inside a null surface under electromagnetic gauge transformations. In this manuscript, we will deal with the possibility of full inversions in a region of spacetime inside a null surface under electromagnetic gauge transformations. Since new tetrads whose construction depends on electromagnetic gauge were introduced it has been proved that the physical kinematic nature of spacetime can be altered as proved previously. In this case, we will see how to create a field configuration that will reverse the flow of time. We will prove that we can turn a future-directed timelike vector into a past-directed timelike vector by physical means. Experiments devised to achieve time reversal or full inversion have never been discussed before.

A definition of a convolution of tensor fields on group manifolds is given, which is then generalised to generic homogeneous spaces. This is applied to the product of gauge fields in the context of ‘gravity = gauge × gauge’. In particular, it is shown that the linear Becchi-Rouet-Stora-Tyutin (BRST) gauge transformations of two Yang-Mills gauge fields generate the linear BRST diffeomorphism transformations of the graviton. This facilitates the definition of the ‘gauge × gauge’ convolution product on, for example, the static Einstein universe, and more generally for ultrastatic spacetimes with compact spatial slices.

In this study, we used data from optical fiber-based Distributed Acoustic Sensor (DAS) and Distributed Temperature Sensor (DTS) to estimate pressure along the fiber. A machine learning workflow was developed and demonstrated using experimental datasets from gas–water flow tests conducted in a 5163-ft deep well instrumented with DAS, DTS, and four downhole pressure gauges. The workflow is successfully demonstrated on two experimental datasets, corresponding to different gas injection volumes, backpressure, injection methods, and water circulation rates. The workflow utilizes the random forest algorithm and involves a two-step process for distributed pressure prediction. In the first step, single-depth predictive modeling is performed to explore the underlying relationship between the DAS (in seven different frequency bands), DTS, and the gauge pressures at the four downhole locations. The single-depth analysis showed that the low-frequency components (2) of 0.96. This can be explained by the unique characteristic of low-frequency DAS which is sensitive to both the strain and temperature perturbations. In the second step, the DTS and the low-frequency DAS data from two gauge locations were used to predict pressures at different depths. The distributed pressure modeling achieved an average R2 of 0.95 and an average root mean squared error (RMSE) of 24 psi for the two datasets across the depths analyzed, demonstrating the distributed pressure measurement capability using the proposed workflow. A majority of the current DAS applications rely on the higher frequency components. This study presents a novel application of the low-frequency DAS combined with DTS for distributed pressure measurement.

We present the one-loop electroweak renormalization of the CP-violating 2-Higgs-Doublet Model with softly broken $\mathbb{Z}_2$ symmetry (C2HDM). The existence of CP violation in the scalar sector of the model leads to a quite unique process of renormalization, since it requires the introduction of several non-physical parameters. The C2HDM will thus have more independent counterterms than independent renormalized parameters. As a consequence, different combinations of counterterms can be taken as independent for the same set of independent renormalized parameters. We compare the behaviour of selected combinations in specific NLO processes, which are assured to be gauge independent via a simple prescription. FeynMaster 2 is used to derive the Feynman rules, counterterms and one-loop processes in a simultaneously automatic and flexible way. This illustrates its use as an ideal tool to renormalize models such as the C2HDM and investigate them at NLO., One equation and one figure were slightly modified. Text and conclusions were not modified

The Kitaev quantum spin liquid epitomizes an entangled topological state, for which two flavors of fractionalized low-energy excitations are predicted: the itinerant Majorana fermion and the Z2 gauge flux. It was proposed recently that fingerprints of fractional excitations are encoded in the phonon spectra of Kitaev quantum spin liquids through a novel fractional-excitation-phonon coupling. Here, we detect anomalous phonon effects in α-RuCl3 using inelastic X-ray scattering with meV resolution. At high temperature, we discover interlaced optical phonons intercepting a transverse acoustic phonon between 3 and 7 meV. Upon decreasing temperature, the optical phonons display a large intensity enhancement near the Kitaev energy, JK~8 meV, that coincides with a giant acoustic phonon softening near the Z2 gauge flux energy scale. These phonon anomalies signify the coupling of phonon and Kitaev magnetic excitations in α-RuCl3 and demonstrates a proof-of-principle method to detect anomalous excitations in topological quantum materials. It was recently proposed that the coupling between phonons and fractional excitations of a Kitaev quantum spin liquid can be detected in its phonon dynamics. Here, the authors report signatures of this coupling, manifested in low-energy phonon anomalies measured by inelastic X-ray scattering with meV resolution.

We analyze the global nonlinear stability of FLRW (Friedmann-Lemaitre-Robertson-Walker) spacetimes in the presence of an irrotational perfect fluid. We assume that the fluid is governed by the so-called (generalized) Chaplygin equation of state p = − A 2 ρ α relating the pressure to the mass-energy density, in which A > 0 and α ∈ ( 0 , 1 ] are constants. We express the Einstein equations in wave gauge as a system of coupled nonlinear wave equations and, after performing a conformal transformation, we analyze the global behavior of solutions toward the future. Under small perturbations, the ( 3 + 1 ) -spacetime metric, the mass-energy density, and the velocity vector describing the geometry and fluid unknowns remain globally close to a reference FLRW solution. Our analysis provides also the precise asymptotic behavior of the perturbed solutions toward the future.

This paper reports the development and verification of a new procedure for formation of a complete stress-strain curve of concrete with a downward region of strain by using a digital image correlation method. A new technique to build spectle patterns on the surface of concrete is described. That makes it possible to accurately enough reproduce the spectle patterns on the surface of concrete and perform a high-quality analysis of strains involving digital image correlation. The advantages of this research technique have been established when predicting the formation of internal cracks in concrete followed by their propagation. In addition, using the digital image correlation methodology makes it possible to obtain strains of the entire studied plane of the sample at each stage of loading. This procedure provides an opportunity to investigate a change in strains and the movement of individual points or areas when studying concrete surfaces. That is a relevant issue as it enables more detailed diagnostics of existing reinforced concrete structures. To check the accuracy of this procedure application, a mechanical gauge with an accuracy of 0.001mm was additionally installed. 2 high-speed monochrome CCD cameras with different lenses were used in determining concrete strains involving the digital image correlation technique. The deformations were controlled with a period of time every 250ms. The load was controlled by an additional third camera with a speed of 50frames/second. The result of the experimental study is the formed full concrete destruction diagram with a downward region of strain. The deviation of the results of strains based on the mechanical gauge with an accuracy of 0.001mm with a base of 200mm from those acquired by the digital image correlation procedure was mainly up to 10%, which confirms the reliability of the results. The results of this work allow a more accurate calculation of reinforced concrete structures in the practice of design, inspection, or reinforcement of existing structures

The gauge theory of the de Sitter group, SO$(1,4)$, in the ambient space formalism has been considered in this article. This method is essential to constructing the de Sitter super-conformal gravity and Quantum gravity. $10$ gauge vector fields are needed, corresponding to $10$ generators of the de Sitter group. Using the gauge-invariant Lagrangian, the field equation of these vector fields has been obtained. The gauge vector field solutions are recalled. Then, the spin-$2$ gauge potentials are constructed from the gauge vector field. There are two possibilities for presenting this tensor field: rank-$2$ symmetric and mixed symmetry rank-$3$ tensor fields. To preserve the conformal transformation, a spin-$2$ field must be represented by a mixed symmetry rank-$3$ tensor field, $\mathcal {K}_{\alpha\beta\gamma}$. This tensor field has been rewritten using a generalized polarization tensor field and a de Sitter plane wave. This generalized polarization tensor field has been calculated as a combination of vector polarization, $\mathcal {E}_{\alpha}$, and tensor polarization of rank-$2$, $\mathcal {E}_{\alpha\beta}$, which can be used in the gravitational wave consideration. For the construction of this polarization tensor, the arbitrary constant vector fields appear. We fix it so that, in the limit, $H=0$, one obtains the polarization tensor in Minkowski space-time. It has been shown that under some simple conditions, the spin-$2$ mixed symmetry rank-$3$ tensor field can be simultaneously transformed by the unitary irreducible representation of de Sitter and conformal groups, SO$(2,4)$., Comment: 11 pages, typos corrected

The two-photon-exchange diagrams for atoms with single valence electrons are investigated. Calculation formulas are derived for an arbitrary state within the rigorous bound-state QED framework utilizing the redefined vacuum formalism. In contrast to other methods, the redefined vacuum approach enables the identification of eight gauge-invariant subsets and, thus, efficiently checks the consistency of the obtained results. The gauge invariance of found subsets is demonstrated both analytically (for an arbitrary state) as well as numerically for $2s, 2{p}_{1/2}$, and $2{p}_{3/2}$ valence electrons in Li-like ions. Identifying gauge-invariant subsets in the framework of the proposed approach opens a way to tackle more complex diagrams, e.g., three-photon exchange, where the fragmentation on simpler subsets is crucial for its successful calculation.

An overview of the existing methods for measuring the liquid level and their disadvantages in the case of surface vibrations is presented. A system for continuous measurement of the mass of liquids in fuel tanks and tanks during rolling and tilting of vehicles and ships, implemented in a level gauge based on intelligent sensors, is proposed. The sensors include a microcontroller with an individual calibration characteristic of the volume-level dependence, taking into account the shape of the tank or fuel tank, and nanosensors built into the intelligent sensor (ID) for measuring density, permittivity and ambient temperature. It is established that the actual metrological characteristics of the ID are significantly higher than the characteristics of traditional sensors. The number and dimensions of the plates of flat capacitors are justified and the scheme of their arrangement on the roof of the tanks is presented. The exclusion of movable elements increased the reliability of operation, simplified maintenance and design requirements of the measuring object. Analytical expressions for calculating the level and mass of the liquid, implemented by the microcontroller, are given. The use of the proposed measurement system with complex computational processing and taking into account corrections for temperature, density, humidity and permittivity of the liquid made it possible to increase the accuracy and stability of the level meter readings. Analytical expressions are derived that relate the liquid level and the output frequency of the generator from the composition of the level gauge.

This study focused on the reflectivity measurement bias (Z-bias) and the rainfall bias (R-bias) in the radar-rainfall estimation process. To correct the Z-bias, the self-consistency constraint method using reflectivity, differential reflectivity, and specific differential phase was carried out. Then, the Mean Field Bias Correction (MFBC) method and the Local Gauge Correction (LGC) method, were conducted to correct the R-bias. All of correction methods were applied to the Radar-AWS Rainrate model to calculate radar-rainfall estimates. The accuracy of the Z-bias correction method in 18 rainfall cases was improved by considering the RMSE (from 7.37 to 7.21 mm/hr) and the Correlation Coefficient (CC) (from 0.83 to 0.84) on average. The accuracy of results in the Changma and local torrential cases was improved by applying the Z-bias correction. The accuracy obtained by the LGC method (by 63.7% in RMSE and 11.7% in CC compared to MFBC) was superior to the MFBC method results because, in the LGC method, different R-biases were applied to each rainfall estimates in each radar pixel.

A Correction to this paper has been published: https://doi.org/10.1007/s00023-020-01015-y

We study the Langevin dynamics of a U(1) lattice gauge theory on the torus, and prove that they converge for short time in a suitable gauge to a system of stochastic PDEs driven by space-time white noises. This also yields convergence of some gauge invariant observables on a short time interval. We fix gauge via a DeTurck trick, and prove a version of Ward identity which results in cancellation of renormalization constants that would otherwise break gauge symmetry. The proof relies on a discrete version of the theory of regularity structures., Comment: 67 pages, rewrote and improved some of the proofs

This article, written to honor Brian Josephson on the occasion of his 80th birthday, discusses the topological nature of an emergent collective variable, namely the gauge-invariant phase difference across the two leads of a superconducting tunnel junction, which plays a central role in Josephson’s discovery of the effect bearing his name.

This paper examines a new, non-conventional, gauge-shaped beam (GSB) cantilever for enhanced vibration energy scavenging. The stress evolution of the GSB as well as its eigenfrequency and energy harvesting capability (when coupled with macro fiber composite (MFC) transducer) are investigated by finite element method. A comparison of performance between the proposed GSB cantilever configuration and conventional harvester of equal mass is also conducted. Both the simulation and experimental validation results showed that the gauge-shaped beam cantilever configuration has lower resonant frequencies and improved power output when used as harvester substrate. Further, we evaluated the effect of tip mass orientation/position on the GSB harvester performance by considering five different configurations namely, Confg A, Confg B, Confg C, Confg D and Confg E. The analysis shows that Confg A with $$5 \times 20 \times 5\,{\text{mm}}^{3}$$ tipmass dimension has the highest effect of 9.8% on the output power of the harvester compared to the other configurations. However, Confg C and D have the lowest resonant frequencies at fundamental vibration mode.

The set of local gauge invariant quantities for linearized gravity on the Kerr spacetime presented by two of the authors (S.A, T.B.) in (arXiv:1803.05341) is shown to be complete. In particular, any gauge invariant quantity for linearized gravity on Kerr that is local and of finite order in derivatives can be expressed in terms of these gauge invariants and derivatives thereof. The proof is carried out by constructing a complete compatibility complex for the Killing operator, and demonstrating the equivalence of the gauge invariants from (arXiv:1803.05341) with the first compatibility operator from that complex., 23 pages. Some remarks added

We find large N gauge theories containing a large number of operators within a band of low conformal dimensions. One of such examples is the four-dimensional N=1 supersymmetric SU(N) gauge theory with one adjoint and a pair of fundamental/anti-fundamental chiral multiplets. This theory flows to a superconformal theory in the infrared upon a superpotential coupling with gauge singlets. The gap in the low-lying spectrum scales as 1/N and the central charges scale as $O(N^1)$ contrary to the usual $O(N^2)$ scaling of ordinary gauge theory coming from the matrix degree of freedom. We find the AdS version of the Weak Gravity Conjecture (WGC) holds for this theory, although it cannot be holographically dual to supergravity. This supports the validity of WGC in a more general theory of quantum gravity., Comment: 5 pages, 5 figures, v2: calculation corrected. reference added

The curvature and torsion of trajectories of charges in external gauge fields, including fields of magnetic monopoles, have been determined. It has been shown that these quantities are effectively calculated with the help of the equations of motion and first integrals. For a wide class of magnetic fields, their form-invariant combination has been revealed.

In completely generic four-dimensional gauge-Yukawa theories, the renormalization group $$ \beta $$ β -functions are known to the 3–2–2 loop order in gauge, Yukawa, and quartic couplings, respectively. It does, however, remain difficult to apply these results to realistic models without the use of dedicated computer tools. We describe a procedure for extracting $$ \beta $$ β -functions using the general results and introduce , a dedicated Mathematica package for extracting the $$ \overline{\text {MS}} $$ MS ¯ $$ \beta $$ β -functions in broad classes of models. The package and example notebooks are available from the GitHub repository.

Dark Yang-Mills sectors, which are ubiquitous in the string landscape, may be reheated above their critical temperature and subsequently go through a confining first-order phase transition that produces stochastic gravitational waves in the early universe. Taking into account constraints from lattice and from Yang-Mills (center and Weyl) symmetries, we use a phenomenological model to construct an effective potential of the semi quark-gluon plasma phase, from which we compute the gravitational wave signal produced during confinement for numerous gauge groups. The signal is maximized when the dark sector dominates the energy density of the universe at the time of the phase transition. In that case, we find that it is within reach of the next-to-next generation of experiments (BBO, DECIGO) for a range of dark confinement scales near the weak scale.

In this paper, we take into account the Gribov copies present in 3D Yang-MIlls-Higgs theory with a constant vector background whose presence breaks the Lorentz symmetry. The constant vector background is introduced within the non-Abelian aether term. Here, we show that this term arises as a one-loop correction. The influence of the aether coupling constant on the system is treated afterwards. As a result, we find that for some values of it the theory can be driven from a nonperturbative regime to a perturbative one. In this paper, we work with the Higgs field in the fundamental representation and in the Landau gauge., Comment: 13 pages, typos corrected, matches final version

This Paper presents the results of a rotating detonation engine rocket sled test demonstration on a 127 mm gauge rail at 100 m long high-speed running track test equipment to evaluate the thrust pe...

Water flow rate measurements are important for monitoring the irrigation practice. It is essential to find the real value of this variable using alternative low-cost methods which are easy to use or readily available. This study aimed to perform a comparative analysis among different methodologies for determining the flow rate in water pumping systems. Seven methodologies were analyzed, with 13 tests each. Three tests were done for adjustment and ten to test the equations. The correlation between the observed value and the values obtained by the methodologies was performed for the adjustment. The equations were subsequently used to obtain the estimated flow rate for comparison with the observed values. The comparative analysis was performed through the following statistical indicators: Precision Index, Agreement Index, Performance index, Root mean square deviation and Nash-Sutcliffe efficiency. The methodology which showed the best adjustment in the flow estimation was the U-tube vacuometer. The pressure showed the best general performance among the tested parameters with the Tensiometer, Bourdon vacuum gauge and U-tube vacuum gauge instruments.

This article applies the Wakeby distribution (WAD) with high-order L-moments estimates (LH-ME) to annual extreme rainfall data obtained from 99 gauge stations in Thailand. The objectives of this study investigate to obtain appropriate quantile estimates and return levels for several return periods, 2, 5, 10, 25 and 50 years. The 95% confidence intervals for the quantiles determined from the WAD are derived using the bootstrap technique. Isopluvial maps of estimated design values that correspond to selected return periods are presented. The LH-ME results are better than estimates from the more primitive L-moments method for a large majority of the stations considered.

Disc cutter has a large diameter and more teeth, and obvious tool runout (δi) is produced during disc milling process, so the irregular distribution of cutting force is generated due to uneven distribution of cutting output per tooth (hi*) caused by tool runout. Therefore, the tool runout (δi) must be considered when milling force model of disc milling is established. In the paper, first, milling force model of disc milling is built with a three-teeth alternating disc cutter considering the tool runout (δi). Second, tool runout (δi) is measured by the dial gauge when the revolving speed of disc cutter is 1 r/min, then cutting output per tooth considering tool runout (hi*) is obtained by the formula between cutting output of each tooth (hi) without considering tool runout (δi) and tool runout (δi). Third, the parameters of frictional angle (βn), normal shear angle (ϕn), and shear yield strength (τs) in model coefficients are calibrated by orthogonal cutting experimental. Then, the predictive model of milling force is obtained. Last, the reliability verification experiment of model is conducted. The experiment results show that the model is with high efficiency and precision and the measured force and predictive force is in good agreement in amplitude and trend, which can be used in the study of milling force of disc milling.

Disk bypass pipeline inspection gauge (PIG) is considered as an efficient device for pigging operations including cleaning, maintaining and inspecting pipelines. The PIG performance is influenced by the fluid flow characteristics as PIG moves forward due to differential pressure of fluid around the PIG. This study focuses on flow characterization of fluid around disk bypass PIG for natural gases pipelines including methane, ethane, and butane using computational fluid dynamics approach. The control volume method with steady state Turbulent k-? model was applied for simulation purposes using ANSYS Fluent 19 software. Fluid velocities at different sections around PIG and differential pressure were investigated for various bypass opening percentages. The results showed that by increasing bypass opening percentages from 5% to 15%, fluid velocity at bypass opening section has reduced 28.28%, 40.43%, and 21.21% for ethane, butane, and methane, respectively, while differential pressure reduced 88%, 86% and 89%. This indicated that 15% bypass opening percentage provided the best flow characteristics among all cases considered. At 15% bypass opening percentage, methane resulted in the lowest fluid velocity at bypass opening section and lowest differential pressure compared to others. Additionally, a correlation of differential pressure of these gases as a function of bypass opening percentage and other parameters was also developed for first time. All results are important for design selection of PIG parameters for efficient pigging operation.

The main object of this paper is to determine experimentally the effect of electrical current flow on the coefficient of friction between two dry rubbing surfaces. The tests were performed utilizing a pin-disc machine (Tribometer) with a pin having a diameter of 6 mm and 200 mm diameter disc. The current was be varied from 0 to 8 amperes with a constant potential difference of 12 volts. The coefficient of friction was calculated, at different loading and electrical current, based on the measured friction force. The measurement was carried out via strain gauge and FFT analyzer. A parametric study was carried out to highlight the effect of material, velocity and load on the coefficient of friction with the electrical current flow. Three sets of materials were used; steel-steel, copper-copper and aluminum-aluminum. Sliding velocity was increased up to 700 r.p.m., while the load changed from 1 to 8 Newton. As a result of this investigation, it was found that the coefficient of friction is depending strongly on the electrical current flow at all operating conditions.

The possibility of synchronous monitoring of coolant levels in the cooling systems of nuclear and thermal power plants before and after the barrier mesh using a specialized level gauge is considered. The block diagram of a level gauge providing current synchronous control of liquid levels in two adjacent channels (reservoirs), as well as the difference in liquid levels in them, is presented. A feature of the structural diagram of a specialized acoustic level gauge is the use of a radiation source common to both channels and a device for dividing the common waveguide path into two channels. An algorithm for the functioning of a specialized level gauge has been developed, in which, based on time diagrams, it is shown how the level is controlled in each channel and the difference in liquid levels before and after the barrier grid is calculated. The description of the algorithm is accompanied by calculated expressions for determining the levels and the difference in liquid levels. For a level gauge made in the acoustic wavelength range, a condition is given that is necessary for the creation of a device that provides matching when dividing a common channel into two independent channels of pulse signal propagation. This condition made it possible to establish the relationship between the inner diameters of cylindrical pipes used as waveguide paths of an acoustic wave. Variants of the implementation of a specialized level gauge based on two modifications of the ZOND-3M level gauge are proposed, in which cylindrical pipes are used as waveguiding systems. It is shown that when using the AP-7VT transceiver, the level gauge will have an operating range of up to 10m with a level resolution of ± 1mm, and when using the AP-70T transceiver, it will have an operating range of up to 20m with a level resolution of ± 1cm.

The interaction between atoms and molecules and intense laser pulses is typically described in either the velocity gauge, length gauge or in the Kramers-Henneberger frame. Here, certain relations between these forms are discussed. In particular expansions of the solution to the time-dependent Schrodinger equation in adiabatic states are considered. Such expansions in adiabatic states could be expected to be attractive for intense long-wavelength infrared laser pulses, where the external field changes on a slow timescale compared with the electron motion. It is shown that an expansion in velocity gauge adiabatic states gives the equations of motions that follow from an expansion in field-free states and by expressing the interaction operator in the length gauge. Likewise, it is shown that an expansion in the Kramers-Henneberger frame adiabatic states gives the equations of motion following an expansion in field-free states and using the velocity gauge interaction operator. Finally, an alternative form for the laser-matter interaction operator is considered, which is similar to the velocity gauge, but shifts the canonical momentum operator by the impulse associated with the Kramers-Henneberger interaction operator, rather than that of the electric field as is the case in the velocity gauge.

This work presents the first simulations of the full optical rotation (OR) tensor at coupled cluster with single and double excitations (CCSD) level in the modified velocity gauge (MVG) formalism. The CCSD-MVG OR tensor is origin independent, and each tensor element can in principle be related directly to experimental measurements on oriented systems. We compare the CCSD results with those from two density functionals, B3LYP and CAM-B3LYP, on a test set of 22 chiral molecules. The results show that the functionals consistently overestimate the CCSD results for the individual tensor components and for the trace (which is related to the isotropic OR), by 10%-20% with CAM-B3LYP and 20%-30% with B3LYP. The data show that the contribution of the electric dipole-magnetic dipole polarizability tensor to the OR tensor is on average twice as large as that of the electric dipole-electric quadrupole polarizability tensor. The difficult case of (1S,4S)-(-)-norbornenone also reveals that the evaluation of the former polarizability tensor is more sensitive than the latter. We attribute the better agreement of CAM-B3LYP with CCSD to the ability of this functional to better reproduce electron delocalization compared with B3LYP, consistent with previous reports on isotropic OR. The CCSD-MVG approach allows the computation of reference data of the full OR tensor, which may be used to test more computationally efficient approximate methods that can be employed to study realistic models of optically active materials.

In this communication, a conformal coupling gravity is discussed in the presence of a complex Coleman–Weinberg potential, which is generated from the contributions from first-, second-, and all higher-order loops. A relation between the cosmological constant, the Hubble mass, and the Higgs vacuum energy is obtained in particular when Weinberg–Landau gauge is used. Moreover, it was observed that the removal of the logarithmic mass boosts the scalar mass from Hubble mass of order 10–33 eV to 2.47 × 10–3 eV, which is comparable to the mass of non-baryonic cold dark matter or axion based on recent observations and which constitutes about 84% of all matter in the Universe.

The gauge dependence of an effective action with composite fields is investigated for general gauge theories arising in the functional renormalization group approach. It is shown that at any finite scale of the IR cutoff, this action is independent of the gauge fixing conditions at their extrema.

Industrial X-ray computed tomography (XCT) is a tool for non-destructive testing and a volumetric analysis method with the ability to measure dimensions and geometry inside a component without destroying it. However, XCT is a relatively young technology in the field of dimensional metrology and thus faces several challenges. The achievement of a high measurement resolution, which is re-quired to detect small geometrical features, depends on a variety of influencing factors. In this arti-cle, the interface structural resolution (ISR) as one of the key challenges will be investigated. The two-sphere standard called the hourglass standard allows the determination of the structural resolu-tion by evaluation of the surrounding area of an ideal point contact of two spheres after the CT re-construction in form of a neck-shaped transition. Close to the contact point of the two spheres two opposing surfaces exist. Their distances from each other increase as the distance from the contact point of the two spheres increase. The determination of the distances between the spheres’ surface allows a statement about the ISR. A new developed specimen or standard with a variable gap size consisting of calibrated parallel gauge blocks allows statements about the ISR, too. Because of the higher number of probing points of the gauge block standard the results of the determined ISR are more stable compared to the hourglass standard. This paper compares the results of the computed tomography measurements for the designed interface structural resolution standard with those of the hourglass standard.

International audience; This paper presents a new solution for 3D steering of flexible needles guided by 3D B-mode ultrasound imaging. It aims to realize a robust steering, by accounting for uncertainties, noise and tissue heterogeneities, while limiting tissue-related disturbances. The proposed solution features interconnected state observer, automatic needle tip segmentation and path planning algorithms. Measurement quality, state uncertainties and tissue heterogeneity are considered for robust needle steering with helical paths of variable curvature. Fast replanning allows for adaptability to unexpected disturbances. An experimental validation has been done through 62 insertions of 24 Gauge bevel-tip nitinol needles in various tissue. Results are promising, characterized by mean targeting errors of less than 1 mm in homogeneous phantoms, 1.5 ± 0.9 mm in heterogeneous phantoms and 1.7 ± 0.8 mm in ex-vivo tissue. This new approach is a step towards a precise and robust patient-specific gesture.

Accurate snowfall measurement is challenging because it depends on the precipitation gauge used, meteorological conditions, and the precipitation microphysics. Upstream of weighing gauges, the flow field is disturbed by the gauge and any shielding used usually creates an updraft, which deflects solid precipitation from falling in the gauge, resulting in significant undercatch. Wind shields are often used with weighing gauges to reduce this updraft, and transfer functions are required to adjust the snowfall measurements to consider gauge undercatch. Using these functions reduces the bias in precipitation measurement but not the root-mean-square error (RMSE). In this study, the accuracy of the Hotplate precipitation gauge was compared to standard unshielded and shielded weighing gauges collected during the WMO Solid Precipitation Intercomparison Experiment program. The analysis performed in this study shows that the Hotplate precipitation gauge bias after wind correction is near zero and similar to wind corrected weighing gauges. The RMSE of the Hotplate precipitation gauge measurements is lower than weighing gauges (with or without an Alter shield) for wind speeds up to 5 m s−1, the wind speed limit at which sufficient data were available. This study shows that the Hotplate precipitation gauge measurement has a low bias and RMSE due to its aerodynamic shape, making its performance mostly independent of the type of solid precipitation.

We have considered the generalized version of chiral schwinger model with the Lorentz covariant masslike term for gauge field with the choice a − r2 = 0. We carry out the quantization by the canonical Dirac method of both the gauge-invariant and non-invariant version of this model to determine the phase space structure. Therefore we have shown that the gauge invariant theory has the same physical spectrum as that of the original gauge noninvariant formulation.

Live load-induced deformation is a significant evaluation index for bridge maintenance. To measure a structural displacement response, a method using several MEMS (Micro Electro Mechanical Systems) accelerometers has previously been developed. However, this method requires several sensors, and for improved practicality, a reduction in the number of sensors is desired. Therefore, in this article, a simple displacement monitoring method is proposed that uses only one MEMS accelerometer, which is installed at the longitudinal center of the target bridge. A wavelet transform-based method is applied to the acceleration records to identify the integration range for displacement estimation. The accuracy was evaluated on an actual in-service bridge. The result indicates high accuracy of displacement measurements, with only 5% error when compared with the values recorded by a contact displacement gauge.

For subway safety, it is important to monitor the convergence deformation of shield tunnels in the long term. However, traditional monitoring methods are constrained by high cost and technical diff...

75D/72f and 100D/96f polyester yarns were knitted to develop three kinds of fabrics with different densities (large, medium and small) on circular knitting machine (gauge E18). It was found that the strength of the fabrics increased with the increase of loop density, and the initial modulus of the fabrics also increased. In order to obtain better strength and lower initial modulus, the washing and heat setting process of the fabric were studied and explored. The strength and initial modulus of the three density fabrics of the two yarn specifications decreased after pre-washing. Finally, the lowest initial modulus (0.36 MPa at warp direction and 0.22 MPa at weft direction) were found in sample (sample no. 3–3) made of 75D filament in longest loop length under 140 °C heat setting. The weft strength and warp strength were 9.54 MPa and 5.28 MPa respectively.

In this paper, the subject of bifurcation for a fractional order predator–prey system involving two nonidentical delays is nicely discussed. The critical values of delays for Hopf bifurcation are exactly calculated for the proposed model by using two nonidentical delays as bifurcation parameter, respectively. In addition, the effects of fractional order and additional delay on the bifurcation point are delicately explored. It detects that the stability performance is extremely pulverized with the enhancement of fractional order and another delay. This hints that the generation of Hopf bifurcation can be advanced as fractional order and another delay increase. The final numerical simulations gauge the correctness of the developed theoretical analysis.