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Directional spreading of ocean waves plays an important role in various aspects of ocean engineering, such as wave-induced loads, nonlinear wave evolution, and wave breaking. Wave following buoys, which are widely deployed across the oceans, offer the potential to measure directional wave properties. To assess the accuracy of directional spreading estimates made using buoy measurements, we compared estimates based on experimentally obtained buoy and wave gauge measurements, first presented in McAllister and van den Bremer (J Phys Oceanogr 50:399–414, 2020) Buoy and gauge measurements were recorded at the same locations and in identical sea states, allowing for a like-for-like comparison. We examine experiments with both following (unimodal in direction) and crossing (bimodal in direction) sea states. In addition to this, we use synthetic wave data to investigate the effects of wave generation and nonlinearity on spreading estimates. Our results show that while directional estimates produced using buoy measurements are reasonably accurate in following sea states, they struggle to identify distinct directional peaks in crossing sea states. We find that spreading estimates made using buoy measurements tend to underestimate the degree of directional spreading by approximately $$9-14\%$$ 9 - 14 % in following sea states, which is most apparent in narrowly spread conditions.

This article discusses the energy-power parameters of forming a pipe billet in the course of continuous molding. In addition, it expounds on the calibration of a roll tool for pipe Dt × St = 50 × 1.5 mm of strength class K52. First, the pipe billet’s deformation state and longitudinal deformation were determined, with the latter ranging from 0.18–0.26 %, which is considered a permissible value. Moreover, the contact surface of the pipe billet and the roll tool were estimated for gauge study. The effective diameters were then calculated for all driven forming rolls. Various options for the location of the effective diameters are described, which divide the contact surfaces into lead and lag zones. A method was then proposed for determining the lead and lag zones and the total pulling forces on the forming mill gauges. Depending on the location of the effective diameter for both upper and lower roll, pulling force distribution graphs were plotted. Finally, the schemes of distribution of energy-power parameters of the deformation process of a pipe billet were determined, which facilitated the rational selection of parameters for a specific pipe grade.

With the availability of satellite-based precipitation products, it is pertinent to develop methods to use these data products to design hydraulic structures. The satellite precipitation products play a vital role in ungauged locations or when information is required on a catchment scale. Before such applications, the accuracy and uncertainty associated with the products have to be investigated. In this study, we develop a framework that includes bias correction for the development of robust IDF curves. The framework is applied to a small region in the southeastern part of India, and the IDF curves were evaluated using the gauge data at nine locations. This study compares Intensity Duration Frequency (IDF) curves using the recent precipitation product Global Precipitation Measurement (GPM-IMERG V6) with ground-based gauge data. Results show that the spatial correlation between the satellite IDF and the gauge-based IDF improves significantly after bias correction, and the value is as high as 0.75 for 2–10 year return period. The bias between the satellite IDF and gauge IDF is low in the north part of the study region and is high in the southeastern part, prone to extreme rainfall. Further, a significant percentage of the satellite-based IDFs (with and without bias correction) lie inside the confidence interval of the gauge-based data. Thus, GPM V6 data have the potential to be used as an alternate data source for IDF generation in developing countries.

This paper is concerned with the construction of the fifth-order inhomogeneous Heisenberg supermagnetic models. Moreover, the Lax representations of the models are presented. By means of the gauge transformation, we establish their gauge equivalent equations with different quadratic constraints, i.e., the super and fermionic fifth-order inhomogeneous nonlinear Schrödinger equations, respectively. In addition, we investigate their Lax representations and Bäcklund transformations from which the solutions of the super integrable systems have been discussed.

We review recent advances in the construction of models of compositeness using four-dimensional gauge theories with fermionic matter. We discuss the group theory data needed to fulfill the basic phenomenological requirements and we touch upon the main predictions of these constructions.

In industrial manufacturing of bright steel rods, one important quality factor is the straightness or straightness deviation. Depending on the application, deviations of less than 0.1 mm per meter rod length are desired and can be reached with state-of-the-art manufacturing equipment. Such high-quality requirements can only be guaranteed with continuous quality control. Manual straightness measurements conducted offline using a dial gauge provide accurate results on single positions of the rod. We propose a contactless, optical measurement technique based on laser scanning which has the potential to be used inline during production to inspect all rods over the entire length. Only for calibration of the system the rod needs to be turned around its axis. For the measurement of straightness deviation, it is not required to turn the rod. The method is based on evaluating the intensity signal of the reflected laser radiation against the scan angle. It is shown that in combination with an accurate calibration, this signal can be used to determine the rod’s deviation from a straight rod. We explain the measurement and calibration principle as well as data evaluation. We present the experimental setup and first measurement results on a single position on several samples. For a homogeneous sample surface and neglecting laser drift, accuracy and precision were determined to be in the range of 10–20 μm. We discuss the working principle of a potential inline system.

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.

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 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

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.

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.

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.

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.

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.

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.

Quantum degenerate systems can be simulated by the classical resonant oscillators in the means of quantum-classical mapping theory. In this work, we show the classical version of shortcuts to adiabaticity-transitionless quantum driving (TQD) for the non-Abelian quantum systems by averaging the quantum version. The non-Abelian geometric angle corresponding to the quantum Wilczek-Zee phase is given and the non-Abelian angle gauge potential is just the opposite of the third term of TQD Hamiltonian or the averaging of Wilczek-Zee gauge potential. An example of Hamiltonian with two degenerate subspaces is employed to illustrate the classical non-Abelian dynamics, geometric angle and shortcuts to adiabaticity. This provides a promising platform to simulate the quantum shortcut or for quantum computation and quantum information processing.

This paper proposes novel modifications to existing solid flame and point source models to better predict the spatial contour of near-field, steady-state radiant heat flux from large circular pool fires (with diameters ranging from 1 m to 20 m) with gasoline and diesel fuel. The proposed models account for partial smoke obscuration of the flames, and the emissive power of the visible flame layer is calculated via a radiative fraction of the fire’s heat release rate as a function of the pool size. The modified discretized solid flame model uses a cylinder + cone shape combination whose surfaces are discretized to enable a flexible summation of total radiative energy emission. The modified point source model places its radiating point at the mid-height of the visible flame layer to capture the location of maximum radiation intensity. Predictions from both proposed models are benchmarked against available data from pool fire experiments, calibrated against computational fluid dynamic simulations, and compared with existing analytical solutions for a range of pool fire diameters at varying standoffs and gauge heights. The results demonstrate that the proposed models can effectively predict the spatial contour and peak value of radiant heat flux on nearby targets (i.e., at distances less than 2.5 times the pool diameter) with low computational effort.

A Herbert pendulum hardness tester can measure the hardness of a sample with a complex shape, such as a drill bit. Hardness is evaluated based on the free decay curve of the Herbert pendulum in the hardness test. The accuracy of a conventional Herbert hardness test is low because the swing of the pendulum is measured using a level gauge attached to the pendulum. The authors previously proposed a Herbert hardness tester that comprises a Herbert pendulum and two laser displacement sensors for swing angle detection. In this study, to increase portability, an accelerometer is used for swing angle detection. A prototype of the proposed Herbert pendulum equipped with an accelerometer is fabricated and its accuracy is evaluated. The damping hardness accuracy of the prototype Herbert hardness tester is equivalent to that of the previously proposed tester. The results show that using an accelerometer for swing angle detection reduces size, weight, and cost of a Herbert pendulum hardness tester without decreasing accuracy.

Let $$\Omega \subseteq \mathbb {R}^n$$ be an open set, where $$n \ge 2$$ . Suppose $$\omega $$ is a locally finite Borel measure on $$\Omega $$ . For $$\alpha \in (0,2)$$ , define the fractional Laplacian $$(-\triangle )^{\alpha /2}$$ via the Fourier transform on $$\mathbb {R}^n$$ , and let G be the corresponding Green’s operator of order $$\alpha $$ on $$\Omega $$ . Define $$T(u) = G(u \omega ).$$ If $$\Vert T \Vert _{L^2(\omega ) \rightarrow L^2 (\omega )}

We examine the relation between the gauge groups of $$\mathrm {SU}(n)$$ SU ( n ) - and $$\mathrm {PU}(n)$$ PU ( n ) -bundles over $$S^{2i}$$ S 2 i , with $$2\le i\le n$$ 2 ≤ i ≤ n , particularly when n is a prime. As special cases, for $$\mathrm {PU}(5)$$ PU ( 5 ) -bundles over $$S^4$$ S 4 , we show that there is a rational or p-local equivalence $$\mathcal {G}_{2,k}\simeq _{(p)}\mathcal {G}_{2,l}$$ G 2 , k ≃ ( p ) G 2 , l for any prime p if, and only if, $$(120,k)=(120,l)$$ ( 120 , k ) = ( 120 , l ) , while for $$\mathrm {PU}(3)$$ PU ( 3 ) -bundles over $$S^6$$ S 6 there is an integral equivalence $$\mathcal {G}_{3,k}\simeq \mathcal {G}_{3,l}$$ G 3 , k ≃ G 3 , l if, and only if, $$(120,k)=(120,l)$$ ( 120 , k ) = ( 120 , l ) .

The optimisation methodology was applied to design a specific geometry for a ring-shaped clip gauge as a quasi-static displacement measurement. The gauge was designed to maximise sensitivity under various types of constraints, including working range, strength, and installation. The analytical expressions of the ring gauge’s responses and constraints were derived to formulate an optimisation problem. The optimal solution was determined by an optimisation solver in the MathCAD Prime 4 program. The sensitivity of the objective function with respect to the parameters in the optimisation problem evaluated at the optimal solution was also determined. The sensitivity and linearity of the designed ring gauge is in the range of commercial gauges. The accuracy of the ring gauge was better than 0.1%, complying with ASTM standard E1820. Performance of the ring gauge, i.e. its linearity, hysteresis, and repeatability, was better than the DCB gauge reproduced from the standard. Applying the ring gauge to a tensile test with a cracked specimen yielded an accurate displacement measurement. Limitations of the analytical formulation are highlighted and recommendations for improving the formulation are discussed.

This paper is a survey of results on the relationship between gauge fields and infinitedimensional equations for parallel transport that contain the Levy Laplacian or the divergence associated with this Laplacian. Also we analyze the deterministic case where parallel transports are operator-valued functionals on the space of curves and the case of the Malliavin calculus where (stochastic) parallel transports are operator-valued Wiener functionals.

In this study, the effect of loading rate on shale fracture behaviors was investigated under dynamic and static loading conditions. Cracked straight through Brazilian disc (CSTBD) shale specimens were tested with a split Hopkinson pressure bar (SHPB) setup and INSTRON1346 servo-testing machine under pure mode I loading conditions. During the test, the crack propagation process was recorded by high-speed (HS) camera, and the acoustic emission (AE) signal generated by the fracture was collected by acoustic emission (AE) system. At the same time, crack propagation gauge (CPG) was used to measure the crack propagation velocity of the specimen. The results show that the crack propagation velocity and fracture toughness of shale have a positive correlation with the loading rate. The relationship among the crack propagation velocity, the fracture toughness and the loading rate is established under the static loading condition. In addition, the characteristics of AE signals with different loading rates are analyzed. It is found that the AE signals generated by microcrack growth decrease with the increase of loading rates. Meanwhile, the turning point of cumulative counting moves forward as the loading rate increases, which shows that the AE signal generated by shale fracture at low loading rate mainly comes from the initiation and propagation of microcracks, while at high loading rate it mainly comes from the formation of macro large-scale cracks. The fracture mechanism that causes shale fracture toughness and crack propagation velocity to vary with loading rate is also discussed based on the analysis results of AE signals.

We establish the Hao–Ng isomorphism for generalized gauge actions of locally compact abelian groups on product systems over abelian lattice orders and we then use it to explore Takai duality in this context. As an application we generalize some recent work of Schafhauser.

The radial design for strain gauge rosettes used for hole-drilling residual stress measurements was established over 50 years ago and has remained almost unchanged since then. The design was developed to promote strain sensitivity, but was made without regard for ability to identify interior stresses. Consequently, only near-surface residual stresses can be identified. The aim of this study is to investigate rosette geometric features that may be refined to enable a significant increase in ability to identify interior stresses without significant loss of strain sensitivity. A finite element analysis was undertaken to model the influence of various geometrical factors on the depth response of a strain gauge rosette. It was found that that circumferentially oriented strain gauges allow residual stress measurements to be made to twice the depth of traditional radial strain gauges, with only minor loss in strain sensitivity. A new circumferential strain gauge rosette design based on the presented analysis is proposed for use where extended depth measurements are desired.

For a smooth irreducible affine algebraic variety we study a class of gauge modules admitting compatible actions of both the algebra $A$ of functions and the Lie algebra $\mathcal{V}$ of vector fields on the variety. We prove that a gauge module corresponding to a simple $\mathfrak{gl}_N$-module is irreducible as a module over the Lie algebra of vector fields unless it appears in the de Rham complex.

Soda-lime glass remains elastic under shock pressures up to approximately 6.5 GPa. In this paper, soda lime glass shock experiments are used to understand the calibration and error propagation in longitudinal and lateral manganin gauge experiments. The errors in the calibration process for both longitudinal and lateral manganin gauge experiments are identified and discussed. Five soda-lime glass experiments up to 3 GPa are analyzed using this refined technique. The results show good agreement between the experimental data and the published calibration by Rosenberg and Moshel. Errors are propagated from the experimental data measurements and the assumptions that are made in the calibration, where the bulk of the error seems to come from uncertainty in the dynamic yield strength of manganin. The method presented in this paper allows for analysis of dynamic shock experiments with longitudinal and lateral manganin gauges including error propagation.

The conversions between different DNA have been observed in many experiments due to the development of technological hicks. Especially, the transformations between B- and Z-type DNA have been found by applying torque on DNA. The elastic rod model can be used to explain the experiments. Different from the elastic rod model, these transformations can be seen as the phase transformation, and then the Landau model and gauge theory were proposed to explain the conversions. The gauge potential describes the inner local interaction of the base pair. We find the equation of the chiral gauge potential and solve the equation. Furthermore, there are two parameters in the solutions; one decides the values of the gauge potential and affects the potential energy of the DNA. The other parameter describes the position the torque applying to.

Plate thermometer (PT) that consists of a thin metal plate and a layer of inorganic insulation material attached to the backside of the metal plate has been used to calculate the incident radiant heat flux by other researchers. However, the incident radiant heat flux is often underestimated using PT as the heat loss from the metal plate is not appropriately reflected in the calculation. Especially when PT is placed in low ambient temperature conditions or in a heating phase, the underestimation becomes more significant. Besides the heat loss effect, some PT properties such as surface emissivity and thermo-physical properties as well as errors of temperature measurements affect the accuracy of incident radiant heat flux calculations. In the current study, a new incident radiant heat flux calculation method is proposed to overcome the aforementioned inaccuracies. The temperature that a thermally thin metal element should ideally achieve with a perfectly insulated back surface is correlated with the actually measured surface temperature under known heat fluxes for calibration. From this correlation, a set of equations to calculate the incident radiant heat flux is derived for a mixed radiation/convection environment. For validation, the incident radiant heat fluxes calculated from the proposed method and measured from a commercially available Schmidt-Boelter type total heat flux gauge were compared and a good agreement was observed.

Background: For the standard ISO 16842 cruciform test specimen, stresses obtained from the gauge area are far below the ultimate tensile strength due to high stress concentrations at the slit ends which lead to premature failure. Objective: To introduce a new cruciform specimen design which has been optimized with respect to the determination of yield surfaces. Methods: The proposed design differs from the ISO standard by an additional thinning of the gauge area and wider slits in the arms to avoid stress singularities. Compared to other cruciform test piece designs found in the literature, the stress distribution is still homogeneous and there is no need to reduce the size of the gauge area, thanks to the specimen’s well-balanced proportions. Results: Biaxial tensile tests have been conducted with aluminium 5754 alloy samples of different thicknesses. For the standard cruciform test piece, the maximum strain achieved at the gauge area is only 25% of the fracture strain. The optimized cruciform test piece can attain about 66% of the fracture strain before breaking. Conclusions: The optimized specimen design enables the measurement of yield surfaces at higher stress levels. In case of other materials such as elastomers, the slit length has be to adjusted accordingly.

An individual motor torque control technology to improve the lateral restoring performance of the independently rotating wheel type railway vehicle, which has been applied for reasons such as low floor structure of the vehicle and application of variable gauge technology, has been developed. A new bogie analysis model and a small-scale roller-rig test bench respectively were developed to verify the control technology. A new bogie analysis model has been developed to improve the accuracy of analysis of the lateral and yaw motion of the actual vehicle. The model was verified through the response of the disturbance and critical velocity analysis. The performances of proposed control logic were verified by accomplishing a small-scale roller-rig test and simulation with improved analytical model. Lateral displacement control performs the opposite phase control by the control torque applying in the opposite direction to the front and rear wheelset, while yaw control performs the same phase control by applying the control torque in the same direction. Afterwards the yaw moments of the wheelset are combined to create a yaw moment of bogie, reducing the yaw angle and lateral displacement together. It was verified through analysis and test that the lateral restoring control performance based on the yaw angle (same phase control) was superior to the based on lateral displacement (opposite phase control).

The rolling mill vibration is characterized by the coupling effects among mechanical, electrical, hydraulic and interfacial subsystems. The influence of the mill modulus control gain in automatic gauge control on the vibration in hot rolling mills was investigated. Firstly, an experiment related to the mill modulus control gain was carried out in the hot rolling mill process, and it was found that the rolling mill vibration increases with the mill modulus control gain. Then, based on the Sims rolling force method, the coupling dynamic model was established to explain this phenomenon. Finally, the influence of mill modulus control gain on the vibration was analyzed numerically on the basis of the coupling dynamic model. Moreover, the agreement between the experimental results and the simulation results was confirmed and the measure reducing the mill modulus control gain was obtained to relieve mill vibration.

Ultracold alkaline-earth atoms are used in precision measurements and quantum simulation. Because of their unique atomic structure, they could enable the study of problems in quantum many-body systems, such as the simulation of synthetic gauge fields, Kondo and SU(N) physics. But to fully exploit this potential, the capability to tune the interatomic interaction to the strongly interacting regime is needed. Several theoretical proposals and experimental demonstrations have shown that both the spin-independent and spin-exchange interaction can be tuned to resonance in the alkaline-earth atoms. In this Perspective, we review these advances and discuss the opportunities brought by these interaction-control tools for future quantum simulation studies. Due to their atomic structure, ultracold alkaline-earth atoms are well suited for quantum simulation and the study of quantum many-body physics. This Perspective overviews the ways to control the interactions between atoms and discusses the new physics that could be uncovered.

We briefly review the manifold incarnations and facets of the notion that gravity, in certain regards, can be re-conceived as the product of two gauge theories. We begin with a short history of the relationship between gauge and gravity theories in the context of “$$\hbox {gravity} = \hbox {gauge} \times \hbox {gauge}$$”. This is followed by modern approaches to gauge/gravity scattering amplitude relations, focussing on the Bern–Carrasco–Johansson colour-kinematic duality and double-copy construction of gravitational amplitudes from gauge amplitudes. This includes a partial characterisation of what gravity theories admit a gauge theory squared origin. We then consider classical and off-shell perspectives on “$$\hbox {gravity} =\hbox {gauge} \times \hbox {gauge}$$”. First we review field theoretic approaches to understanding the colour-kinematic duality and the double-copy prescription, including kinematic algebras and colour-kinematic duality and double-copy manifesting Lagrangians. We then consider classical double-copy-like methods for constructing gravitational solutions from gauge theory solutions. To close, we consider a purely field theoretic take on “$$\hbox {gravity} =\hbox {gauge} \times \hbox {gauge}$$”. This framework centres on a convolutive product of gauge theories, at the level of spacetime fields themselves, that yields gravitational theories.

The conventional way to present Integral Method calibration data for hole-drilling residual stress measurements is in the form of a large triangular table of numbers. In the common case where 20 drilling steps are used for the hole-drilling measurement, 231 numerical coefficients are needed. While such tables are effective, their bulk inhibits their use for other than the most common experimental arrangements; the convenience and usefulness of the hole-drilling method would be much extended if the bulk of the calibration data could be reduced. Here, a two-variable polynomial formulation is proposed to represent the hole-drilling calibration data. It comprises 15 numerical coefficients and provides calibration data with average accuracy within 1%, with occasional outliers reaching around 2%. The compactness of the calibration stimulated exploration of hole-drilling response beyond the conventional “thick” specimen case, also to include finite thickness specimens down to very thin (through-hole) geometries. Tables of calibration data are provided here for ASTM E837 Type A, B and C strain gauge rosettes, for various hole diameters, for conventional “thick” specimens, and for finite thickness specimens down to the through-hole case.

Gauge fields play important roles in condensed matter, explaining for example nonreciprocal and topological transport phenomena. Establishing gauge potentials for phonon transport in nanomechanical systems would bring quantum Hall physics to a new domain, which offers broad applications in sensing and signal processing, and is naturally associated with strong nonlinearities and thermodynamics. In this work, we demonstrate a magnetic gauge field for nanomechanical vibrations in a scalable, on-chip optomechanical system. We exploit multimode optomechanical interactions, which provide a useful resource for the necessary breaking of time-reversal symmetry. In a dynamically modulated nanophotonic system, we observe how radiation pressure forces mediate phonon transport between resonators of different frequencies, with a high rate and a characteristic nonreciprocal phase mimicking the Aharonov-Bohm effect. We show that the introduced scheme does not require high-quality cavities, such that it can be straightforwardly extended to explore topological acoustic phases in many-mode systems resilient to realistic disorder., Corrected small typographic errors in v2

Repairs of concrete irrigation channels in Japan are guided to a large extent by the degree to which their walls have degraded over decades of use. Current methods of estimating Manning roughness coefficients from the roughness of the channel wall are based on linear profiles of arithmetic mean roughness. This study developed a method to estimate Manning roughness coefficients for a planar region directly from the peak-to-peak value of a reflected aerial ultrasonic wave, using a transceiver-based ultrasonic device. Model channel experiments using manufactured materials of known roughness were undertaken to confirm the strong correlation between peak-to-peak values and Manning roughness coefficients and to derive a conversion equation that was incorporated in the ultrasonic device. The device yielded Manning roughness coefficients for handmade concrete panels that matched estimates made by a conventional moulage gauge technique. It also matched the results of estimates by the commonly used Manning–Strickler equation. A field experiment in an operating irrigation channel confirmed these results, showing that aerial ultrasonic measurements of surface roughness are as accurate as those by existing techniques.

Despite its importance for hydrology and water resources, accurate estimation of snowfall rate over snow-covered regions has remained a major observational challenge from both in-situ and remote sensing instruments. Snowfall accumulation can be measured by either accumulating snowfall estimates or measuring snowpack properties such as Snow Water Equivalent (SWE) and mass. By focusing on snowfall over snow accumulation period and using case studies and long-term average (2003 to 2015) over CONUS, this study compares snowfall accumulation from gauge stations (using GPCC and PRISM products), satellite products (GPCP and the suite of IMERG products), and reanalysis (ERA-interim, ERA5, and MERRA-2). Changes in SWE based on the recent UA-SWE product together with mass change observation from GRACE were used for assessment of precipitation products. We also investigated two popular gauge undercatch correction factors (CFs) used to mitigate precipitation undercatch in GPCC and GPCP. The results show that snow accumulation from most of the products is bounded by GPCC with and without correction, highlighting the critical importance of selecting proper CFs for gauge-undercatch correction. The CF based on Legates and Willmott method was found to be more consistent with the SWE-based analysis than CF based on the Fuchs method. Reanalysis show very similar spatial pattern among themselves, but represent large variation in simulating snow accumulation, with ERA-interim showing the least accumulation and MERRA-2 showing the highest accumulation and closest to the snow accumulation suggested by SWE.

We investigate the quantum dynamics of neutral atoms subject to a uniform spin-dependent gauge field. In particular, we analyze a simple experimental scheme to generate the Landau quantization in a two dimensional atomic gas with internal three-level $\Lambda$-type configuration. We show how energy eigenfunctions and eigenvalues are obtained and discuss the experimental conditions for which a variety of physical quantities of the atomic gas can exhibit quantum oscillations., Comment: 11 pages, two figures

An analysis of the structure and content of verification technique MP 002.D4-14, extends to coating thickness gauges TM-2, TM-3, TM-4, and TM-4T, technique MP 159-261-2016 for verification of SaluTrjn coating thickness gauges, and a technique for verification of coating thickness gauges regulated by GOST 8.502–84 is performed. It is shown that the first two techniques do not take into account the random component of the error, while the third technique does take into account the random component but not correctly. These factors all lead to a high probability of a wrong identification of a model of a thickness gauge that is, in reality, defective to be, instead, a working model or, on the other hand working devices may be incorrectly identified as being defective. To increase the reliability of the results of a verification of coating thickness gauges, recommendations that suggest incorporating them into the content of a verification technique regulated by GOST 8.502–84 are proposed.

Small instantons can play an important role in Yang-Mills theories whose gauge couplings are sizeable at small distances. An interesting class of theories where this could occur is in weakly-gauged holographic models (dual to Yang-Mills theories interacting with strongly-coupled CFTs), since gauge couplings are indeed enhanced towards the UV boundary of the 5D AdS space. However, contrary to expectations, we show that small instantons in these non-asymptotically-free models are highly suppressed and ineffective. This is due to the conservation of topological charge that forbids instantons to be localized near the UV boundary. Despite this fact we find non-trivial UV localized instanton-anti-instanton solutions of the Yang-Mills equations where the topological charges annihilate in the AdS bulk. These analytic solutions arise from a 5D conformal transformation of the uplifted 4D instanton. Our analysis therefore reveals unexpected nonperturbative configurations of Yang-Mills theories when they interact with strongly-coupled CFTs., Comment: 23 pages, 8 figures

Simulation of pharmaceutical unit operations by the discrete element method (DEM) has elevated our understanding of the impact of single-particle interactions on themselves, and on the entire tablets/powder. Studies in the past have shown how this knowledge helps to mitigate/solve multiple challenges during conventional formulation and process development/modernization/troubleshooting, with minimal use of active drug material. This communication adds to this- highlighting the tool's potential for a rapid preliminary assessment of the mechanistic attributes of multiple unit particle system (MUPS) based tablet and capsule drug products.

We have investigated the relativistic quantum dynamics of a scalar field in an anisotropic background governed by the Lorentz symmetry violation. This analysis is done through a non-minimal coupling in the Klein–Gordon equation, which is inspired by the CPT-odd gauge sector of the standard model extension. From the elaboration of a vector and electromagnetic field configuration as a possible Lorentz break scenario, we induced an electric field which influences the scalar field. In this scenario, we show that it is possible to determine two energy profiles for the system, that is, a description of the relativistic quantum dynamics of the scalar field in the xy -plane and in all space-time.

This paper describes a generalization of decomposition in orbifolds. In general terms, decomposition states that two-dimensional orbifolds and gauge theories whose gauge groups have trivially-acting subgroups decompose into disjoint unions of theories. However, decomposition can be, at least naively, broken in orbifolds if the orbifold has discrete torsion in the trivially-acting subgroup. (Formally, this breaks finite global one-form symmetries.) Nevertheless, even in such cases, one still sees rudiments of decomposition. In this paper, we generalize decomposition in orbifolds to include such examples of discrete torsion, which we check in numerous examples. Our analysis includes as special cases (and in one sense generalizes) quantum symmetries of abelian orbifolds., 71 pages, LaTeX; v2: reference added; v3: typos fixed

Quantum states can acquire a geometric phase called the Berry phase after adiabatically traversing a closed loop, which depends on the path not the rate of motion. The Berry phase is analogous to the Aharonov-Bohm phase derived from the electromagnetic vector potential, and can be expressed in terms of an Abelian gauge potential called the Berry connection. Wilczek and Zee extended this concept to include non-Abelian phases -- characterized by the gauge independent Wilson loop -- resulting from non-Abelian gauge potentials. Using an atomic Bose-Einstein condensate, we quantum-engineered a non-Abelian SU(2) gauge field, generated by a Yang monopole located at the origin of a 5-dimensional parameter space. By slowly encircling the monopole, we characterized the Wilczek-Zee phase in terms of the Wilson loop, that depended on the solid-angle subtended by the encircling path: a generalization of Stokes' theorem. This observation marks the observation of the Wilson loop resulting from a non-Abelian point source., 11 pages, 8 figures

We introduce a first order description of linearized non-minimal (n = −1) supergravity in superspace, using the unconstrained prepotential superfield instead of the conventionally constrained super one forms. In this description, after integrating out the connection-like auxiliary superfield of first-order formalism, the superspace action is expressed in terms of a single superfield which combines the prepotential and compensator superfields. We use this description to construct the supersymmetric cubic interaction vertex 3/2 − 3/2 − 1/2 which describes the electromagnetic interaction between two non-minimal supergravity multiplets (superspin Y = 3/2 which contains a spin 2 and a spin 3/2 particles) and a vector multiplet (superspin Y = 1/2 contains a spin 1 and a spin 1/2 particles). Exploring the trivial symmetries emerging between the two Y = 3/2 supermultiplets, we show that this cubic vertex must depend on the vector multiplet superfield strength. This result generalize previous results for non-supersymmetric electromagnetic interactions of spin 2 particles. The constructed cubic interaction generates non-trivial deformations of the gauge transformations.