Original Gauge Research Articles

Strain Gauge Location Optimization for Operational Load Monitoring of an Aircraft Wing Using an Improved Correlation Measure

Operational loads of an aircraft are the prerequisite for assessing its safety or fatigue life. Traditionally, numerous strain gauge sensors are installed to monitor the operational loads, which inevitably increase the weight and system complexity of the aircraft. Therefore, in order to decrease the maintenance costs and data redundancy, the number and location of strain sensors should be optimized for accurate and reliable operational load monitoring. In this paper, a novel two-stage strain gauge location optimization method is proposed to reduce the number of strain gauges while maintaining the operational load monitoring accuracy, which is validated by a numerical case study of an aircraft wing. In the first stage, the traditional Pearson correlation measure is harnessed to initially eliminate numerous correlated strain gauge monitoring points, reducing 996 original strain gauge measurement points to 13 for the aircraft wing box. In the second stage, an improved correlation measure method is proposed to further reduce the 13 strain gauge points to 2, which can evaluate the correlation degree of several variables and simultaneously determine the optimal strain monitoring locations for the two load actuators in this study. The relative errors between the predicted loads and the actual loads for both load actuators are less than 4% when only two optimized monitoring points are adopted. In addition, a comparison study with LASSO regression and principal component regression methods is conducted. The results demonstrate that the proposed method has the characteristics of less monitoring points and higher load prediction precision.

Neutrino anarchy from flavor deconstruction

Flavor deconstruction refers to non-universal gauge extensions where the original gauge symmetry is deconstructed into separate copies, one for each family. A hierarchical chain of symmetry breaking provides an attractive low-scale solution to the flavor puzzle, consistent with flavor-changing neutral currents and finite naturalness. Although successful in explaining the origin of flavor hierarchies in the quark and charged lepton sectors, existing models have struggled with the large and seemingly anarchic mixing observed in neutrino oscillations. This letter identifies conditions under which neutrino anarchy may arise from flavor deconstruction in generic models with right-handed neutrinos. When deconstruction is applied to carefully chosen subgroups of the extended gauge symmetry, hierarchies in the seesaw formula cancel out.

The influence of pre-strain levels on the microstructure and performance of aircraft 7b04 aluminum alloy skin

The study focuses on the 7B04 alloy sheet. It investigates the effects of different pre-strain levels on the microstructure, mechanical properties, and fatigue behavior of the alloy through the use of optical microscopy, scanning electron microscopy, and DIC (Digital Image Correlation) system. The experimental results demonstrate that the yield strength and tensile strength of the alloy increase with the increase in pre-strain levels. At the same time, the elongation decreases with the increase in tensile deformation. In the non-uniform region, the plastic deformation capacity index of the material (denoted as ψ) follows the order ψ (non-uniform region (DIC value)) > ψ (original gauge length value) > ψ (uniform region (DIC value)). It is recommended to control the maximum local strain below ψ (uniform region (DIC value)) during production to avoid deformation instability or concentration. Furthermore, the thickness of the material decreases linearly with increasing tensile deformation, with each 4% increase in tensile deformation resulting in a 1.2% reduction in thickness. The fatigue life of the alloy increases gradually with the increase in pre-strain levels in the direction perpendicular to the fiber. At the same time, it decreases in the direction parallel to the fiber. Different deformation levels and loading directions exhibit similar fatigue fracture characteristics. Within the range of 12% pre-strain levels, the microstructure of the material remains continuous and intact without noticeable cracks at grain boundaries or phase boundaries. At the macroscopic level, when the pre-strain level exceeds 6%, distinct slip bands appear on the sheet, which is correlated with the micro-scale grain slip. This is accompanied by deformation bands and micro-cracks in the microstructure. The findings of this study are of significant importance for understanding the influence of pre-strain levels on the mechanical properties and fatigue behavior of the 7B04 alloy. The study provides valuable references for engineering practices in related fields, thereby ensuring the integrity and usability of manufactured components.

Orographic amplification of El Niño teleconnections on winter precipitation across the Intermountain West of North America

A large proportion of western North America experiences regular water stress, compounded by high seasonal and interannual variability. In the Intermountain West region, the El Niño/Southern Oscillation (ENSO) is a critical control on winter precipitation, but the nature of this signal is entangled with a combination of orographic effects and long-term climate trends. This study employs a spatially distributed, nonlinear spline model to isolate ENSO impacts from these other factors using gauge-based observations starting in 1871. In contrast to previous modelling approaches, our approach uses original gauge data, without shortening the record to accommodate a common period. This enables more detailed separation of ENSO effects from the confounding influence of topography and long-term trends, whereas the longer time frame permits more robust correlation with the ENSO signal. Here we show that the complex topography of the Intermountain West exaggerates the underlying ENSO signal, producing a 2.3–5.8 times increase in the range of ENSO-induced precipitation changes along high-elevation western slopes relative to lower elevations. ENSO effects on winter precipitation can be as large as ± 100 mm at high elevations. Further, our approach reveals that the previously recognized dipolar pattern of positive (negative) association of ENSO with precipitation in the south (north) manifests as an incremental relationship in the south but as a near-binary switch in effects between El Niño and La Niña in the north. The location and extent of the strongest precipitation differences vary during the positive and negative ENSO phases within each region. The intricacies of these spatial- and elevation-based modulations of ENSO impacts are especially informative for the northern centre of this dipole, where ENSO-precipitation relationships have previously been difficult to resolve.

FLPR model: Nilpotent (anti-)co-BRST symmetries

We demonstrate the existence of a set of novel off-shell nilpotent and absolutely anticommuting continuous symmetry transformations, within the framework of the Becchi-Rouet-Stora-Tyutin (BRST) formalism, which are over and above the usual off-shell nilpotent and absolutely anticommuting (anti-)BRST transformations that are respected by the quantum version of the classical first-order Lagrangian for the Friedberg-Lee-Pang-Ren (FLPR) model that describes the motion of a single non-relativistic particle of unit mass (moving under the influence of a general rotationally invariant spatial two-dimensional potential). We christen these novel set of fermionic transformations as the (anti-)co-BRST transformations because the gauge-fixing terms remain invariant under them. We derive the conserved and off-shell nilpotent (anti-)BRST and (anti-)co-BRST charges and comment on the physicality criteria with respect to them where we establish the presence of the operator forms of the first-class constraints (of the original classical gauge theory) at the quantum level which is consistent with the Dirac-quantization conditions.

Generalized gauge transformation and the corresponding Hermitian counterparts of SU(1, 1), SU(2) pseudo-Hermitian Hamiltonians

We study in this paper both the stationary and time-dependent pseudo-Hermitian Hamiltonians consisting respectively of SU(1, 1), SU(2) generators. The pseudo-Hermitian Hamiltonians can be generated from kernel Hermitian-Hamiltonians by a generalized gauge transformation with a non-unitary but Hermitian operator. The metric operator of the biorthogonal sets of eigenstates is simply the square of the transformation operator, which is formulated explicitly. The exact solutions of pseudo-Hermitian Hamiltonians are obtained in terms of the eigenststates of the Hermitian counterparts. We observe a critical point G c of coupling constant, where all eigenstates of the stationary Hamiltonians are degenerate with a vanishing eigenvalue. This critical point is modified as G c (ω) in the time-dependent case including the frequency of external field. Returning to the original gauge we obtain analytically the wave functions and associated non-adiabatic Berry phase, which diverges at the critical point for the SU(2)Hamiltonian. Beyond the critical point Berry phase becomes a complex domain.

Quintic vertices of spin 3, vector and scalar fields

As a result of special deformations of free gauge models of massless spin 3, massive vector and real scalar fields, quintic vertices within new approach Buchbinder and Lavrov (2021) [32]; Buchbinder and Lavrov (2021) [33]; Lavrov (2022) [34] are constructed. They are described by local functionals which are invariant under original gauge transformations.

Confinement on the moose lattice

In this work we present a new class of mathcal{N} = 1 supersymmetric confining gauge theories, with strikingly simple infrared theories that descend from intricate interconnected networks of product gauge groups. A diagram of the gauge groups and the charged matter content of the ultraviolet theory has the structure of a triangular lattice, with SU(N) or SU(3N) gauge groups at each of the vertices, connected by bifundamental chiral superfields. This structure admits a U(1)R conserving superpotential with marginal (trilinear) operators. With the introduction of this superpotential, the SU(3N) and SU(N) gauge groups confine: in the far infrared limit of the supersymmetric theory, the relevant degrees of freedom are gauge invariant “mesons” and “baryons.” In this paper we show how the properties of the infrared degrees of freedom depend on the topology and shape of the moose/quiver “lattice” of the original gauge theory. Between the local structure of the moose lattice at higher energies, and the boundary dependence that emerges in the infrared, the 4d moose lattice theory reproduces features of a 6d spacetime with two compact dimensions. We investigate various deformations of the theory, and propose some phenomenological applications for BSM models.

The evaluation of IMERG and ERA5-Land daily precipitation over China with considering the influence of gauge data bias

Evaluating the accuracy of the satellite and reanalysis precipitation products is very important for understanding their uncertainties and potential applications. However, because of underestimation existing in commonly used evaluation benchmark, gauge precipitation data, it is necessary to investigate the influence of systematic errors in gauge data on the performance evaluation of satellite and reanalysis precipitation datasets. Daily satellite-based IMERG and model-based ERA5-Land, together with gauge precipitation data, were collected with the period from 2005 to 2016 over China in this study. Daily corrections for precipitation biases from wind-induced undercatch, wetting loss, and trace error were made for gauge measurements. A set of metrics, including relative bias, Kling-Gupta efficiency, frequency bias, and critical success index, were used to evaluate and intercompare the performances of IMERG and ERA5-Land against original and bias-corrected gauge data in different locations, years, seasons, climatic zones, classes of precipitation events, and precipitation phases. The results have shown that: After removing the bias in gauge data, the relative biases of IMERG and ERA5-Land both significantly decline. The noticeable changes of their accuracy occur and vary with different locations, years, seasons, climatic zones, and precipitation phases. Furthermore, the frequency biases of IMERG and ERA5-Land rise in no precipitation events and decline in light, moderate, heavy, and extreme precipitation events. The detection capability of IMERG and ERA5-Land in no and light precipitation events is also obviously affected. Therefore, this study has demonstrated the significant influence of systematic gauge precipitation errors on the assessment of IMERG and ERA5-Land and reinforces the necessity to remove negative bias in gauge data before using it as the benchmark.

Particle on a torus knot: symplectic analysis

We quantize a particle confined to move on a torus knot satisfying constraint condition ( $$p\theta +q\phi ) \approx 0$$ , within the context of a geometrically motivated approach—the Faddeev–Jackiw formalism. We also deduce the constraint spectrum and discern the basic brackets of the theory. We further reformulate the original gauge non-invariant theory into a physically equivalent gauge theory, which is free from any additional Wess–Zumino variables, by employing symplectic gauge invariant formalism. In addition, we analyze the reformulated gauge invariant theory within the framework of BRST formalism to establish the off-shell nilpotent and absolutely anti-commuting (anti-)BRST symmetries. Finally, we construct the conserved (anti-)BRST charges which satisfy the physicality criteria and turn out to be the generators of corresponding symmetries.

Center vortex and confinement in Yang–Mills theory and QCD with anomaly-preserving compactifications

Abstract We construct an anomaly-preserving compactification of 4D gauge theories, including SU(N) Yang–Mills theory, $\mathcal {N}=1$ supersymmetric Yang–Mills theory, and quantum chromodynamics (QCD), down to 2D by turning on the ’t Hooft flux through T2. This provides a new framework to analytically calculate nonperturbative properties such as confinement, chiral symmetry breaking, and the multi-branch structure of vacua. We give a semiclassical description of these phenomena based on the center vortex and show that it enjoys the same anomaly-matching condition as the original 4D gauge theory. We conjecture that the weak-coupling vacuum structure on small $T^2 \times \mathbb {R}^2$ is adiabatically connected to the strong-coupling regime on $\mathbb {R}^4$ without any phase transitions. In QCD with fundamental quarks as well, we can turn on the ’t Hooft flux either by activating the SU(Nf)V symmetry twist for Nf = N flavors or by introducing a magnetic flux of baryon number U(1)B for arbitrary Nf flavors. In both cases, the weak-coupling center-vortex theory gives a prediction consistent with the chiral Lagrangian of 4D QCD.

The Standard Model quiver in de Sitter string compactifications

We argue that the Standard Model quiver can be embedded into compact Calabi-Yau geometries through orientifolded D3-branes at del Pezzo singularities dPn with n ≥ 5 in a framework including moduli stabilisation. To illustrate our approach, we explicitly construct a local dP5 model via a combination of Higgsing and orientifolding. This procedure reduces the original dP5 quiver gauge theory to the Left-Right symmetric model with three families of quarks and leptons as well as a Higgs sector to further break the symmetries to the Standard Model gauge group. We embed this local model in a globally consistent Calabi-Yau flux compactification with tadpole and Freed-Witten anomaly cancellations. The model features closed string moduli stabilisation with a de Sitter minimum from T-branes, supersymmetry broken by the Kähler moduli, and the MSSM as the low energy spectrum. We further discuss phenomenological and cosmological implications of this construction.

Study on Gage Widening Methods for Small-Radius Curves

Existing gage widening standards and the influence of gage widening on the curve passing performance of trains and rail wear were examined. The existing gage widening theory can determine the minimum curve radius that needs to be widened, the widening value required by curves with different radii, and whether multiaxle locomotives can pass small-radius curves. However, it does not quantify the influence of the gage widening value on the curve passing performance and track maintenance workload. The range of the minimum curve radius that needs to be widened is 220–350 m, whereas some countries adopt a radius of 600 m; the maximum gage widening range is 15–20 mm, and few countries adopt gage widening values exceeding 30 mm. When the gage widening value increases from 0 to 10 mm, the lateral force of the curved wheel or rail with a radius less than 300 m is reduced by 16–20%, and that with a radius exceeding 300 m is reduced by 10–15%. The results of this study reveal that using proper gage widening values can reduce the lateral force of the wheel or rail and improve the curve passing performance. In the rail lifecycle, the implementation of the current gage widening standard requires only one gage adjustment operation, whereas the implementation of the original gage widening standard requires doubling gage adjustment operations.

Notes on two-dimensional pure supersymmetric gauge theories

In this note we study IR limits of pure two-dimensional supersymmetric gauge theories with semisimple non-simply-connected gauge groups including SU(k)/ℤk, SO(2k)/ℤ2, Sp(2k)/ℤ2, E6/ℤ3, and E7/ℤ2 for various discrete theta angles, both directly in the gauge theory and also in nonabelian mirrors, extending a classification begun in previous work. We find in each case that there are supersymmetric vacua for precisely one value of the discrete theta angle, and no supersymmetric vacua for other values, hence supersymmetry is broken in the IR for most discrete theta angles. Furthermore, for the one distinguished value of the discrete theta angle for which supersymmetry is unbroken, the theory has as many twisted chiral multiplet degrees of freedom in the IR as the rank. We take this opportunity to further develop the technology of nonabelian mirrors to discuss how the mirror to a G gauge theory differs from the mirror to a G/K gauge theory for K a subgroup of the center of G. In particular, the discrete theta angles in these cases are considerably more intricate than those of the pure gauge theories studied in previous papers, so we discuss the realization of these more complex discrete theta angles in the mirror construction. We find that discrete theta angles, both in the original gauge theory and their mirrors, are intimately related to the description of centers of universal covering groups as quotients of weight lattices by root sublattices. We perform numerous consistency checks, comparing results against basic group-theoretic relations as well as with decomposition, which describes how two-dimensional theories with one-form symmetries (such as pure gauge theories with nontrivial centers) decompose into disjoint unions, in this case of pure gauge theories with quotiented gauge groups and discrete theta angles.

Determination of Phase Space Spectra of the Generalized Chiral Schwinger model with the Lorentz invariant Mass like Term for the Choice a − r2 = 0

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.

Integrability and cycles of deformed [formula omitted] gauge theory

To analyse pure N=2SU(2) gauge theory in the Nekrasov-Shatashvili (NS) limit (or deformed Seiberg-Witten (SW)), we use the Ordinary Differential Equation/Integrable Model (ODE/IM) correspondence, and in particular its (broken) discrete symmetry in its extended version with two singular irregular points. Actually, this symmetry appears to be ‘manifestation’ of the spontaneously broken Z2 R-symmetry of the original gauge problem and the two deformed SW one-cycle periods are simply connected to the Baxter's T and Q functions, respectively, of the Liouville conformal field theory at the self-dual point. The liaison is realised via a second order differential operator which is essentially the ‘quantum’ version of the square of the SW differential. Moreover, the constraints imposed by the broken Z2 R-symmetry acting on the moduli space (Bilal-Ferrari equations) seem to have their quantum counterpart in the TQ and the T periodicity relations, and integrability yields also a useful Thermodynamic Bethe Ansatz (TBA) for the periods (Y(θ,±u) or their square roots, Q(θ,±u)). A latere, two efficient asymptotic expansion techniques are presented. Clearly, the whole construction is extendable to gauge theories with matter and/or higher rank groups.

Analytical relations for the bound state spectrum of gauge theories with a Brout-Englert-Higgs mechanism

We apply the method proposed by Fr\"ohlich, Morchio, and Strocchi to analyze the bound state spectrum of various gauge theories with a Brout-Englert-Higgs mechanism. These serve as building blocks for theories beyond the standard model but also stress the exceptional role of the standard model weak group. We will show how the Fr\"ohlich-Morchio-Strocchi mechanism relates gauge-invariant bound state operators to invariant objects of the remaining unbroken gauge group after gauge fixing. In particular, this provides a strict gauge-invariant formulation of the latter in terms of the original gauge symmetry without using the terminology of spontaneous gauge symmetry breaking. We also demonstrate that the Fr\"ohlich-Morchio-Strocchi approach allows us to put new constraints on theories beyond the standard model by pure field-theoretical considerations. Particularly the conventional construction of grand unified theories has to be rethought.

Quasicircular inspirals and plunges from nonspinning effective-one-body Hamiltonians with gravitational self-force information

The self-force program aims at accurately modeling relativistic two-body systems with a small mass ratio (SMR). In the context of the effective-one-body (EOB) framework, current results from this program can be used to determine the effective metric components at linear order in the mass ratio, resumming post-Newtonian (PN) dynamics around the test-particle limit in the process. It was shown in [Akcay et al., Phys. Rev. D 86 (2012)] that, in the original (standard) EOB gauge, the SMR contribution to the metric component $g^\text{eff}_{tt}$ exhibits a coordinate singularity at the light-ring (LR) radius. In this paper, we adopt a different gauge for the EOB dynamics and obtain a Hamiltonian that is free of poles at the LR, with complete circular-orbit information at linear order in the mass ratio and non-circular-orbit and higher-order-in-mass-ratio terms up to 3PN order. We confirm the absence of the LR-divergence in such an EOB Hamiltonian via plunging trajectories through the LR radius. Moreover, we compare the binding energies and inspiral waveforms of EOB models with SMR, PN and mixed SMR-3PN information on a quasi-circular inspiral against numerical-relativity predictions. We find good agreement between NR simulations and EOB models with SMR-3PN information for both equal and unequal mass ratios. In particular, when compared to EOB inspiral waveforms with only 3PN information, EOB Hamiltonians with SMR-3PN information improves the modeling of binary systems with small mass ratios $q \lesssim 1/3$, with a dephasing accumulated in $\sim$30 gravitational-wave (GW) cycles being of the order of few hundredths of a radian up to 4 GW cycles before merger.

On constant solutions of SU(2) Yang-Mills equations with arbitrary current in Euclidean space ℝn

In this paper, we present all constant solutions of the Yang-Mills equations with SU(2) gauge symmetry for an arbitrary constant non-Abelian current in Euclidean space ℝn of arbitrary finite dimension n. Using the invariance of the Yang-Mills equations under the orthogonal transformations of coordinates and gauge invariance, we choose a specific system of coordinates and a specific gauge fixing for each constant current and obtain all constant solutions of the Yang-Mills equations in this system of coordinates with this gauge fixing, and then in the original system of coordinates with the original gauge fixing. We use the singular value decomposition method and the method of two-sheeted covering of orthogonal group by spin group to do this. We prove that the number (0, 1, or 2) of constant solutions of the Yang-Mills equations in terms of the strength of the Yang-Mills field depends on the singular values of the matrix of current. The explicit form of all solutions and the invariant F2 can always be written using singular values of this matrix. The relevance of the study is explained by the fact that the Yang-Mills equations describe electroweak interactions in the case of the Lie group SU(2). Non-constant solutions of the Yang-Mills equations can be considered in the form of series of perturbation theory. The results of this paper are new and can be used to solve some problems in particle physics, in particular, to describe physical vacuum and to fully understand a quantum gauge theory.

Fronsdal fields from gauge functions in Vasiliev\u2019s higher spin gravity

In this paper, we revisit a number of issues in Vasiliev’s theory related to gauge functions, ordering schemes, and the embedding of Fronsdal fields into master fields. First, we parametrize a broad equivalence class of linearized solutions using gauge functions and integration constants, and show explicitly how Fronsdal fields and their Weyl tensors arise from these data in accordance with Vasiliev’s central on mass shell theorem. We then gauge transform the linearized piece of exact solutions, obtained in a convenient gauge in Weyl order, to the aforementioned class, where we land in normal order. We spell out this map for massless particle and higher spin black hole modes. Our results show that Vasiliev’s equations admit the correct free-field limit for master field configurations that relax the original regularity and gauge conditions in twistor space. Moreover, they support the off-shell Frobenius-Chern-Simons formulation of higher spin gravity for which Weyl order plays a crucial role. Finally, we propose a Fefferman-Graham-like scheme for computing asymptotically anti-de Sitter master field configurations, based on the assumption that gauge function and integration constant can be adjusted perturbatively so that the full master fields approach free master fields asymptotically.