Linear Gauge Research Articles

Application of Machine Learning Algorithms in Real-Time Monitoring of Conveyor Belt Damage

This paper is devoted to the real-time monitoring of close transportation devices, namely, belt conveyors. It presents a novel measurement system based on the linear strain gauges placed on the tail pulley surface. These gauges enable the monitoring and continuous collection and processing of data related to the process. An initial assessment of the machine learning application to the load identification was made. Among the tested algorithms that utilized machine learning, some exhibited a classification accuracy as high as 100% when identifying the load placed on the moving belt. Similarly, identification of the preset damage was possible using machine learning algorithms, demonstrating the feasibility of the system for fault diagnosis and predictive maintenance.

Soft wearable electronics for evaluation of biological tissue mechanics

Flexible wearable devices designed to evaluate the biomechanical properties of deep tissues not only facilitate continuous and effective monitoring in basic performance but also exhibit significant potential in broader disease assessments. Recent advancements are highlighted in the structural and principled design of platforms capable of capturing various biomechanical signals. These advancements have led to enhanced testing capabilities concerning spatial scales and resolution modes at different depths. This review discusses the engineering of soft wearable devices for the biomechanical evaluation of deep tissue signals. It encompasses different measurement modes, device design and fabrication methods, integrated circuit (IC) integration schemes, and the characteristics of measurement depth and accuracy. The core discussion focuses on platform development, targeting different monitoring sites and platform structure design, ranging from linear strain gauges and conformal stretchable sensors to complex three-dimensional (3D) circuit-integrated stretchable arrays. We further explore various technologies associated with different measurement mechanisms and engineering designs, as well as the penetration depth and spatial resolution of these wearable sensors. The practical applications of these technologies are evident in the monitoring of deep tissue signals and changes in tissue characteristics. The results suggest that wearable biomechanical sensing systems hold substantial promise for applications in healthcare and research.

On the conformal limit of a QED-inspired model

A conformal invariant QED-inspired model is solved for a general covariant linear gauge using the Dyson–Schwinger equations for the propagators assuming a pure vector like interaction. The leading corrections to the asymptotic solutions and the exponents, that characterize the corrections to each of the two fermion propagator functions, are computed as a function of the coupling and gauge fixing parameter ξ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\xi $$\\end{document}. For the scalar component of the fermion propagator our findings generalizes for linear covariant gauges previous results found in the literature and reproduce the outcome of the perturbative analysis of quenched QED in the Landau gauge. Our solution for the exponent associated with vector component of the fermion propagator is new and, in the weak coupling regime, agrees with the estimation based on the perturbative analysis of quenched QED. Of the two critical exponents describing the conformal limit of the vector interaction, one of them is, in QED, associated with the regime where chiral symmetry is broken dynamically, which demands one mass scale, namely the Miransky scaling. A second mass scale has to be introduced at larger coupling constants and is associated with a change on the nature of the fermion wave function. This provides one example, that it is possible to find two interwoven cycles in Quantum Field Theory, albeit in a truncated framework, as it is known in the quantum few-body problem in the limit of a zero-range interaction.

Photon quantization in cosmological spaces

Canonical quantization of the photon—a free massless vector field—is considered in cosmological spacetimes in a two-parameter family of linear gauges that treat all the vector potential components on equal footing. The goal is setting up a framework for computing photon two-point functions appropriate for loop computations in realistic inflationary spacetimes. The quantization is implemented without relying on spacetime symmetries, but rather it is based on the classical canonical structure. Special attention is paid to the quantization of the canonical first-class constraint structure that is implemented as the condition on the physical states. This condition gives rise to subsidiary conditions that the photon two-point functions must satisfy. Some of the de Sitter space photon propagators from the literature are found not to satisfy these subsidiary conditions, bringing into question their consistency. Published by the American Physical Society 2024

Fine‐Tunable CO2 Colorimetric Sensors and CO2 Level Indicator Meter with Horizontal Linear Gauge via Inter‐Chain Spacers

AbstractFine‐tuning the sensing properties of carbon dioxide (CO2) colorimetric sensors is a challenging task. In this study, a short synthetic route is developed for CO2‐responsive nanoparticles with diverse sensitivity and detection range across a wide range of CO2 concentrations. This involves the addition of oily liquids as inter‐chain spacers, which changes the diffusivity of CO2 gas into the sensing matrices without other chemical modifications. R values and the limit of detection (LOD) are estimated from Euclidean distance (ED) curves, indicating a ten‐fold difference in sensitivity. Optical and physical analyses revealed that these results arise from intercalating inter‐chain spacers between polymeric chains and modifying the gas diffusivity. Furthermore, the sensitivity and detection range can be easily tuned by mixing two CO2‐responsive nanoparticles having different inter‐chain spacers, allowing the fabrication of the sensors with subtle differences in sensitivity and detection range. Based on these results, a CO2 level meter with a horizontal linear gauge that allows visible identification of the level of CO2 over the entire range of CO2 concentrations (from 0% to 100%) is developed. Consequently, the findings will be helpful in achieving a better understanding of gas information and finding an effective way to control the characteristics of colorimetric sensors.

Explicit no- π2 renormalization schemes in QCD at five loops

We examine a variety of renormalization schemes in QCD based on its 3-point vertices where the β-functions, gluon, ghost, quark and quark mass anomalous dimensions in each scheme do not depend on ζ4 or ζ6 in an arbitrary linear covariant gauge at five loops. We comment on the C-scheme. Published by the American Physical Society 2024

Dynamically massive linear covariant gauges: Setup and first results

We discuss the possibility to obtain a massive Landau gauge, based on the local composite operator effective action framework combined with the Zimmermann reduction of couplings prescription. As a way to deal with the gauge ambiguity, we check that the ghost propagator remains positive, a necessary condition for gluon field configurations beyond the Gribov region to be negligible. We pay attention to the Becchi-Rouet-Stora-Tyutin invariance of the construction, allowing for a future generalization to a class of massive linear covariant gauges. As a litmus test, we compare our predictions to the lattice data for the two-point functions in Landau gauge introducing the “dynamically infrared-safe” renormalization scheme, including the renormalization group optimization of both the gap equation and the two-point functions. We also discuss the relation to and differences with the Curci-Ferrari model, the usefulness of which in providing an effective perturbative description of nonperturbative Yang-Mills theories became clear during recent years. Published by the American Physical Society 2024

Landau-Khalatnikov-Fradkin Gauge Transformations for the Propagator and Vertex in QED and QED2

The non-perturbative Landau-Khalatnikov-Fradkin (LKF) transformations describe how Green functions in quantum field theory transform under a change in the photon field’s linear covariant gauge parameter (denoted ξ). The transformations are framed most simply in coordinate space where they are multiplicative. They imply that information on gauge-dependent contributions from higher order diagrams in the perturbative series is contained in lower order contributions, which is useful in multi-loop calculations. We study the LKF transformations for the propagator and the vertex in both scalar and spinor QED, in some particular dimensions. A novelty of our work is to derive momentum-space integral representations of these transformations; our expressions are also applicable to the longitudinal and transverse parts of the vertex. Applying these transformations to the tree-level Green functions, we show that the one-loop terms obtained from the LKF transformation agree with the gauge dependent parts obtained from perturbation theory. Our results will be presented in more comprehensive form elsewhere.

Crestal strain of two-implant mandibular overdentures with implants placed at different positions: An in vitro 3D printed simulation study

Statement of problemThe 2-implant mandibular overdenture (2IMO) is a popular treatment for patients with mandibular edentulism. However, information on the influence of implant positions on crestal strain is lacking. PurposeThe purpose of this in vitro study was to evaluate the crestal strain around 2 implants to support mandibular overdentures when placed at different positions. Material and methodsEdentulous mandibles were 3-dimensionally (3D) designed separately with 2 holes for implant placement at similar distances of 5, 10, 15, and 20 mm from the midline, resulting in 4 study conditions. The complete denture models were 3D designed and printed from digital imaging and communications in medicine (DICOM) images after scanning the patient’s denture. Two 4.3×12-mm dummy implants were placed in the preplanned holes. Two linear strain gauges were attached on the crest of the mesial and distal side of each implant (CH1, CH2, CH3, and CH4) and connected to a computer to record the electrical signals. Male LOCATOR attachments were attached, the mucosal layer simulated, and the denture picked up with pink female nylon caps. A unilateral and bilateral force of 100 N was maintained for 10 seconds for each model in a universal testing machine while recording the maximum strains in the DCS-100A KYOWA computer software program. Data were analyzed by using 1-way analysis of variance, the Tukey post hoc test, and the paired t test (α=.05). ResultsUnder bilateral loading, the strain values indicated a trend with increasing distance between the implants with both right and left distal strain gauges (CH4 and CH1). The negative (-ve) values indicated the compressive force, and the positive (+ve) values indicated the tensile force being applied on the strain gauges. The strain values for CH4 ranged between −166.08 for the 5-mm and −251.58 for the 20-mm position; and for CH1 between −168.08 for the 5-mm and −297.83 for the 20-mm position. The remaining 2 mesial strain gauges for all 4 implant positions remained lower than for CH4 and CH1. Under unilateral-right loading, only the right-side distal strain gauge CH4 indicated the increasing trend in the strain values with −147.5 for the 5-mm, −157.17 for the 10-mm, −209.33 for the 15-mm, and −234.75 for the 20 mm position. The remaining 3 strain gauges CH3, CH2, and CH1 ranged between −28.33 and −107.17. For each position for both implants, significantly higher (P<.05) strain values were observed on the distal strain gauge channels CH4 and CH1 than on the mesial channels CH3 and CH2 under bilateral loading and on the right side under unilateral loading. ConclusionsPeri-implant crestal strains in the 2IMO increased by increasing the distance of the implants from the midline. The stress values progressively increased from 5 to 10 mm to 15 to 20 mm from midline, represented as lateral incisor, canine, and premolar positions. The distal side of the implants exhibits higher strains than the mesial side of the implants.

Half-Bridge Silicon Strain Gauges with Arc-Shaped Piezoresistors.

Half-bridge silicon strain gauges are widely used in the fabrication of diaphragm-type high-pressure sensors, but in some applications, they suffer from low output sensitivity because of mounting position constraints. Through a special design and fabrication approach, a new half-bridge silicon strain gauge comprising one arc gauge responding to tangential strain and another linear gauge measuring radial strain was developed using Silicon-on-Glass (SiOG) substrate technology. The tangential gauge consists of grid patterns, such as the reciprocating arc of silicon piezoresistors on a thin glass substrate. When two half-bridges are connected to form a full bridge with arc-shaped gauges that respond to tangential strain, they have the advantage of providing much higher output sensitivity than a conventional half-bridge. Pressure sensors tested under pressure ranging from 0 to 50 bar at five different temperatures indicate a linear output with a typical sensitivity of approximately 16 mV/V/bar, a maximum zero shift of 0.05% FS, and a span shift of 0.03% FS. The higher output level of pressure sensing gauges will provide greater signal strength, thus maintaining a better signal-to-noise ratio than conventional pressure sensors. The offset and span shift curves are quite linear across the operating temperature range, giving the end user the advantage of using very simple algorithms for temperature compensation of offset and span shift.

Synchronous coordinates and gauge-invariant observables in cosmological spacetimes

We consider the relational approach to construct gauge-invariant observables in cosmological perturbation theory using synchronous coordinates. We construct dynamical synchronous coordinates as non-local scalar functionals of the metric perturbation in the fully non-linear theory in an arbitrary gauge. We show that the observables defined in this dynamical coordinate system are gauge-independent, and that the full perturbed metric has the expected form in these coordinates. Our construction generalises the familiar synchronous gauge in linearised gravity, widely used in cosmological perturbation theory, to the non-linear theory. We also work out the expressions for the gauge-invariant Einstein equation, sourced either by an ideal fluid or a scalar field up to second order in perturbation theory, and give explicit expressions for the Hubble rate—as measured by synchronous observers or by observers co-moving with the matter field—up to that order. Finally, we consider quantised linear perturbations around Minkowski and de Sitter backgrounds, and compute the two-point function of the gauge-invariant metric perturbation in synchronous coordinates, starting with two-point function in a general linear covariant gauge. Although the gauge-fixed two-point function contains gauge modes, we show that the resulting gauge-invariant two-point function only contains the physical tensor modes and it is thus positive, i. e. it has a spectral representation.

Lower Bounds for QCDCL via Formula Gauge

QCDCL is one of the main algorithmic paradigms for solving quantified Boolean formulas (QBF). We design a new technique to show lower bounds for the running time in QCDCL algorithms. For this we model QCDCL by concisely defined proof systems and identify a new width measure for formulas, which we call gauge. We show that for a large class of QBFs, large (e.g. linear) gauge implies exponential lower bounds for QCDCL proof size. We illustrate our technique by computing the gauge for a number of sample QBFs, thereby providing new exponential lower bounds for QCDCL. Our technique is the first bespoke lower bound technique for QCDCL.

An Improved Mathematical Theory for Designing Membrane Deflection-Based Rain Gauges

This paper is devoted to developing a more refined mathematical theory for designing the previously proposed membrane deflection-based rain gauges. The differential-integral equations governing the large deflection behavior of the membrane are improved by modifying the geometric equations, and more accurate power-series solutions of the large deflection problem are provided, resulting in a new and more refined mathematical theory for designing such rain gauges. Examples are presented to illustrate how to analyze the convergence of the power-series solutions and how to numerically calibrate membrane deflection-based linear rain gauges. In addition, some important issues are demonstrated, analyzed, and discussed, such as the superiority of the new mathematical theory over the old one, the reason why the classical geometric equations cause errors, and the influence of changing design parameters on the input–output relationships of rain gauges.

Looking at QED with Dyson–Schwinger Equations: Basic Equations, Ward–Takahashi Identities and the Two-Photon-Two-Fermion Irreducible Vertex

A minimal truncated set of the integral Dyson–Schwinger equations, in Minkowski spacetime, that allows to explore QED beyond its perturbative solution is derived for general linear covariant gauges. The minimal set includes the equations for the fermion and photon propagators, the photon-fermion vertex, and the two-photon-two-fermion one-particle-irreducible diagram. If the first three equations are exact, to build a closed set of equations, the two-photon-two-fermion equation is truncated ignoring the contribution of Green functions with large number of external legs. It is shown that the truncated equation for the two-photon-two-fermion vertex reproduces the lowest-order perturbative result in the limit of the small coupling constant. Furthermore, this equation allows to define an iterative procedure to compute higher order corrections in the coupling constant. The Ward–Takahashi identity for the two-photon-two-fermion irreducible vertex is derived and solved in the soft photon limit, where one of the photon momenta vanish, in the low photon momenta limit and for general kinematics. The solution of the Ward–Takahashi identity determines the longitudinal component of the two-photon-two-fermion irreducible vertex, while it is proposed to use the Dyson–Schwinger equation to determine the transverse part of this irreducible diagram. The two-photon-two-fermion DSE is solved in heavy fermion limit, considering a simplified version of the QED vertices. The contribution of this irreducible vertex to a low-energy effective photon-fermion vertex is discussed and the fermionic operators that are generated are computed in terms of the fermion propagator functions.

Bending behavior and bond analysis on adhesively bonded glulam-concrete panels fabricated with wet bonding technique

In this paper, we report on the effect of adhesive type on the bending behavior of adhesively bonded glulam-concrete composite panels. Steel-reinforced and unreinforced concrete were bonded to glued-laminated timber (GL-24 h) panels with polyurethane (PUR) and epoxy adhesives using the wet bonding technique. The PUR and epoxy adhesives (both were two-component adhesives) were selected to represent brittle and ductile adhesive behaviors. Four-point bending load was applied to glulam-concrete composite panels to investigate their bending behavior. The bending behavior measured includes bending load vs. mid-span deflection, strain distribution at the mid-span of the panel, and strain distribution between the loading point and its adjacent support. These were determined by linear variable differential transformers (LVDTs), strain gauges, and digital image correlation (DIC) technique. The experimental results showed that polyurethane-bonded glulam-unreinforced concrete panels showed similar load vs. mid-span deflection curves to epoxy-bonded glulam-unreinforced concrete panels and epoxy-bonded glulam-reinforced concrete panels. The shear stress, shear deformation, and peel strain analyses at the adhesive bond line showed that debonding at the glulam-concrete interface was more likely to occur for panels bonded with the ductile polyurethane.

Load-Bearing Performance of Non-Prismatic RC Beams Wrapped with Carbon FRP Composites

This study investigated the influence of CFRP composite wrapping techniques on the load–deflection and strain relationships of non-prismatic RC beams. A total of twelve non-prismatic beams with and without openings were tested in the present study. The length of the non-prismatic section was also varied to assess the effect on the behavior and load capacity of non-prismatic beams. The strengthening of beams was performed by using carbon fiber-reinforced polymer (CFRP) composites in the form of individual strips or full wraps. The linear variable differential transducers and strain gauges were installed at the steel bars to observe the load–deflection and strain responses of non-prismatic RC beams, respectively. The cracking behavior of unstrengthened beams was accompanied by excessive flexural and shear cracks. The influence of CFRP strips and full wraps was primarily observed in solid section beams without shear cracks, resulting in enhanced performance. In contrast, hollow section strengthened beams exhibited minor shear cracks alongside the primary flexural cracks within the constant moment region. The absence of shear cracks was reflected in the load–deflection curves of strengthened beams, which demonstrated a ductile behavior. The strengthened beams demonstrated 40% to 70% higher peak loads than control beams, whereas the ultimate deflection was increased up to 524.87% compared to that of the control beams. The improvement in the peak load was more prominent as the length of the non-prismatic section increased. A better improvement in ductility was achieved for the case of CFRP strips in the case of short non-prismatic lengths, whereas the efficiency of CFRP strips was reduced as the length of the non-prismatic section increased. Moreover, the load–strain capacity of CFRP-strengthened non-prismatic RC beams was higher than the control beams.

Phase structure of linear quiver gauge theories from anomaly matching

We consider the phase structure of the linear quiver gauge theory, using the 't Hooft anomaly matching condition. This theory is characterized by the length $K$ of the quiver diagram. When $K$ is even, the symmetry and its anomaly are the same as those of massless QCD. Therefore, one can expect that the spontaneous symmetry breaking similar to the chiral symmetry breaking occurs. On the other hand, when $K$ is odd, the anomaly matching condition is satisfied by the massless composite fermions. We also consider the thermal partition function under the twisted boundary conditions. When $K$ is even, from the anomaly at finite temperature, we estimate the relation between the critical temperatures associated with the confinement/deconfinement and the breaking of the global symmetry. Finally we discuss the anomaly matching at finite temperature when $K$ is odd.

Five loop anomalous dimension of non-singlet quark currents in the RI{}^prime scheme

We construct the five loop anomalous dimensions of the basic fields in Quantum Chromodynamics in a linear covariant gauge in the modified Regularization Invariant (textrm{RI}^prime ) scheme. Using these core results we also compute the four loop Green’s function where the quark mass operator and vector current are separately inserted in a quark 2-point function. These are necessary for measurements of the same quantities on the lattice. The Green’s functions are provided in both the modified Minimal Subtraction (overline{textrm{MS}}) and textrm{RI}^prime schemes. All the results are available for a general Lie group.

Five loop minimal MOM scheme field and quark mass anomalous dimensions in QCD

We determine the anomalous dimensions of the gluon, Faddeev–Popov ghost and quark in the minimal momentum subtraction scheme to five loops for a general colour group when quantum chromodynamics is fixed in a linear covariant gauge. The quark mass anomalous dimension is also constructed in the same scheme.

Toda equations for surface defects in SYM and instanton counting for classical Lie groups

The partition function of super Yang-Mills theories with arbitrary simple gauge group coupled to a self-dual Ω background is shown to be fully determined by studying the renormalization group equations relevant to the surface operators generating its one-form symmetries. The corresponding system of equations results in a non-autonomous Toda chain on the root system of the Langlands dual, the evolution parameter being the RG scale. A systematic algorithm computing the full multi-instanton corrections is derived in terms of recursion relations whose gauge theoretical solution is obtained just by fixing the perturbative part of the IR prepotential as its asymptotic boundary condition for the RGE. We analyze the explicit solutions of the τ-system for all the classical groups at the diverse levels, extend our analysis to affine twisted Lie algebras and provide conjectural bilinear relations for the τ-functions of linear quiver gauge theory.