Center Symmetry Research Articles

The Geometry of the Centre Symmetry Set of a Planar Curve

The Geometry of the Centre Symmetry Set of a Planar Curve

Deconfinement, center symmetry and the ghost propagator in Landau gauge pure SU(3) Yang-Mills theory

The temperature dependence of the Landau gauge ghost propagator is investigated in pure SU(3) Yang-Mills theory with lattice QCD simulations. Its behavior around the confined-deconfined phase transition temperature, Tc ∼ 270 MeV, is investigated. The simulations show that in the deconfined phase, the ghost propagator is enhanced for small momenta, ≲ 1 GeV. Furthermore, the analysis of the spontaneous breaking of center symmetry on the ghost propagator is studied. Similarly as observed for the gluon propagator, the simulations result in a decoupling of the sectors where the phase of the Polyakov loop is either 0 or ±2π/3 sectors, with the latter remaining indistinguishable. The results point to the possible use of the ghost propagator as an “order parameter” for the confined-deconfined phase transition.

A New Perspective on Thermal Transition in QCD

Abstract Motivated by the picture of partial deconfinement developed in recent years for large-N gauge theories, we propose a new way of analyzing and understanding thermal phase tsuppransition in QCD. We find nontrivial support for our proposal by analyzing the WHOT-QCD collaboration’s lattice configurations for SU(3) QCD in 3 + 1 spacetime dimensions with up, down, and strange quarks. We find that the Polyakov line (the holonomy matrix around a thermal time circle) is governed by the Haar-random distribution at low temperatures. The deviation from the Haar-random distribution at higher temperatures can be measured via the character expansion, or equivalently, via the expectation values of the Polyakov loop defined by the various nontrivial representations of SU(3). We find that the Polyakov loop corresponding to the fundamental representation and loops in the higher representation condense at different temperatures. This suggests that there are three phases, one intermediate phase existing in between the completely-confined and the completely-deconfined phases. Our identification of the intermediate phase is supported also by the condensation of instantons: by studying the instanton numbers of the WHOT-QCD configurations, we find that the instanton condensation occurs for temperature regimes corresponding to what we identify as the completely-confined and intermediate phases, whereas the instantons do not condense in the completely-deconfined phase. Our characterization of confinement based on the Haar-randomness explains why the Polyakov loop is a good observable to distinguish the confinement and the deconfinement phases in QCD despite the absence of the $\mathbb {Z}_3$ center symmetry.

Noninvertible symmetries and anomalies from gauging 1-form electric centers

We devise a general method for obtaining 0-form noninvertible discrete chiral symmetries in 4-dimensional SU(N)/ℤp and SU(N) × U(1)/ℤp gauge theories with matter in arbitrary representations, where ℤp is a subgroup of the electric 1-form center symmetry. Our approach involves placing the theory on a three-torus and utilizing the Hamiltonian formalism to construct noninvertible operators by introducing twists compatible with the gauging of ℤp. These theories exhibit electric 1-form and magnetic 1-form global symmetries, and their generators play a crucial role in constructing the corresponding Hilbert space. The noninvertible operators are demonstrated to project onto specific Hilbert space sectors characterized by particular magnetic fluxes. Furthermore, when subjected to twists by the electric 1-form global symmetry, these surviving sectors reveal an anomaly between the noninvertible and the 1-form symmetries. We argue that an anomaly implies that certain sectors, characterized by the eigenvalues of the electric symmetry generators, exhibit multi-fold degeneracies. When we couple these theories to axions, infrared axionic noninvertible operators inherit the ultraviolet structure of the theory, including the projective nature of the operators and their anomalies. We discuss various examples of vector and chiral gauge theories that showcase the versatility of our approach.

Hot rolled prognostic approach based on hybrid Bayesian progressive layered extraction multi-task learning

Hot-rolled strip products have diverse applications, and enhancing the detection, diagnostics, and prognostics of product quality during hot rolling is essential. Nevertheless, the multivariable, strong coupling, nonlinear, and time-varying nature of the production process poses a rigorous challenge for accurate hot-rolled prognostics. This paper implements a progressive layered extraction (PLE) multi-task learning (MTL) framework to simultaneously estimate multiple quality indicators, such as strip crown, center line deviation, exit temperature, wedge, width, and symmetry flatness. Additionally, the paper proposes the implements of Hybrid Bayesian Neural Network (HBNN) experts and a gating network with attention mechanism to integrate private and shared task features. It also puts forth an auxiliary task involving a Variational Autoencoder with Generative Adversarial Networks (VAE-GAN) to extract latent states from the original sequence. Moreover, an adaptive joint loss optimization is employed to update the weight of individual task losses for MTL training problems, and three sets of field hot-rolled datasets are used for model evaluation. In the experimental validation, considering the noisy field data and limited conditions in the real hot rolled production, comparative experiments are conducted to demonstrate the improved generalization and robustness of the proposed MTL approach. These experiments involve different percentages of the total data, ranging from 5% to 20%, and various prediction horizons ranging from 1 to 50 steps for model establishment. In addition, the paper discusses the interpretation of the model and strategies for further enhancing model performance.

On Thermal Transition in QCD

Abstract We describe how the general mechanism of partial deconfinement applies to large-N QCD and a partially deconfined phase inevitably appears between completely confined and completely deconfined phases. Furthermore, we propose how partial deconfinement can be observed in real-world QCD with the SU(3) gauge group. For this purpose, we employ lattice configurations obtained by the WHOT-QCD Collaboration and examine our proposal numerically. In the discussion, the Polyakov loop plays a crucial role in characterizing the phases, without relying on center symmetry, and hence we clarify the meaning of the Polyakov loop in QCD at large N and finite N. At both large N and finite N, the complete confinement is characterized by the Haar-random distribution of the Polyakov line phases. Haar-randomness, which is stronger than unbroken center symmetry, indicates that Polyakov loops in any nontrivial representations have vanishing expectation values, and deviation from the Haar-random distribution at higher temperatures is quantified with the loops. We discuss that the transitions separating the partially deconfined phase are characterized by the behaviors of Polyakov loops in various representations. The lattice QCD data provide us with the signals exhibiting two different characteristic temperatures: deconfinement of the fundamental representation and deconfinement of higher representations. As a nontrivial test for our proposal, we also investigate the relation between partial deconfinement and instanton condensation and confirm the consistency with the lattice data. To make the presentation more easily accessible, we provide a detailed review of the previously known aspects of partial deconfinement.

Dual-Band All-Optical Logic Gates by Coherent Absorption in an Amorphous Silicon Graphene Metasurface.

The dual-band polarization-independent all-optical logic gate by coherent absorption effect in an amorphous silicon (a-Si) graphene metasurface is investigated theoretically and numerically. Taking the substrate effect into consideration, the coherent perfect absorption condition of the a-Si graphene metasurface is derived on the basis of the Cartesian multipole method. The coherent nearly perfect absorption of the a-Si graphene metasurface is realized by the interference of multipole moments and the interband transition of monolayer graphene, achieving peak values of 91% and 92% at 894.5 nm and 991.5 nm, respectively. The polarization independence of the coherent absorption is revealed due to the center symmetry of the structure of the a-Si graphene metasurface. The dual-band polarization-independent all-optical XOR and OR logic gates are implemented at 894.5 nm and 991.5 nm by the a-Si graphene metasurface based on the coherent nearly perfect absorption, which has the opportunity to be utilized in all-optical computing, all-optical data processing, and future all-optical networks.

Center-symmetric Landau gauge: Further signatures of confinement

In a recent article [D. M. van Egmond and U. Reinosa, ], we have identified new signatures for the Yang-Mills deconfinement transition, based on the finite-temperature or gluon propagator as computed in the center-symmetric Landau gauge. Here, we generalize these considerations into a systematic study of the center symmetry identities obeyed by the correlation functions in this gauge. Any violation of these constraints signals the breaking of center symmetry and can thus serve as a probe for the deconfinement transition. Published by the American Physical Society 2024

Thermodynamics of quark matter with multiquark clusters in an effective Beth-Uhlenbeck type approach

We describe multiquark clusters in quark matter within a Beth-Uhlenbeck approach in a background gluon field coupled to the underlying chiral quark dynamics using the Polyakov gauge. An effective potential for the traced Polyakov loop is used to establish the center symmetry of the SU(3) color which suppresses colored states and its dynamical breaking as an aspect of the confinement/deconfinement transition. Quark confinement is modeled by a large quark mass in vacuum which is motivated by a confining density functional approach. A multiquark cluster containing n quarks and antiquarks is described as a binary composite of smaller subclusters n1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$n_1$$\\end{document} and n2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$n_2$$\\end{document} (n1+n2=n\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$n_1+n_2=n$$\\end{document}). It has a spectrum consisting of a bound state and a scattering state continuum. For the corresponding cluster-cluster phase shifts we use simple ansätze that capture the Mott dissociation of clusters as a function of temperature and chemical potential. We go beyond the simple “step-up-step-down” model that ignores continuum correlations and introduce an improved model that includes them in a generic form. In order to explain the model, we restrict ourselves here to the cases where the cluster size is 1≤n≤6\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$1 \\le n \\le 6$$\\end{document}. A striking result is the suppression of the abundance of colored multiquark clusters at low temperatures by the coupling to the Polyakov loop and their importance for a quantitative description of lattice QCD thermodynamics at non-vanishing baryochemical potentials. An important ingredient are Polyakov-loop generalized distribution functions of n-quark clusters which are derived here for the first time. Within our approach we calculate thermodynamic properties such as baryon density and entropy. We demonstrate that the limits of a hadron resonance gas at low temperatures and O(g2)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {O}(g^2)$$\\end{document} perturbative QCD at high temperatures are correctly reproduced. A comparison with lattice calculations shows that our model is able to give a unified, systematic approach to describe properties of the quark-gluon-hadron system.

Experimental study on municipal sludge/coal co-combustion preheated by self-preheating burner: Self-preheating two-stage combustion and NOx emission characteristics

To achieve efficient and low-pollution sludge treatment, this study explored the first-time application of self-preheating combustion technology in sludge/coal co-combustion, and subsequently investigated the influences of sludge blending ratio (BR) and tertiary air types on self-preheating two-stage combustion and NOx emission characteristics in a 30 kW self-preheating combustion system with a novel two-stage down-fired combustor (DFC). This system was well adaptable for fuels, and still ran steadily even if BR was as high as 50 %. During preheating, properly increasing BR improved carbon microcrystalline structure of preheated carbon-based fuel and increased its specific surface area, but its carbon microcrystalline structure was gradually deteriorated at BR>20 %. Fuel properties of preheated coal gas were deteriorated with increasing BR. During combustion, combustion efficiency (η) increased first and then decreased with increasing BR, while NOx emission increased. For tertiary air nozzle located at top of burnout region, the structures of center symmetry and ring hedge had less effect on η and NOx emission, both of which remained at high levels, exceeding 98.5 % and 160 mg/m3. Notably, properly shifting injection position down reduced NOx emission significantly, albeit at the expense of reduction in η. Excessively low injection position had less effect on further NOx emissdddction.

Method for determining eigen numbers in heat conduction problems for a cylinder

RELEVANCE. Due to the difficulties of finding eigenvalues and proper functions for bodies with axial (cylinder) and central (ball) symmetries defined in classical methods from the edge Sturm-Liouville problems, including Bessel equations whose exact analytical solutions are not obtained (known only numerical solutions, described by approximation formulas), there is a need to develop analytical methods of their solution.THE PURPOSE. Using orthogonal methods of weighted residuals, an approximate analytical method for determining eigenfunctions and eigenvalues in boundary value problems with axial and central symmetry (cylinder, ball) has been developed.METHODS. The method is based on the use of orthogonal systems of coordinate functions and additional boundary conditions. Latter are in such a form that their fulfillment by the desired solution is equivalent to the fulfillment of the differential equation of the boundary value problem at the boundary points of the region, leading to its fulfillment inside the considered region. Moreover, the accuracy of the equation depends on the number of approximations, which, in turn, depends on the number of additional boundary conditions used. Using the orthogonality property of trigonometric coordinate functions included in a series representing eigenfunctions makes it possible to increase the accuracy of the fulfillment of the differential equation of the Sturm-Liouville boundary value problem and the accuracy of determining the eigenvalues. To satisfy the initial condition, its residual is compiled and the condition of its orthogonality to all coordinate functions is required. The orthogonality of trigonometric systems of coordinate functions with respect to the unknown constants of integration leads to a system of algebraic linear equations, the number of which is equal to the number of approximations. As a result, the fulfillment of the initial condition is simplified and the accuracy of its fulfillment is increased.RESULTS. The advantage of the method is that the resulting solution contains only simple algebraic expressions, excluding special functions (Bessel function, Legendre function, gamma function).CONCLUSION. Thus, bypassing direct integration over a spatial variable, the use of additional boundary conditions makes it possible to find a solution of any complexity of the equations of the Sturm-Liouville boundary value problem, which reduces to the definition of simple integrals.

Non-invertible Gauss law and axions

In axion-Maxwell theory at the minimal axion-photon coupling, we find non-invertible 0- and 1-form global symmetries arising from the naive shift and center symmetries. Since the Gauss law is anomalous, there is no conserved, gauge-invariant, and quantized electric charge. Rather, using half higher gauging, we find a non-invertible Gauss law associated with a non-invertible 1-form global symmetry, which is related to the Page charge. These symmetries act invertibly on the axion field and Wilson line, but non-invertibly on the monopoles and axion strings, leading to selection rules related to the Witten effect. We also derive various crossing relations between the defects. The non-invertible 0- and 1-form global symmetries mix with other invertible symmetries in a way reminiscent of a higher-group symmetry. Using this non-invertible higher symmetry structure, we derive universal inequalities on the energy scales where different infrared symmetries emerge in any renormalization group flow to the axion-Maxwell theory. Finally, we discuss implications for the Weak Gravity Conjecture and the Completeness Hypothesis in quantum gravity.

Numerical simulation of pressure relief stress distribution of diamond beaded rope saw cutting in low permeability coal seam

The diamond bead slit is a practical method for changing the stress distribution of low permeability coal seam and achieving pressure relief and reflection improvement. The stress distribution of coal seam in large scale is not clear due to the influence of diamond bead slit parameters and geological parameters, making it difficult to identify. In this paper, the finite element model with built-in Coulomb friction contact surface is used to simulate the stress distribution in coal with different angles, seam length, working face length, seam friction coefficient and different in-situ stress difference. This investigation is conducted to examine the stress distribution of parallel working face, vertical coal seam, and advance working face. The simulation results show that the mechanism of stress transfer in large scale diamond beaded rope saw cutting coal seam is mainly due to the tangential slip of coal body on both sides of seam surface, forming concentrative zone and pressure relief zone with axial distribution, center symmetry and phase. The pressure relief range and maximum pressure relief range of all three direction present a "single peak" distribution with the change of angel α between slit and maximum in-situ stress, i.e. when α = 45°, both of them are maximum. The slit length mainly affects the stress distribution in the advancing direction of the working face, and the length of working face mainly affects the stress distribution in the direction of parallel working face and vertical coal seam, both of which are positively correlated with the pressure relief range and the maximum pressure relief amplitude. The friction coefficient of seam surface and the difference of in-situ stress affect the relative dislocation of coal body on both sides of seam surface, and they inhibit and promote the pressure relief range and the maximum pressure relief amplitude respectively, and are greatly affected by α. The simulation results above suggest that it is reasonable to select fracture and geological parameters in practical engineering.

Noninvertible anomalies in SU(N) × U(1) gauge theories

We study 4-dimensional SU(N) × U(1) gauge theories with a single massless Dirac fermion in the 2-index symmetric/antisymmetric representations and show that they are endowed with a noninvertible 0-form {overset{sim }{mathbb{Z}}}_{2left(Npm 2right)}^{upchi} chiral symmetry along with a 1-form {mathbb{Z}}_N^{(1)} center symmetry. By using the Hamiltonian formalism and putting the theory on a spatial three-torus mathbbm{T} 3, we construct the non-unitary gauge invariant operator corresponding to {overset{sim }{mathbb{Z}}}_{2left(Npm 2right)}^{upchi} and find that it acts nontrivially in sectors of the Hilbert space characterized by selected magnetic fluxes. When we subject mathbbm{T} 3 to {mathbb{Z}}_N^{(1)} twists, for N even, in selected magnetic flux sectors, the algebra of {overset{sim }{mathbb{Z}}}_{2left(Npm 2right)}^{upchi} and {mathbb{Z}}_N^{(1)} fails to commute by a ℤ2 phase. We interpret this noncommutativity as a mixed anomaly between the noninvertible and the 1-form symmetries. The anomaly implies that all states in the torus Hilbert space with the selected magnetic fluxes exhibit a two-fold degeneracy for arbitrary mathbbm{T} 3 size. The degenerate states are labeled by discrete electric fluxes and are characterized by nonzero expectation values of condensates. In an appendix, we also discuss how to construct the corresponding noninvertible defect via the “half-space gauging” of a discrete one-form magnetic symmetry.

Adjustable symmetry on the dynamics of a new chaotic system with cyclic symmetry: theoretical study, control and experimental investigation

In this study, we propose a new chaotic autonomous system with adjustable cyclic and central symmetries. The new 3D system, with rich dynamics, is constructed based on the Thomas model. A detailed study of the nonlinear dynamics arising from the model allows us to reveal complex behaviors of different phenomena such as hysteresis dynamics, offset boosting, total amplitude control, and coexistence of several homogeneous and heterogeneous attractors in both regimes (symmetric and asymmetric). The control of multistability of the new cyclic system is studied by following the technique of linear augmentation. An analog electronic version of the model is designed and then simulated using the Pspice software. Moreover, a physical implementation using the arduino microcontroller makes it possible to validate the results of the theoretical analysis.

Analysis of Dynamic Characteristics of Attached High Rise Risers

The exhaust chimney of third-generation nuclear power units is a typical attached high-rise riser structure. In this paper, the simplified mechanical model and dynamic model of China’s third-generation nuclear power Hualong-1 VNA system, including multiple nonlinear factors, are established for the first time. The DTM (differential transformation method) was first applied to solve the natural vibration characteristics of a multi-point constrained variable cross-section riser structure, and the effects of variable cross-section, variable mass, variable axial force, and different elastic constraint parameters on the natural vibration characteristics of the system were studied. The dynamic behavior of the VNA system under the combined action of internal flow velocity, vortex excitation, and foundation excitation was studied. The results show that the outer diameter function of the VNA system pipeline should be designed as a quadratic function or a near quadratic multi-segment constant value function. The “limiting” effect of constraining large stiffness can force low-order vibration modes with high constraint stiffness to jump to high-order vibration modes with low constraint stiffness. The elastic constraint arrangement scheme with near center symmetry can make the system vibration mode present a half stable and half-curved form. A new optimization design scheme has been proposed regarding the layout and stiffness parameters of the VNA system guide bracket. This can enable the VNA system pipeline to avoid severe oscillations near the response extreme values caused by multiple frequency excitations of seismic loads under design and accident conditions and ensure the service life of the equipment.

Single-atom molybdenum array bound to distorted 1 T′ ReS2 quantum dots triggers highly intrinsic piezoelectricity for hierarchical porous electret piezo-catalysis

Piezoelectricity in 2D transition metal dichalcogenides (TMDs) has gathered significant interest due to their massive exposure of unsaturated edge sites and high piezoelectric modulus. Nevertheless, the piezoelectricity in 1 T′ phase TMDs is inhibited by its center symmetry of space group. Herein, to break the shackles of piezoelectric polarization, we synthesize a piezoelectric material composed of an atomic molybdenum array bound to distorted 1 T′ ReS2 (MDR). The phase transition from 1 T′ to distorted 1 T′ (D-1 T′) removes the special Peierl's distortion of ReS2, breaking its center symmetry and allowing for piezoelectric generation. Remarkably, MDR exhibits a large piezoelectric coefficient (d33) value of 15.45 pm/V, which is an order of magnitude higher than those reported in other TMDs. Combining with excellent piezocatalytic activity, a 0D/3D di-piezoelectric porous electret featuring an enhanced quantum confinement piezoelectric effect based on the MDR quantum dots (QDs) and inverse opal g-C3N4 (IOCN) is demonstrated for high-efficiency piezoelectric catalysis.

Computing symmetries of implicit algebraic surfaces

We present a complete algorithm to compute the rotational, axial, reflectional and central symmetries of an algebraic surface defined by means of its implicit equation. The algorithms rely on the fact that the symmetries of the surface satisfy an algebraic condition verified by the polynomial defining the surface, and use a variety of ideas, some of them extensions to space of ideas already used to compute the symmetries of planar implicit curves, and some of them new. We flesh out our algorithms with several examples.

Effective model for pure Yang-Mills theory on T2×R2 with Polyakov loops

We investigate the phase diagram and thermodynamics of $SU(N)$ pure Yang-Mills theory on a manifold $\mathbb{T}^2\times \mathbb{R}^2$ with an effective model that includes two Polyakov loops along two compactified directions. We find that a rich phase structure can appear owing to the spontaneous breaking of two center symmetries for $N=2$ and $3$. Thermodynamic quantities are obtained in the model and compared with recent lattice results. It is shown that two Polyakov loops play significant roles in thermodynamics on $\mathbb{T}^2\times \mathbb{R}^2$.

Topological features of the deconfinement transition

The first order transition between the confining and the center symmetry breaking phases of the SU(3) Yang-Mills theory is marked by discontinuities in various thermodynamics functions, such as the energy density or the value of the Polyakov loop. We investigate the nonanalytical behavior of the topological susceptibility and its higher cumulant around the transition temperature and make the connection to the curvature of the phase diagram in the $T\ensuremath{-}\ensuremath{\theta}$ plane and to the latent heat.