Symmetry Model Research Articles

Simulating continuous symmetry models with discrete ones

Especially in one dimension, models with discrete and continuous symmetries display different physical properties, starting from the existence of long-range order. In this work, we that, by adding topological frustration, an antiferromagnetic $XYZ$ spin chain, characterized by a discrete local symmetry, develops a region in parameter space that mimics the features of models with continuous symmetries. For instance, frustration closes the mass gap and we describe a continuous crossover between ground states with different quantum numbers, a finite (Fermi) momentum for low energy states, and the disappearance of the finite order parameter. Moreover, we observe nontrivial ground-state degeneracies, nonvanishing chirality, and a singular foliation of the ground-state fidelity. Across the boundary between this chiral region and the rest of the phase diagram, any discontinuity in the energy derivatives vanishes in the thermodynamic limit.

On singularity points in elastic orthorhombic media

The analysis of singularity points in anisotropic models of low symmetry is very important for seismic modelling and seismic data processing. Ray tracing: the group velocity vector dramatically changes the orientation in vicinity of singularity point. Seismic amplitudes: the relative geometrical spreading of seismic wave tends to zero in singularity point. Seismic wave polarization: the polarization vectors dramatically change in vicinity of singularity point. Multiarrival: one of the waves has triplication associated with singularity point, another wave has a lacuna.The singularity points are considered for elastic anisotropic model with orthorhombic symmetry. The conditions for the presence of singularity points are derived depending on location of these points, in symmetry plane and in-between the symmetry planes. The explicit equations for images of the singularity points in group velocity domain are derived. The conditions for different types of degeneracy of these images are defined. We also perform the analysis of interaction of the group velocity images of different singularity points.

Parsimonious Bivariate T-distribution Type Symmetry Models for Square Contingency Tables

For square contingency tables with ordered categories, Iki, Ishihara and Tomizawa (2013) considered the t-distribution type symmetry model and Iki, Okada and Tomizawa (2018) extended this model. These models are appropriate for a square contingency table if it is reasonable to assume an underlying bivariate t-distribution having any degrees of freedom. This study proposes three kinds of parsimonious models for these models. Additionally, this paper provides the decompositions of the parsimonious symmetry model using the proposed model. Some simulation studies based on bivariate t-distribution show the performances of the proposed models.

Study on Combustion Kinetic Characteristics of Lignite and Semi-coking Dust.

In order to master the combustion kinetic characteristics of semi-coking dust in the early pyrolysis stage of lignite combustion explosion, a vacuum tube furnace was used to prepare semi-coking dust with different pyrolysis degrees, and the experimental samples were studied by a synchronous differential thermal analyzer. By means of theoretical analysis, the reaction mechanism of lignite and semi-coking dust was revealed. The results show that when the final pyrolysis temperature rises to 920 °C, the percentage of volatile matter decreases by 94.6%. The reaction in this process also causes the original pores to be cross-linked and collapsed, and a large number of new pores are generated, and the original pore structure is significantly enlarged. With the increase of the final temperature of pyrolysis, the ignition temperature (Tb) of the dust increased from 354 to 455 °C, the fastest reaction temperature (Tc) increased from 399 to 495 °C, and the ember temperature (Td) increased from 558 to 658 °C. The maximum combustion rate decreased by 65.97%, and the average combustion rate decreased by 84.67%. The apparent activation energy increased by 4.7 times from 45.219 to 257.665 kJ/mol, and the combustion kinetics of semi-coke became worse. The thermal reaction of lignite and semi-coking dust conforms to the diffusion mechanism of the three-dimensional spherical symmetry model. The research results provide a new idea for discussing the mechanism of coal dust explosion and the development of explosion suppression technology.

Discrete Dynamic Model of a Disease-Causing Organism Caused by 2D-Quantum Tsallis Entropy

Many aspects of the asymmetric organ system are controlled by the symmetry model (R&L) of the disease-causing organism pathway, but sensitive matters like somites and limb buds need to be shielded from its influence. Because symmetric and asymmetric structures develop from similar or nearby matters and utilize many of the same signaling pathways, attaining symmetry is made more difficult. On this note, we aim to generalize some important measurements in view of the 2D-quantum calculus (q-calculus, q-analogues or q-disease), including the dimensional of fractals and Tsallis entropy (2D-quantum Tsallis entropy (2D-QTE)). The process is based on producing a generalization of the maximum value of the Tsallis entropy in view of the quantum calculus. Then by considering the maximum 2D-QTE, we design a discrete system. As an application, by using the 2D-QTE, we depict a discrete dynamic system that is afflicted with a disease-causing organism (DCO). We look at the system’s positive and maximum solutions. Studies are done on equilibrium and stability. We will also develop a novel design for the fundamental reproductive ratio based on the 2D-QTE.

Nonlinear nonreciprocal transport in antiferromagnets free from spin-orbit coupling

We theoretically propose a realization of a nonlinear nonreciprocal transport in antiferromagnets without relying on the relativistic spin-orbit coupling. Through the symmetry and microscopic model analyses, we show that a local spin scalar chirality to induce an asymmetric band modulation becomes a source of a Drude-type nonlinear transport, while an electric polarization induced by a collinear spin configuration in a triangle unit leads to a Berry-curvature-dipole-type nonlinear transport. We demonstrate that 120$^\circ$ antiferromagnetic ordering on a triangular lattice and a breathing kagome lattice in an external magnetic field are typical examples. Our results open a new direction of designing and engineering functional materials with showing rich parity-violating transport phenomena by spontaneous magnetic phase transitions.

Impact of Information Asymmetry on the Operation of Green Closed-Loop Supply Chain under Government Regulation

Recycling subsidy and carbon tax policies are ways to achieve energy and environmental sustainability. The implementation of these policies has changed the operating environment of traditional closed-loop supply chains, while the privacy of relevant information increases the difficulty of decision-making. Under the background, this paper considers the green closed-loop supply chain (GCLSC) under the hybrid policy of recycling subsidy and carbon tax where the manufacturer is in charge of recycling and the retailer invests in green marketing. Taking green marketing cost coefficient as the retailer’s private information, this paper explores the influence of information asymmetry on optimal decisions and performance of the GCLSC. By constructing game models of information symmetry and asymmetry, the optimal decisions, economic and environmental performance, and social welfare are provided. Combined with numerical analysis, the influence of uncertainty of the manufacturer’s estimation, subsidies and carbon tax on the GCLSC is proposed. The results indicate that the uncertainty in the manufacturer’s estimation can improve the social welfare under certain conditions, but it cannot reduce carbon emissions. Recycling subsidy and carbon tax policies oppositely affect the manufacturer’s optimal decisions and carbon emissions. Information asymmetry is beneficial to the retailer. However, less uncertainty in estimation is not always better for the manufacturer. The manufacturer needs to proactively adopt strategies to stimulate the retailer’s information sharing.

Analysis of the SU(3) symmetry versus rotor model

The SU(3) symmetry, the subgroup in the dynamic chain of the SU(6) group in the interacting boson model (IBM), corresponds to the Bohr-Mottelson rotor model for axially symmetric deformed nuclei. It is synonymous but not identical to it. The common characteristics of the two models and their contrasting features are illustrated. The effect of adding the pairing term in the IBM SU(3) Hamiltonian to bring it closer to the rotor model is highlighted. The modified SU(3) Hamiltonian expression breaks the degeneracy of the \ensuremath{\beta} and \ensuremath{\gamma} bands in the SU(3) spectrum. The different ways to produce the forbidden $E2$ transitions across the different (\ensuremath{\lambda}, \ensuremath{\mu})-multiplets are discussed. The related features of SL(3, R) symmetry group are illustrated. We point out that the additional pairing term affects only certain states, preserving the rotational features of the other states in the SU(3) spectrum.

Downhole microseismic data interpretation for media anisotropy evaluation with limited acquisition geometry in Western Siberia

We have evaluated the results of processing and interpretation for one of the first projects in Russia for downhole microseismic monitoring of hydraulic fracturing in Western Siberia. The data are characterized by large distance to the acquisition array and noisy recordings. We illustrate that preliminary quality control of microseismic array installation is a useful tool that may predict some of the issues and help to promote better acquisition quality. Therefore, it is important to reiterate the significance of the supervision for microseismic field measurements, especially when the technology is tested in new regions. Despite limited acquisition aperture and a comparatively small number of observed microseismic events, it is possible to derive valuable interpretation results from the data set. The geometry of the event locations suggests significant unplanned development of the hydraulic fractures, including a significant shift of the fracture from the initiation point. Records with clear S-wave splitting allowed us to determine arrival times of P waves and two S waves for several microseismic events. Arrival times were then used for simultaneous kinematic inversion for microseismic-event location and anisotropic velocity-model update (layered transversely isotropic with the vertical axis of symmetry model). We estimate significant anisotropy from microseismic data. Thomsen parameters [Formula: see text] and [Formula: see text] are well constrained, whereas parameter [Formula: see text] is constrained only for one of the layers.

A Novel Undeniable (t, n)-Threshold Signature with Cheater Identification

A digital signature is one of the most widely used cryptographic primitives in asymmetry cryptography. According to the security requirements in different symmetry or asymmetry network models, various digital signatures have been developed in the literature. To protect the right of the signer, Chaum and Antrepen first introduced the concept of an undeniable signature, where interactive protocols are needed for the verification process. Besides, a signer can, also, perform a disavowal protocol to prove that they did not sign the message. On the other hand, threshold cryptography is, usually, used to protect the system from a single point of failure. In a (t,n)-threshold signature scheme, as long as t people in the group of n people participate, the signature can be smoothly signed. By combining these two features, an undeniable threshold signature enjoys the advantages from both sides. After our survey, we found that the existing undeniable threshold signature schemes are either insecure or apply impractical assumptions. Thus, in this manuscript, we aim at designing a novel and provably secure undeniable threshold signature scheme. The proposed scheme is formally proven to be unforgeable and invisible. Besides, our scheme supports cheater identification, which allows one to find the cheater, when a signing protocol fails. Moreover, the proposed scheme can be performed without the help of trusted third parties or secure cryptographic modules, which would be more practical when our scheme is deployed in real-world applications.

Numerical Modeling and Symmetry Analysis of a Pine Wilt Disease Model Using the Mittag–Leffler Kernel

The existence of man is dependent on nature, and this existence can be disturbed by either man-made devastations or by natural disasters. As a universal phenomenon in nature, symmetry has attracted the attention of scholars. The study of symmetry provides insights into physics, chemistry, biology, and mathematics. One of the most important characteristics in the expressive assessment and development of computational design techniques is symmetry. Yet, mathematical models are an important method of studying real-world systems. The symmetry reflected by such a mathematical model reveals the inherent symmetry of real-world systems. This study focuses on the contagious model of pine wilt disease and symmetry, employing the q-HATM (q-Homotopy Analysis Transform Method) to the leading fractional operator Atangana–Baleanu (AB) to arrive at better understanding. The outgrowths are exhibited in the forms of figures and tables. Finally, the paper helps to analyze the practical theory, assisting the prediction of its manner that corresponds to the guidelines when contemplating the replica.

Advances in Quasi-Symmetry for Square Contingency Tables

Contingency tables highlight relationships between categorical variables. Typically, the symmetry or marginal homogeneity of a square contingency table is evaluated. The original symmetry model often does not accurately fit a dataset due to its restrictions. Caussinus proposed a quasi-symmetry model which served as a bridge between symmetry and marginal homogeneity in square contingency tables. This study significantly influenced methodological developments in the statistical analysis of categorical data. Herein recent advances in quasi-symmetry are reviewed with an emphasis on four topics related to the author’s results: (1) modeling based on the f-divergence, (2) the necessary and sufficient condition of symmetry, (3) partition of test statistics for symmetry, and (4) measure of the departure from symmetry. The asymmetry model based on f-divergence enables us to express various asymmetries. Additionally, these models are useful to derive the necessary and sufficient conditions of symmetry with desirable properties. This review may be useful to consider the statistical modeling and the measure of symmetry for contingency tables with the same classifications.

Asymmetry Model Based on Quasi Local Odds Symmetry for Square Contingency Tables

For the analysis of square contingency tables, the primary objective is to estimate an unknown distribution from presented data. To achieve this objective, we generally use a statistical model that fits the presented data well and has a parsimony. The recently proposed quasi local odds symmetry (QLOS) model was compared to various models that represent the structure of symmetry or asymmetry, and it provided the best fit performance compared with other models for real data. However, the QLOS model has many parameters, that is, the QLOS model is not the parsimonious model. To address this issue, this study proposes a new model that is more parsimonious than the QLOS model. The proposed model is identical to the QLOS model under the specified condition; it is the asymmetry model based on the QLOS model.Moreover, we compare the proposed model with the existing models, including the QLOS model, and show that the proposed model provides better fit performance than the existing models for real datasets.

Controlled Wrinkling Analysis of Buckled Thin Films on Gradient Elastic Substrate System: A Numerical Study

Continuous change in wrinkle patterns process of thin films to a gradient substrate is the most challenging problem regarding applying reliable and robust numerical methods for postbuckling analysis of the film/substrate system. For example, in the finite element method, the postbuckling simulation suffers from the convergence issue, while, in spectral methods, it is very difficult to capture the localized behavior in soft matters when the boundary conditions are complex. When a thin film is compressed, it can form a wrinkle of a certain amount of wavelength when the compression exceeds a critical value. The compressed compliant substrate system translates to sinusoidal wrinkles and then to period-doubling wrinkling after further compression. In this work, we investigate the mathematical model arising from the changing nature of wrinkle patterns of postbuckled thin films using a robust and efficient numerical algorithm based on the spectral method to evolve the wrinkle patterns. We consider the gradient substrates of three typical variations in the modulus, namely, the symmetry, exponential, and power-law model. It has been observed that the stable equilibrium path has two bifurcation points. At the first bifurcation point, the buckling instability of wrinkling occurs, while the period-doubling buckling instability occurs at the second bifurcation point. For the substrates of material gradients of various types, the amplitude and wavelength are obtained. This study may help in better understanding of wrinkle patterns formation which could be very useful for the designing of stretchable and flexible electronic devices of most substrate systems and to avoid resonance in the noise environment.

Spin-Group Symmetry in Magnetic Materials with Negligible Spin-Orbit Coupling

Symmetry formulated by group theory plays an essential role with respect to the laws of nature, from fundamental particles to condensed matter systems. Here, by combining symmetry analysis and tight-binding model calculations, we elucidate that the crystallographic symmetries of a vast number of magnetic materials with light elements, in which the neglect of relativistic spin-orbit coupling (SOC) is an appropriate approximation, are considerably larger than the conventional magnetic groups. Thus, a symmetry description that involves partially-decoupled spin and spatial rotations, dubbed as spin group, is required. Spin group permits more symmetry operations and thus more energy degeneracies that are disallowed by the magnetic groups. One consequence of the spin group is the new anti-unitary symmetries that protect SOC-free Z_2 topological phases with unprecedented surface node structures. Our work not only manifests the physical reality of materials with weak SOC, but also shed light on the understanding of all solids with and without SOC by a unified group theory.

Comparison between Cylindrical, Trigonal, and General Symmetry Models for the Analysis of Polarization-Dependent Second Harmonic Generation Measurements Acquired from Collagen-Rich Equine Pericardium Samples

Polarization-dependent second harmonic generation (PSHG) microscopy is used as an innovative, high-resolution, non-destructive, and label-free diagnostic imaging tool to elucidate biological issues with high significance. In the present study, information on the structure and directionality of collagen fibers in equine pericardium tissue was collected using PSHG imaging measurements. In an effort to acquire precise results, three different mathematical models (cylindrical, trigonal, and general) were applied to the analysis of the recorded PSHG datasets. A factor called the “ratio parameter” was calculated to provide quantitative information. The implementation of the trigonal symmetry model to the recorded data led to the extraction of improved results compared with the application of the widely used cylindrical symmetry model. The best outcome was achieved through the application of the general model that does not include any kind of symmetry for the data processing. Our findings suggest that the trigonal symmetry model is preferable for the analysis of the PSHG datasets acquired from the collagenous tissues compared with the cylindrical model approach although an increased computational time is required.

Investigation of phase and temperature perturbations induced by a candle using Hilbert optics methods

The method of multiwave RGB-optical Hilbert diagnostics of the phase and temperature spatial structure of the flame (in an air flow heated by a candle flame) at a fixed moment of time is discussed. The object of study satisfies the model of axial symmetry of the torch associated with the vertical orientation of the candle. The reliability of the received results is confirmed by comparing the reconstructed radial temperature by experimental hilbertogram with data measured by a thermocouple. The flickering effect of the flame was not taken into account in the work, this is the subject of further research.

Chiral models of composite axions and accidental Peccei-Quinn symmetry

We introduce a class of composite axion models that provide a natural solution to the strong CP problem, and possibly account for the observed dark matter abundance. The QCD axion arises as a composite Nambu-Goldstone boson (NGB) from the dynamics of a chiral gauge theory with a strongly-interacting and confining SU(N) factor and a weakly-interacting U(1), with no fundamental scalar fields. The Peccei-Quinn (PQ) symmetry is accidental and all the mass scales are generated dynamically. We analyze specific models where the PQ symmetry is broken only by operators of dimension 12 or higher. We also classify several other models where the PQ symmetry can be potentially protected up to the dimension 15 or 18 level. Our framework can be easily extended to a scenario where the Standard Model (SM) is unified into a simple gauge group, and we discuss the case of non-supersymmetric SU(5) unification. The GUT models predict the existence of additional pseudo NGBs, parametrically lighter than the GUT and PQ scales, which could have an impact on the cosmological evolution and leave observable signatures. We also clarify the selection rules under which higher-dimensional PQ-violating operators can generate a potential for the axion in the IR, and provide a discussion of the discrete symmetries in composite axion models associated to the number of domain walls. These results can be of general interest for composite axion models based on a QCD-like confining gauge group.

Encyclopedia of emergent particles in type-IV magnetic space groups

The research on emergent particles in condensed matters has been attracting tremendous interest, and recently it is extended to magnetic systems. Here, we study the emergent particles stabilized by the symmetries of type-IV magnetic space groups (MSGs). Type-IV MSGs feature a special time reversal symmetry $\{\mathcal{T}|\boldsymbol{t}_0\}$, namely, the time reversal operation followed by a half lattice translation, which significantly alters the symmetry conditions for stabilizing the band degeneracies. In this work, based on symmetry analysis and modeling, we present a complete classification of emergent particles in type-IV MSGs by studying all possible (spinless and spinful, essential and accidental) particles in each of the 517 type-IV MSGs. Particularly, the detailed correspondence between the emergent particles and the type-IV MSGs that can host them are given in easily accessed interactive tables, where the basic information of the emergent particles, including the symmetry conditions, the effective Hamiltonian, the band dispersion and the topological characters can be found. According to the established encyclopedia, we find that several emergent particles that are previously believed to exist only in spinless systems will occur in spinful systems here, and vice versa, due to the $\{{\cal T}|\boldsymbol{t}_{0}\}$ symmetry. Our work not only deepens the understanding of the symmetry conditions for realizing emergent particles but also provides specific guidance for searching and designing materials with target particles.

Mild steel metal rotating spray transfer behavior in magnetically controlled gas metal arc welding

Welding efficiency is important for the development of the manufacturing industry. Gas metal arc welding (GMAW) is a popular welding method, and a reasonable approach for increasing the wire melting rate is to increase the welding current. However, the metal transfer mode changes from stable free-flight transfer to unstable rotating spray transfer, which worsens the welding quality. In this study, alternating axial magnetic fields were applied to control the metal rotating angle, frequency, and spatter by acting with the radial current in the conductive metal liquid column. Using the experimental high-speed photograph method and numerical simulation method, a three-dimensional rotating spray transfer model considering the applied external alternating axial magnetic field, main acting forces such as gravity, electromagnetic forces, plasma shear stress, and surface tension on the molten metal is established. Additionally, two-dimensional axial symmetry models of globular and spray transfer are provided for verification. By utilizing the externally applied electromagnetic forces, the rotating motion of the metal liquid column is constricted and mildly controlled, and the control mechanism is revealed in the numerical analysis. The advantages and disadvantages of the simplified numerical model compared with the mass–heat fully coupled model are examined.