Tensor Theory Research Articles

Chiral photoelectron spectroscopy using unpolarized light

This Letter studies the symmetry properties of general vector correlations resulting from one-photon excitation of chiral molecules. We show that the parity-odd second rank tensor is nonzero for molecules in all chiral point groups Cn, Dn, T, O, and I. This chirality-sensitive tensor is nonzero even for chiral isotopomers excited by linearly polarized or even unpolarized light. We develop an irreducible tensor theory based on Curie's limiting groups. As an example of vector correlations, recoil-frame photoelectron angular distributions (RFPADs) are calculated for methyloxirane and CHFCl35Cl37. The difference in the RFPAD between a chiral molecule and its mirror image reaches ±35% of the maximum value for the RFPAD for unpolarized light and ±55% of the value for linearly polarized light. Chiral sensitivity in vector correlation is a quite general phenomenon arising from one-photon excitation by unpolarized and linearly polarized light, and we expect it to be of great importance in time-resolved spectroscopy of ultrafast chemical reactions. Published by the American Physical Society 2024

Source types of induced earthquakes in underground mines: Revealed by regional moment tensor inversion

Mining-induced earthquakes have been very frequent in recent years due to increasing mechanized mining. Compared with natural earthquakes, even a small one may cause significant damage to the mine area and its surroundings. Source type identification is important for better understanding the physical processes and is a crucial and fundamental issue for hazard assessment and emergency rescue in the mining environment. The moment tensor (MT) theory plays a pivotal role in distinguishing different source types. In this study, we concentrated on two strong reported “mine collapse earthquakes” in Qufu (ML 3.2, July 13, 2020) and Zoucheng (ML2.9, June 09, 2020), Shandong Province, China. Seismograms from regional seismic stations were utilized to calculate the full moment tensors through low-frequency full-waveform inversion. Our results show that the two studied events exhibit notably different source types. The DC (Double-Couple) component of both events are 5% (Qufu) and 60% (Zoucheng), respectively. The Qufu event which contains approximately 75% closing crack component, is more consistent with the theoretical models of collapse seismic source. However, the Zoucheng event, which exhibits a significant proportion of DC components, demonstrates characteristics typical of shear failure. Focusing on the Zoucheng event, which occurred at the Dongtan Coal Mine, further research was conducted on a local mining scale. Analyzed in conjunction with microseismic sensor data, geologic setting, and mining progress, we illustrated that the source type of Zoucheng event is not a collapse one. The fracture slip of a thick-hard roof due to an overlying load, characterized by a large DC component, is a plausible geomechanical interpretation.

Dielectrophoretic motion of a red blood cell in a microfluidic environment: Insights from numerical simulations

This research delves into the dielectrophoresis (DEP) behavior of a biological cell within a sinusoidal-shaped microchannel utilizing the Maxwell stress tensor (MST) theory. A red blood cell (RBC), immersed in a viscoelastic fluid, is studied considering the Oldroyd-B model. The study aims to fill a gap in the literature by examining the DEP characteristics of RBC in a realistic geometric configuration and fluid environment, bridging the divide between theoretical modeling and practical application. This work uniquely explores the DEP behavior of an RBC within a sinusoidal microchannel in the presence of a viscoelastic flow regime, which simulates plasma properties, marking a novel contribution to the field. The two-dimensional numerical model incorporates the finite element method to accurately simulate the DEP effect and describe the behavior of the viscoelastic fluid. Validation results confirm the accuracy of the MST model. Crucially, numerical findings highlight the strong dependence of DEP force on electric potential and fluid permittivity. As a consequence of their heightened levels, there is an associated increase in both the DEP force and velocity. While the augmentation of fluid viscosity merely results in a deceleration of DEP velocity. The study provides valuable insights into the interplay between physical parameters and particle behavior, paving the way for advancements in microfluidic particle manipulation techniques.

Kinematics analysis of planetary roller screw mechanism with misalignment

The misalignment is unavoidable for planetary roller screw mechanism (PRSM) in practical application due to many uncertainties. The misalignment has a strong effect on the kinematic characteristics of PRSM. However, the relevant research has been rarely reported in the past. In order to clearly present the motion characteristics, a novel kinematics model of PRSM with misalignment is established in this article. The rotational tensor theory is introduced to obtain the coordinate transformation equations. The position vectors of PRSM with misalignment are acquired to calculate the position of the contact point. The motion model of PRSM with misalignment is derived by analyzing the velocity of the contact point. Compared with some published literature, the kinematic model of PRSM is verified. Moreover, a relationship between the misalignment variates, which are the misalignment angle, the misalignment azimuth angle, and the offset distance of the nut's ending point, respectively, and the kinematic characteristics of PRSM are investigated. The results indicate that those misalignment variates have a great influence on the kinematics of PRSM and lead to fluctuations in the PRSM's transmission velocity and angular velocity ratio. The fluctuation amplitude of transmission velocity is positively correlated with misalignment angle.

Optimization of Digital Inheritance Pathway of Folk Art in Information Age

How to make full use of digital information technology to realize the digital heritage of folk art has become a key concern in the field of non-legacy. Based on digital information technology, this paper proposes image restoration technology to assist folk art digital heritage research. Folk art images are acquired by double mirror reflection method, and pre-processing operations such as defogging, denoising and edge detection are carried out on the images to reduce the influence of interference information in the original pictures on the image restoration effect. The Criminisi algorithm is improved and optimized by combining the structure tensor theory, the improved priority calculation function, the matching criterion and the confidence updating method, and then the research design of image restoration technology assisting folk art digitization is completed and analyzed by examples. The results show that the repair effect of the improved Criminisi algorithm is better than that of the classical Criminisi algorithm, but the repair time of the improved Criminisi algorithm is longer than that of the traditional algorithm by 64.25%, but it is still less than 0.500 seconds, which is within the acceptable range, and it has certain practicability for the digitization and inheritance of folk art in the information age. algorithm has some practicality. Compared with other digital inheritance paths, the method proposed in this study can restore the original appearance of folk art to the maximum extent, and it has theoretical guidance value for the study of optimizing the digital inheritance of traditional folk art.

Aether Scalar Tensor (AeST) theory: quasistatic spherical solutions and their phenomenology

ABSTRACT There have been many efforts in the last three decades to embed the empirical Modified Newtonian Dynamics (MOND) programme into a robust theoretical framework. While many such theories can explain the profile of galactic rotation curves, they usually cannot explain the evolution of the primordial fluctuations and the formation of large-scale structures in the Universe. The Aether Scalar Tensor theory seems to have overcome this difficulty, thereby providing the first compelling example of an extension of general relativity able to successfully challenge the particle dark matter hypothesis. Here, we study the phenomenology of this theory in the quasistatic weak-field regime and specifically for the idealized case of spherical isolated sources. We find the existence of three distinct gravitational regimes, that is, Newtonian, MOND, and a third regime characterized by the presence of oscillations in the gravitational potential which do not exist in the traditional MOND paradigm. We identify the transition scales between these three regimes and discuss their dependence on the boundary conditions and other parameters in the theory. Aided by analytical and numerical solutions, we explore the dependence of these solutions on the theory parameters. Our results could help in searching for interesting observable phenomena at low redshift pertaining to galaxy dynamics as well as lensing observations, however, this may warrant proper N-body simulations that go beyond the idealized case of spherical isolated sources.

Unifying ordinary and null memory

Based on a recently proposed reinterpretation of gravitational wave memory that builds up on the definition of gravitational waves pioneered by Isaacson, we provide a unifying framework to derive both ordinary and null memory from a single well-defined equation at leading order in the asymptotic expansion. This allows us to formulate a memory equation that is valid for any unbound asymptotic energy-flux that preserves local Lorentz invariance. Using Horndeski gravity as a concrete example metric theory with an additional potentially massive scalar degree of freedom in the gravitational sector, the general memory formula is put into practice by presenting the first account of the memory correction sourced by the emission of massive field waves. Throughout the work, physical degrees of freedom are identified by constructing manifestly gauge invariant perturbation variables within an SVT decomposition on top of the asymptotic Minkowski background, which will in particular prove useful in future studies of gravitational wave memory within vector tensor theories.

How does the uncut chip thickness affect the deformation states within the primary shear zone during metal cutting?

The deformation states within the primary shear zone (PSZ) significantly affect material removal during machining. Uncut chip thickness (UCT) is an important factor that influences the material deformation states. However, the specific mechanism by which UCT influences the deformation states within PSZ remains unknown. This study aims to investigate the relationship between the deformation states in PSZ and UCTs via in-situ measurement and microscopic characterization techniques. Using the digital image correlation (DIC) technique, strain and strain rate distributions were derived to reveal the discrepant deformation in PSZ with increasing UCT. Furthermore, velocity vector fields and Electron Back-Scattered Diffraction (EBSD) characterizations were employed to examine the heterogeneity of deformation modes. To determine the specific deformation information, a deformation extraction framework based on the deformation gradient tensor theory was developed. Thus, strong and weak shear modes within PSZ were revealed based on the full-field deformation information of compression and extension. As the UCT increased, the transition of deformation states from a strong shear state to a hybrid shear state was determined. This work presents a new understanding of the deformation mechanism within PSZ in a ductile material of pure iron. A critical UCT was proposed to guide the cutting process to avoid inefficient weak shear mode.

Weyl–invariant scalar–tensor gravities from purely metric theories

We describe a method to generate scalar–tensor theories with Weyl symmetry, starting from arbitrary purely metric higher derivative gravity theories. The method consists in the definition of a conformally-invariant metric g^μν\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hat{g}_{\\mu \ u }$$\\end{document}, that is a rank (0,2)-tensor constructed out of the metric tensor and the scalar field. This new object has zero conformal weight and is given by ϕ2/Δgμν\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\phi ^{2/\\Delta }g_{\\mu \ u }$$\\end{document}, where (-Δ)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(-\\Delta )$$\\end{document} is the conformal dimension of the scalar. As gμν\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$g_{\\mu \ u }$$\\end{document} has conformal dimension of 2, the resulting tensor is trivially a conformal invariant. Then, the generated scalar–tensor theory, which we call the Weyl uplift of the original purely metric theory, is obtained by replacing the metric by g^μν\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hat{g}_{\\mu \ u }$$\\end{document} in the action that defines the original theory. This prescription allowed us to define the Weyl uplift of theories with terms of higher order in the Riemannian curvature. Furthermore, the prescription for scalar–tensor theories coming from terms that have explicit covariant derivatives in the Lagrangian is discussed. The same mechanism can also be used for the derivation of the equations of motion of the scalar–tensor theory from the original field equations in the Einstein frame. Applying this method of Weyl uplift allowed us to reproduce the known result for the conformal scalar coupling to Lovelock gravity and to derive that of Einsteinian cubic gravity. Finally, we show that the cancellation of the volume divergences in the theory given by the conformal scalar coupling to Einstein–Anti-de Sitter gravity is achieved by the Weyl uplift of the original theory augmented by counterterms, which is relevant in the framework of conformalrenormalization.

Surface crack effect on frequency and vibration mode switching of solar-powered aerospace structures

In the engineering design of modern wing panels and their optimal control system, the first step is to find and predict their dynamic characteristics. These characteristics are dependent on material properties, panel geometry, and boundary conditions. In addition, possible fracture existence, imperfections and environmental conditions may unpredictably change the frequency and modes shape of the panel and then the parameters of a control system. In the present paper, the effect of surface fracture depth and orientation on frequency and vibration mode switching of perovskite solar cells-based aircraft wing panels is investigated for the first time. The PSC (perovskite solar cell) panel is made of a polymer substrate reinforced with even-distributed graphene platelets (GPLs) and thin solar layers to enhance the overall electromechanical performance of the whole structure. Equations of motion of the panel are obtained by the Hamilton approach based on the properties of Reddy's third-order shear deformation theory and linear components of the Green-Lagrange strain tensor. The novel aspect is a line-spring model of surface crack by Cartmell et al. adapted to the model of the PSC panel under consideration. The discretization of the established equations of motion for the cracked panel is carried out by the element-free IMLS-Ritz method with mesh-free features. Validation of the obtained solutions is carried out by comparisons with results from previous studies for cracked laminated plates.First, material and geometric properties effect on vibration characteristics of the PSC structure was investigated. Next, partial surface crack depth and orientation angle are examined to show changes in frequency and vibration modes shape of the panel. It is shown, that there is a mode swapping between the second and third modes when transitioning from an intact panel to a cracked one. As the crack length increases, higher-order mode variations become more noticeable, potentially leading to their swapping or the excitation of new ones. Additionally, the findings demonstrate that the surface crack orientation angle significantly impacts the higher-order modes of the panel. When the orientation angle is 90°, the first six modes align with those of the intact plate. Mode shapes and frequency shifts are significant for crack orientation angles between 0° and 90°.

Bouncing and collapsing universes dual to late-time cosmological models

We use the Jordan frame–Einstein frame correspondence to explore dual universes with contrasting cosmological evolutions. We study the mapping between Einstein and Jordan frames where the Einstein frame universe describes the late-time evolution of the physical universe, which is driven by dark energy and non-relativistic matter. The Brans–Dicke theory of gravity is considered to be the dual scalar–tensor theory in the Jordan frame. We show that an Einstein frame universe, with cosmological evolution of the Λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Lambda $$\\end{document}CDM model, always corresponds to a bouncing Jordan frame universe governed by a Brans–Dicke theory. On the other hand, quintessence models of dark energy with non-relativistic matter component are shown to be always dual to a Brans–Dicke Jordan frame with a turn-around, i.e., a bounce or a collapse. The evolution of the equation of state of the quintessence field determines whether the turn-around is a bounce or a collapse. The point of the Jordan frame turn-around for all the cases can be tuned anywhere by choosing an appropriate Brans–Dicke parameter. This essentially leads to alternative descriptions of the late-time evolution of the physical universe, in terms of bouncing or collapsing Brans–Dicke universes in the Jordan frame. Therefore, the effect of dark energy can equivalently be seen as collapse of space in a conformally connected universe. We further study the stability of such conformal maps against linear perturbations. The effective bouncing and collapsing descriptions of the current accelerating universe may have interesting implications for the evolutions of perturbations and quantum fluctuations in the cosmological background.

Anisotropic Bianchi Type-1 Cosmological Model Containing Dark Energy

Considering the LRS Bianchi type I metric here we studied the spatial homogeneous and anisotropic dark energy cosmological models in the frame work of B-D scalar tensor theory of gravity along with variable equation of parameter and deceleration parameter. Exact solutions of field equations are obtained with certain physical assumptions in different cases. The physical behavior of the model is also discussed in details.

Towards a possible solution to the Hubble tension with Horndeski gravity

The Hubble tension refers to the discrepancy in the value of the Hubble constant H0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$H_0$$\\end{document} inferred from the cosmic microwave background observations, assuming the concordance Λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Lambda $$\\end{document}CDM model of the Universe, and that from the distance ladder and other direct measurements. In order to alleviate this tension, we construct a plausible dark energy scenario, within the framework of Horndeski gravity which is one of the most general scalar–tensor theories yielding second-order equations. In our set-up, we include the self-interactions and nonminimal coupling of the dynamical dark energy scalar field which enable very interesting dynamics leading to a phantom behaviour at low redshifts along with negative dark energy densities at high redshifts. These two features together make this model a promising scenario to alleviate the Hubble tension for appropriate choices of the model parameters. Towards a consistent model building, we show that this set-up is also free from both the gradient and ghost instabilities. Finally, we confront the predictions of the model with low redshift observations from Pantheon, SH0ES, cosmic chronometers and BAO, to obtain best fit constraints on model parameters.

Tensor-Based Forward–Backward Algorithms in the Physics-Informed Coupled Hidden Markov Model

Imposing data-driven with physical laws for user activity prediction could effectively solve various physical problems such as smart care, surveillance and human-robot. In the growing field of artificial intelligence, the application of activity prediction based on physical Coupled Hidden Markov Model (CHMM) and tensor theory with physical properties has attracted increasing attentions. However, existing CHMMs usually only consider the time-series characteristic of data, while ignoring physical characteristics of user activity such as periodicity, timing and correlation. Moreover, they are all matrix-based models, which could not holistically analyze the dependencies among physical states. The above disadvantages lead to lower prediction accuracy of CHMM. To remove these disadvantages, three physics-informed tensor-based CHMMs are first constructed by incorporating prior physical knowledge. Then the corresponding forward-backward algorithms are designed for resolving the evaluation problem of CHMM. These algorithms could overall model multiple physical features by imposing physics and prior knowledge into CHMM during training to improve the precision of probabilistic computing. The algorithms reduce the dependence of the model on training data by adding physical features. Finally, the comparative experiments show that our algorithms have better performances than existing prediction methods in precision and efficiency. In addition, further selfcomparison experiments verify that our algorithms are effective and practical.

A correction method of magnetic gradient tensor system to improve magnet localization accuracy

The magnetic gradient tensor systems using vector magnetic sensors are easily affected by single sensor error and sensor array misalignment, significantly affecting target localization accuracy. To address this problem, based on the differential measurement theory of magnetic gradient tensor, a vector sensor error model was established, and the single sensor errors were corrected using the total least square (TLS) ellipsoid fitting method. Besides, a misalignment error correction model for the sensor is obtained by constructing a rotation matrix for the magnetic sensor's three-axis orthogonal coordinate system transformation, and the tensor system can be aligned by performing the TLS estimation of the rotation angle. After calibration, the experimental results show that the outputs of each sensor have high coincidence and coaxiality. The root mean square error (RMSE) of the total magnetic intensity (TMI) is reduced to within 100 nT, and the RMSE of the tensor component is reduced to within 85 nT/m. Within a range of 5 m, the magnetic target positioning error is reduced to less than 25.1 cm. This technology can improve the measurement accuracy of the magnetic gradient tensor system with high stability and reliability.

On the Possibility of a Static Universe

After a century of cosmological observations, we have a solid standard model of cosmology. However, from a theoretical viewpoint, it is a compelling question if the cosmological data inevitably require an expanding universe independently of the theoretical framework. The possibility of obtaining a viable cosmological model with a constant scale-factor is discussed in the context of the Brans–Dicke class of scalar–tensor theories. It is shown that a flat spatial section requires the presence of a stiff matter fluid. However, some kinematical properties of the standard cosmological model can be reproduced. A realistic scenario may require a more complex class of scalar–tensor theories.

Scalar-multi-tensor approach to fT,B,∇μT,∇μB teleparallel gravity

In this work we analyze, in the context of modified teleparallel gravity, the equivalence between scalar-vector-tensor theories and geometrical theories of the type fT,B,∇μT,∇μB , where T and B are respectively the scalar torsion and the boundary scalar. This analysis is performed in the Jordan and Einstein frames. In particular, in the latter frame, two distinct cases are analyzed, where the role of surface terms is discussed. The equivalence between the geometrical and the scalar-vector-tensor approaches is verified for regular systems, i.e. for systems that present a regular Hessian matrix. An example is presented and the analysis of the Cauchy problem is made for the different approaches. An extension for systems that include higher-order derivatives of T and B is briefly presented, showing the equivalence between the geometrical and scalar-multi tensor theories.

The Brans–Dicke field in non-metricity gravity: cosmological solutions and conformal transformations

We consider the Brans–Dicke theory in non-metricity gravity, which belongs to the family of symmetric teleparallel scalar–tensor theories. Our focus lies in exploring the implications of the conformal transformation, as we derive the conformal equivalent theory in the Einstein frame, distinct from the minimally coupled scalar field theory. The fundamental principle of the conformal transformation suggests the mathematical equivalence of the related theories. However, to thoroughly analyze the impact on physical variables, we investigate the spatially flat Friedmann–Lemaître–Robertson–Walker geometry, defining the connection in the non-coincidence gauge. We construct exact solutions for the cosmological model in one frame and compare the physical properties in the conformal related frame. Surprisingly, we find that the general physical properties of the exact solutions remain invariant under the conformal transformation. Finally, we construct, for the first time, an analytic solution for the symmetric teleparallel scalar–tensor cosmology.

Bayesian test of Brans–Dicke theories with planetary ephemerides: Investigating the strong equivalence principle

Aims. We are testing the Brans–Dicke class of scalar tensor theories with planetary ephemerides. Methods. In this work, we apply our recently proposed Bayesian methodology to the Brans–Dicke case, with an emphasis on the issue of the strong equivalence principle (SEP). Results. We use an MCMC approach coupled to full, consistent planetary ephemeris construction (from point-mass body integration to observational fit) and compare the posterior distributions obtained with and without the introduction of potential violations of the SEP. Conclusions. We observe a shift in the confidence levels of the posteriors obtained. We interpret this shift as marginal evidence that the effect of violation of the SEP can no longer be assumed to be negligible in planetary ephemerides with the current data. We also notably report that the constraint on the Brans–Dicke parameter with planetary ephemerides is getting closer to the figure reported from the Cassini spacecraft alone, and also to the constraints from pulsars. We anticipate that data from future spacecraft missions, such as BepiColombo, will significantly enhance the constraints based on planetary ephemerides.

Strength Analysis and Research of Composite Material Bridge Deck

The strength of each layer of composite bridge deck under different load conditions is analyzed and studied by Tsai-Wu tensor theory. The results indicate that, the characteristic strength values calculated in the predetermined reinforcement fabric are significantly smaller than those in the E-glass fiber layer, and the damage will first occur in E-glass fiber layer. Under various operating conditions, the characteristic strength values in each layer of FRP bridge panel are smaller than 1, and have a certain safety factor. The weak positions of each layer are related to the configuration of bridge panel. Tsai-Wu tensor theory can accurately evaluate the status of each layer, and supervise the design work of GFRP bridge panel.