Tensor Theory Research Articles

General solutions of Einstein gravity at Drightarrow 2

Einstein gravity at Drightarrow 2 limit can be obtained from the Kaluza–Klein procedure by taking the dimensions of the internal space to zero while keeping only the breathing mode. The resulting scalar–tensor theory can be further reduced to JT gravity or the Liouville CFT at the large central charge limit, bridging the two important 2d models. We construct the general solutions of the theory, including black holes and wormholes for both positive and negative cosmological constants. We obtain the on-shell action of the nearly AdS_2 and show that for suitable boundary slices, the Schwarzian action governs the leading-order dynamics at the finite boundary cutoff in later time. For positive cosmological constant, we find that the scalar is well defined on the 2-sphere.

Dynamical Analysis of the Covarying Coupling Constants in Scalar–Tensor Gravity

A scalar–tensor theory of gravity was considered, wherein the gravitational coupling G and the speed of light c were admitted as space–time functions and combined to form the definition of the scalar field ϕ. The varying c participates in the definition of the variation of the matter part of the action; it is related to the effective stress–energy tensor, which is a result of the requirement of symmetry under general coordinate transformations in our gravity model. The effect of the cosmological coupling Λ is accommodated within a possible behavior of ϕ. We analyzed the dynamics of ϕ in the phase space, thereby showing the existence of an attractor point for reasonable hypotheses on the potential V(ϕ) and no particular assumption on the Hubble function. The phase space analysis was performed both with the linear stability theory and via the more general Lyapunov method. Either method led to the conclusion that the condition G˙/G=σc˙/c, where σ=3 must hold for the rest of cosmic evolution after the system arrives at the globally asymptotically stable fixed point and the dynamics of ϕ ceases. This result realized our main motivation: to provide a physical foundation for the phenomenological model admitting G/G0=c/c03, used recently to interpret cosmological and astrophysical data. The thus covarying couplings G and c impact the cosmic evolution after the dynamical system settles to equilibrium. The secondary goal of our work was to investigate how this impact occurs. This was performed by constructing the generalized continuity equation in our scalar–tensor model and considering two possible regimes for the varying speed of light—decreasing c and increasing c—while solving our modified Friedmann equations. The solutions to the latter equations make room for radiation- and matter-dominated eras that progress to a dark-energy-type of accelerated expansion.

Acoustic emission characteristics and fracture mechanism of cemented tailings backfill under uniaxial compression: experimental and numerical study

Cemented tailings backfill (CTB) is the most cost-effective and environmentally friendly method to recycle tailings for filling mining. It is of great significance to study the fracture mechanism of CTB for safe mining. In this study, three cylindrical CTB samples with a cement-tailings ratio of 1:4 and a mass fraction of 72% were prepared. An acoustic emission (AE) test under uniaxial compression (UC) with WAW-300 microcomputer electro-hydraulic servo universal testing machine and DS2 series full information AE signal analyzer was carried out to discuss the AE characteristics of CTB, such as hits, energy, peak frequency, and AF-RA. Combined with particle flow and moment tensor theory, a meso AE model of CTB was constructed to reveal the fracture mechanism of CTB. The results show that (1) the AE law of CTB under UC has periodic characteristics, which can be divided into the rising stage, stable stage, booming stage, and active stage. (2) The peak frequency of the AE signal is mainly focused on three frequency bands. The ultra-high frequency AE signal may be the precursor information for CTB failure. (3) The low frequency band AE signals represent shear crack, while the medium and high frequency band AE signals represent tension crack. The shear crack initially decreases and then increases, and the tension crack is the opposite. (4) The fracture types of the AE source are divided into tension crack, mixed crack, and shear crack. The tension crack is dominant, while a larger magnitude AE source is frequently shear crack. The results can provide a basis for the stability monitoring and fracture prediction of CTB.

Modeling of material removal in magnetic finishing based on Maxwell's stress tensor theory and its experimental validation

Magnetic finishing is an extremely suitable process for processing high quality surface aluminum alloy mirrors due to the low damage. Obtaining an accurate removal function is essential to achieve a controlled finishing of aluminum alloy mirror. In this study, the magnetic field between the magnetized abrasive particles was simplified by equivalent substitution method after modeling the geometry of the abrasive and simulating its magnetic field. Distribution of finishing pressure was calculated based on Maxwell's stress tensor theory. Distribution of the finishing pressure was uneven, and the finishing pressure in the center of the finishing area was about 10 times that of the edges. And the removal amount was calculated with Preston's equations. The experimental results of the removal amount show that the removal amount increases and then decreases as the magnetic abrasive content in the abrasive decreases. The removal amount has a negative correlation with the finishing gap. Stronger magnetic fields can increase the removal amount. After 10 minutes of machining, the surface roughness Ra of the aluminum plate decreased from 0.189 μ m to 0.030 μ m . The relative error is less than 7% compared to the simulation results when the finishing gap is 2-3 mm. The removal depth experimental results show that the maximum removal depth reaches 117 nm after 10 minutes of machining at 950r/min, with a relative error of 3.5%. This accurate removal function can provide a theoretical basis for achieving controlled magnetic finishing.

Complex-tensor theory of simple smectics

Matter self-assembling into layers generates unique properties, including structures of stacked surfaces, directed transport, and compact area maximization that can be highly functionalized in biology and technology. Smectics represent the paradigm of such lamellar materials — they are a state between fluids and solids, characterized by both orientational and partial positional ordering in one layering direction, making them notoriously difficult to model, particularly in confining geometries. We propose a complex tensor order parameter to describe the local degree of lamellar ordering, layer displacement and orientation of the layers for simple, lamellar smectics. The theory accounts for both dislocations and disclinations, by regularizing singularities within defect cores and so remaining continuous everywhere. The ability to describe disclinations and dislocation allows this theory to simulate arrested configurations and inclusion-induced local ordering. This tensorial theory for simple smectics considerably simplifies numerics, facilitating studies on the mesoscopic structure of topologically complex systems.

Some aspects of Morris–Thorne wormhole in Scalar–Tensor theory

In this work, we reach the equations of motion of Morris–Thorne wormhole geometry by means of the Einstein Field Equations and Klein–Gordon Equation of Scalar–Tensor Theory. We discuss the anisotropic matter energy distribution. We determine a relation between the radial and the transverse pressures. Hence, we express the anisotropic energy–momentum tensor in terms of one pressure class, by means of that relation. Besides that, we check the isotropic case and show that there is no traversable wormhole (WH), in the zero redshift function situation, if the energy–momentum distribution of the universe is isotropic. In addition, we represent the conditions in order that the Null Energy Condition (NEC) is satisfied in the zero redshift function case, for anisotropic distribution. We also propose a special class of traversable WH shape functions. We will be calling the WHs corresponding to that class of functions as the Yukawa Type WHs. We expressed the NEC for those WHs particularly. Furthermore, we determine the radial and the transverse pressures in zero redshift function situation.

Spinor-helicity formalism for massive and massless amplitudes in five dimensions

Five-dimensional gauge and gravity theories are known to exhibit striking properties. D = 5 is the lowest dimension where massive tensor states appear naturally, providing a testing ground for perturbative insights into six-dimensional tensor theories. Five-dimensional supergravities are highly constrained and admit elegant geometric and algebraic formulations, with global symmetries manifest at the Lagrangian level.In this paper, we take a step towards the systematic investigation of amplitudes in five dimensions, and present a five-dimensional version of the spinor-helicity formalism, applicable to massless, massive and supersymmetric states. We give explicit representations for on-shell spinor and polarization variables such that the little-group symmetry and gauge redundancy are manifest. Massive self-dual tensor states are discussed in some detail, as well as all the on-shell supermultiplets that can appear in matter-coupled gauge and supergravity theories. As a byproduct of considering supersymmetry in the presence of central charge, we obtain massless ten-dimensional Majorana-Weyl spinors as products of five-dimensional massive spinors.We present compact expressions for superamplitudes at multiplicity three and four, including several novel superamplitudes that either do not straightforwardly uplift to six dimensions, or have not appeared in the six-dimensional literature. We discuss several examples of five-dimensional double-copy constructions in the context of gravitational theories with massive vectors and tensors, illustrating that the formalism we construct can also be used to considerably streamline the double-copy construction of mathcal{N} = 2 Maxwell-Einstein supergravities.

The dual laterolog response of fractured-vuggy reservoirs based on conductivity tensor and Maxwell–Garnett mixing rule

Dual laterologs measure reservoir resistivity at deep and shallow depths around a wellbore, a thorough understanding of the dual laterolog response of fractured-vuggy reservoirs is key for reservoir identification and saturation evaluation. The joint development of the fracture and vugs complicates the laterolog response of fractured-vuggy reservoirs. In this study, the conductivity model of the dipping anisotropic structure on the horizontal plane was analyzed according to the theory of the conductivity tensor. Then, based on the Maxwell–Garnett mixing rule, a conductivity model of the vuggy reservoirs was established. On this basis, the dual lateral conductivity model of fractured-vuggy reservoirs was established by equating the vuggy reservoir to the matrix and the dipping anisotropic structure plane to the fracture plane. Furthermore, based on the dual lateral conductivity model and physical experiments, the dual laterolog responses with respect to the fracture dip angle, fracture porosity, and vug porosity were systematically analyzed. The study revealed that (1) the fracture dip angle significantly affects the separation of the dual laterolog. In other words, at a low dip angle, the fracture shows a negative separation of the dual laterolog, whereas a positive separation at a high dip angle; (2) for vuggy reservoirs, the development of vugs decreases the deep and shallow laterologs, and the more the vugs developed, the greater the decrease; (3) for fractured-vuggy reservoirs, the dual laterolog response is mainly controlled by fractures. The development of vugs did not change the negative or positive separation of dual laterologs with different fracture dip angles.

Numerical modelling of spatially and temporally distributed on-fault induced seismicity: implication for seismic hazards

Induced seismicity is strongly related to various engineering projects that cause anthropogenic in-situ stress change at a great depth. Hence, there is a need to estimate and mitigate the associated risks. In the past, various simulation methods have been developed and applied to induced seismicity analysis, but there is still a fundamental difference between simulation results and field observations in terms of the spatial distribution of seismic events and its frequency. The present study aims to develop a method to simulate spatially distributed on-fault seismicity whilst reproducing a complex stress state in the fault zone. Hence, an equivalent continuum model is constructed, based on a discrete fracture network within a fault damage zone, by employing the crack tensor theory. A fault core is simulated at the center of the model as a discontinuous plane. Using the model, a heterogeneous stress state with stress anomalies in the fault zone is first simulated by applying tractions on the model outer boundaries. Subsequently, the effective normal stress on the fault plane is decreased in a stepwise manner to induce slip. The simulation result is validated in terms of the b-value and other seismic source parameters, hence demonstrating that the model can reproduce spatially and temporally distributed on-fault seismicity. Further analysis on the parameters shows the variation of frequency-magnitude distribution before the occurrence of large seismic events. This variation is found to be consistent with field observations, thus suggesting the potential use of this simulation method in evaluating the risk for seismic hazards in various engineering projects.

Extending the symmetry of the massless Klein–Gordon equation under the general disformal transformation

The Klein–Gordon equation, one of the most fundamental equations in field theory, is known to be not invariant under conformal transformation. However, its massless limit exhibits symmetry under Bekenstein’s disformal transformation, subject to some conditions on the disformal part of the metric variation. In this study, we explore the symmetry of the Klein–Gordon equation under the general disformal transformation encompassing that of Bekenstein and a hierarchy of “sub-generalizations” explored in the literature (within the context of inflationary cosmology and scalar–tensor theories). We find that the symmetry in the massless limit can be extended under this generalization provided that the disformal factors take a special form in relation to the conformal factor. Upon settling the effective extension of symmetry, we investigate the invertibility of the general disformal transformation to avoid propagating nonphysical degrees of freedom upon changing the metric. We derive the inverse transformation and the accompanying restrictions that make this inverse possible.

MOND as a peculiar case of the SIV theory

ABSTRACTThe scale invariant theory is preserving the fundamental physical properties of General Relativity, while enlarging the group of invariances subtending gravitation theory (Dirac 1973; Canuto et al. 1977). The scale-invariant vacuum (SIV) theory assumes as gauging condition that ‘The macroscopic empty space is scale invariant, homogeneous, and isotropic’. Some basic properties in Weyl’s Integrable Geometry and cotensor calculus are examined in relation with scalar–tensor theories. Possible scale invariant effects are strongly reduced by matter density, both at the cosmological and local levels. The weak field limit of SIV tends to MOND when the scale factor is taken as constant, an approximation valid (<1 per cent) over the last 400 Myr. A better understanding of the a0-parameter is obtained: it corresponds to the equilibrium point of the Newtonian and SIV dynamical acceleration. Parameter a0 is not a universal constant, it depends on the density and age of the Universe. As MOND is doing, SIV theory avoids the call to dark matter, moreover the cosmological models predict accelerated expansion.

Tensor-Empowered Federated Learning for Cyber-Physical-Social Computing and Communication Systems

The deep fusion of human-centered Cyber-Physical-Social Systems (CPSSs) has attracted widespread attention worldwide and big data as the blood of CPSSs could lay a solid data cornerstone for providing more proactive and accurate wisdom services. However, due to concerns about data privacy and security, traditional data centralized learning paradigm is no longer suitable. Federated Learning (FL) as an emerging distributed privacy-preserving machine learning paradigm would have great research significance and application values. Although few survey papers on FL already exist in the literature, the survey about FL from the perspective of human-centered CPSSs and tensor theory is lacking. Toward this end, we first introduce the CPSSs and deeply analyze the correlations among humans, cyber space, physical space and social space, as well as the opportunities brought by it. Afterwards, we present an overview of FL and then review extensive researches on FL in terms of resources management, communication, security and privacy protection, which provides a shortcut for readers to quickly understand and learn FL. Furthermore, the theory about tensor representation, operation and decomposition for handling massive, multi-source heterogeneous big data and corresponding applications are described. By leveraging the advantages of tensor in unified modeling, dimensionality reduction, and feature extraction, a framework and three tensor-empowered solutions are provided to solve these challenges about heterogeneous resource management, communication overhead together with security and privacy. Finally, some future research directions are listed for looking forward to inspiring more readers to devote themselves to researching tensor-empowered FL for human-centered CPSSs in the future.

Despeckling Multitemporal Polarimetric SAR Data Based on Tensor Decomposition

Despeckling is an essential task in polarimetric synthetic aperture radar (PolSAR) image processing. Most existing filters developed for multi-temporal SAR images make use of either real or complex information. Real information refers to amplitude or intensity values, whereas complex information refers to complex covariance matrix (CCM) derived from either interferometric SAR (InSAR) or PolSAR data. The InSAR CCM is formed using images of the same polarimetric channel but acquired at different dates, and the PolSAR CCM contains information acquired simultaneously in different polarimetric channels. Therefore, these despeckling methods may present a good performance in some applications and scenes but fail in other cases, due to differences in input sources. In order to achieve a more robust result in all cases, we develop a method for multi-temporal polarimetric SAR data filtering based on tensor decomposition (TD-MPF), which aims at improving the identification of homogeneous pixels for spatially adaptive filtering. The key element of this approach consists of exploiting tensor theory to construct a new CCM that contains both polarimetric and interferometric information, as well as multi-temporal information for each pixel. The effectiveness of the proposed method and its performance are evaluated with simulated and real SAR data in comparison with several established methods.

Kantowski Sachs macroscopic body cosmological models in scalar tensor theories of gravitation

In this paper, we have obtained the field equations in scalar-tensor theories of gravitation proposed by Brans-Dicke [5] and Saez-Ballester [28] with the aid of Kantowski Sachs Space time in the presence of macroscopic body. Both theories' field equations can be solved definitively by using transformation. The present discussion explores into the expression involving energy density, energy flow vector, stress tensor, and specific physical features of both of these models.

Classifying compact 4-manifolds via generalized regular genus and G-degree

$(d+1)$-colored graphs, i.e., edge-colored graphs that are $(d+1)$-regular, have already been proved to be a useful representation tool for compact PL $d$-manifolds, thus extending the theory (known as crystallization theory) originally developed for the closed case. In this context, combinatorially defined PL invariants play a relevant role. The present paper focuses in particular on generalized regular genus and G-degree: the first one extending to higher dimension the classical notion of Heegaard genus for 3-manifolds, the second one arising, within theoretical physics, from the theory of random tensors as an approach to quantum gravity in dimension greater than two. We establish several general results concerning the two invariants, in relation with invariants of the boundary and with the rank of the fundamental group, as well as their behaviour with respect to connected sums. We also compute both generalized regular genus and G-degree for interesting classes of compact $d$-manifolds, such as handlebodies, products of closed manifolds by the interval and $\mathbb D^2$-bundles over $\mathbb S^2.$ The main results of the paper concern dimension 4, where we obtain the classification of all compact PL manifolds with generalized regular genus at most one, and of all compact PL manifolds with G-degree at most 18; moreover, in case of empty or connected boundary, the classifications are extended to generalized regular genus two and to G-degree 24.

Annihilating Entanglement Between Cones

Every multipartite entangled quantum state becomes fully separable after an entanglement breaking quantum channel acted locally on each of its subsystems. Whether there are other quantum channels with this property has been an open problem with important implications for entanglement theory (e.g., for the distillation problem and the PPT squared conjecture). We cast this problem in the general setting of proper convex cones in finite-dimensional vector spaces. The max-entanglement annihilating maps transform the k-fold maximal tensor product of a cone {textsf{C}}_1 into the k-fold minimal tensor product of a cone {textsf{C}}_2, and the pair ({textsf{C}}_1,{textsf{C}}_2) is called resilient if all max-entanglement annihilating maps are entanglement breaking. Our main result is that ({textsf{C}}_1,{textsf{C}}_2) is resilient if either {textsf{C}}_1 or {textsf{C}}_2 is a Lorentz cone. Our proof exploits the symmetries of the Lorentz cones and applies two constructions resembling protocols for entanglement distillation: As a warm-up, we use the multiplication tensors of real composition algebras to construct a finite family of generalized distillation protocols for Lorentz cones, containing the distillation protocol for entangled qubit states by Bennett et al. (Phys Rev Lett 76(5):722, 1996) as a special case. Then, we construct an infinite family of protocols using solutions to the Hurwitz matrix equations. After proving these results, we focus on maps between cones of positive semidefinite matrices, where we derive necessary conditions for max-entanglement annihilation similar to the reduction criterion in entanglement distillation. Finally, we apply results from the theory of Banach space tensor norms to show that the Lorentz cones are the only cones with a symmetric base for which a certain stronger version of the resilience property is satisfied.

Role of anisotropy on topological structures of elasticity, anisotropy, brittleness and phonon in Al3Ti

Based on tensor theory and Bond matrix model, the anisotropy, brittleness/plasticity, and stress–strain under bulk and point stresses are systematically studied, in order to find the effect of anisotropy on their structures. The applications of the Kelvin-Christoffel tensor are mainly focused on phonon focusing and phonon image with Gaussian curvature method. The investigation of phonon entropy shows that the 3-branche lattice waves are mainly composed of long acoustic waves and long optical waves. The slowness of the three lattice waves is influenced by anisotropy as follows: the slow shear wave is the largest, the fast shear wave is the second, and the longitudinal wave is the smallest. This is well explained by the 3D anisotropy of phonon amplification coefficients.PACS: 62.20.D-; 74.25.Ld; 62.30. +d; 63.20.-e; 74.25.Ld; 94.20.Bb

Generalized disformal Horndeski theories: Cosmological perturbations and consistent matter coupling

Abstract Invertible disformal transformations are a useful tool to investigate ghost-free scalar–tensor theories. By performing a higher-derivative generalization of the invertible disformal transformation on Horndeski theories, we construct a novel class of ghost-free scalar–tensor theories, which we dub generalized disformal Horndeski theories. Specifically, these theories lie beyond the quadratic/cubic DHOST class. We explore cosmological perturbations to identify a subclass where gravitational waves propagate at the speed of light and clarify the conditions for the absence of ghost/gradient instabilities for tensor and scalar perturbations. We also investigate the conditions under which a matter field can be consistently coupled to these theories without introducing unwanted extra degrees of freedom.

Randomized algorithms for tensor response regression

AbstractIn this paper, we consider the estimation algorithm of tensor response on vector covariate regression model. Based on projection theory of tensor and the idea of randomized algorithm for tensor decomposition, three new algorithms named SHOLRR, RHOLRR and RSHOLRR are proposed under the low‐rank Tucker decomposition and some theoretical analyses for two randomized algorithms are also provided. To explore the nonlinear relationship between tensor response and vector covariate, we develop the KRSHOLRR algorithm based on kernel trick and RSHOLRR algorithm. Our proposed algorithms can not only guarantee high estimation accuracy but also have the advantage of fast computing speed, especially for higher‐order tensor response. Through extensive synthesized data analyses and applications to two real datasets, we demonstrate the outperformance of our proposed algorithms over the stat‐of‐art.

Further considerations about the traversability of thin-shell wormholes

Traversability in relation with tides in thin-shell wormholes is revisited to investigate the possibility of improving recently noted restrictive conditions for a safe travel across a wormhole throat. We consider wormholes mathematically constructed starting from background geometries which are solutions of scalar–tensor theories as dilaton gravity and Brans–Dicke gravity. The advantages of working within such frameworks are studied by examining the dependence of the extrinsic curvature and tides at the throat with the parameters determining the departure from pure relativity; the associated behaviour of tides in the smooth regions of the geometries is also analyzed. Other related but different approaches within pure relativity are discussed in the appendices.