Tensor Analysis Method Research Articles

Surface Pressure Calculation Method of Multi-Field Coupling Mechanism under the Action of Flow Field

At present, the majority of fluid mechanisms are multi-field coupling mechanisms, and their function is also achieved in the flow field. Therefore, calculating the aerodynamic characteristics of the multi-field coupling mechanism in a symmetric flow field is very important. However, at present, the strong coupling algorithm in the domain has the problems of low accuracy and computational efficiency, which make it more difficult to solve the coupling problem. This article obtains the vector potential of the law of conservation of momentum using the tensor analysis method in a Cartesian coordinate system. Meanwhile, the generalized operator of Navier–Stokes equations and the fundamental solution of the generalized operator are obtained on this basis. Then, this article proposes the boundary integral equation of the Navier–Stokes equations by combining the fundamental solution of the Laplace equation with generalized potential theory. Based on this boundary integral equation, this article has developed a new calculation method that can help achieve integral calculation without domains, greatly reducing the problem’s difficulty. Finally, by comparing the ellipsoid example solution with the experimental results, the algorithm’s reliability in solving the incompressible problem is verified.

Dislocation nucleation from Zr–Nb bimetal interfaces cooperating with the dynamic evolution of interfacial dislocations

The nucleation of lattice dislocations (LDs) from bimetal interfaces is critical to the interface-mediated deformation and strengthening mechanism in nanoscale multilayered metallic composites. Such nucleation not only depends on external loadings but also closely correlates with interfacial dislocation (ID) networks and their dynamic evolution. In this study, we focused on LD nucleation cooperating with IDs dynamic evolution from Zr/Nb bimetal interfaces following Pitch-Schrader and Burgers orientation relationships. To mimic the cross interactions between Zr and Nb atoms in molecular dynamic simulations, an empirical embedded-atom method potential was developed. The automatic Nye tensor analysis method was employed to directly identify the characteristics of IDs, which showed that: (1) many segments with obvious directivity, named main segments, were regularly distributed within IDs networks; and (2) main segments were connected by several atomic steps at regions where IDs intersected with each other. These characteristics have demonstrated, for the first time, the significant details of hcp/bcc interfaces. The further analyses of IDs dynamic evolution as LDs nucleation indicated: (1) the nucleation, which preferred at or by IDs intersections, is attributed to the flexible movement of atomic steps, by which the line orientations of ID segments at intersections can be adaptively altered to be parallel to the traces of LDs glide planes; (2) the weakened block effect of main segments in low strain concentrations is responsible for the unexpected nucleation across main segments in a direction which largely deviates from main segments. This investigation gives helpful understanding of the interface-mediated deformation in not only Zr/Nb but also other hcp/bcc (especially hcp crystals with low c/a ratios) nanolayered composites, and can satisfy the renewed interest in the fundamental scientific field of dislocations-interfaces interactions.

Full-Spectrum-Knowledge-Aware Tensor Model for Energy-Resolved CT Iterative Reconstruction.

Energy-resolved computed tomography (ErCT) with a photon counting detector concurrently produces multiple CT images corresponding to different photon energy ranges. It has the potential to generate energy-dependent images with improved contrast-to-noise ratio and sufficient material-specific information. Since the number of detected photons in one energy bin in ErCT is smaller than that in conventional energy-integrating CT (EiCT), ErCT images are inherently more noisy than EiCT images, which leads to increased noise and bias in the subsequent material estimation. In this work, we first deeply analyze the intrinsic tensor properties of two-dimensional (2D) ErCT images acquired in different energy bins and then present a F ull- S pectrum-knowledge-aware Tensor analysis and processing (FSTensor) method for ErCT reconstruction to suppress noise-induced artifacts to obtain high-quality ErCT images and high-accuracy material images. The presented method is based on three considerations: (1) 2D ErCT images obtained in different energy bins can be treated as a 3-order tensor with three modes, i.e., width, height and energy bin, and a rich global correlation exists among the three modes, which can be characterized by tensor decomposition. (2) There is a locally piecewise smooth property in the 3-order ErCT images, and it can be captured by a tensor total variation regularization. (3) The images from the full spectrum are much better than the ErCT images with respect to noise variance and structural details and serve as external information to improve the reconstruction performance. We then develop an alternating direction method of multipliers algorithm to numerically solve the presented FSTensor method. We further utilize a genetic algorithm to tackle the parameter selection in ErCT reconstruction, instead of manually determining parameters. Simulation, preclinical and synthesized clinical ErCT results demonstrate that the presented FSTensor method leads to significant improvements over the filtered back-projection, robust principal component analysis, tensor-based dictionary learning and low-rank tensor decomposition with spatial-temporal total variation methods.

Multi-channel EEG epileptic spike detection by a new method of tensor decomposition

Objective. Epilepsy is one of the most common brain disorders. For epilepsy diagnosis or treatment, the neurologist needs to observe epileptic spikes from electroencephalography (EEG) data. Since multi-channel EEG records can be naturally represented by multi-way tensors, it is of interest to see whether tensor decomposition is able to analyze EEG epileptic spikes. Approach. In this paper, we first proposed the problem of simultaneous multilinear low-rank approximation of tensors (SMLRAT) and proved that SMLRAT can obtain local optimum solutions by using two well-known tensor decomposition algorithms (HOSVD and Tucker-ALS). Second, we presented a new system for automatic epileptic spike detection based on SMLRAT. Main results. We propose to formulate the problem of feature extraction from a set of EEG segments, represented by tensors, as the SMLRAT problem. Efficient EEG features were obtained, based on estimating the ‘eigenspikes’ derived from nonnegative GSMLRAT. We compared the proposed tensor analysis method with other common tensor methods in analyzing EEG signal and compared the proposed feature extraction method with the state-of-the-art methods. Experimental results indicated that our proposed method is able to detect epileptic spikes with high accuracy. Significance. Our method, for the first time, makes a step forward for automatic detection EEG epileptic spikes based on tensor decomposition. The method can provide a practical solution to distinguish epileptic spikes from artifacts in real-life EEG datasets.

Investigations of physical aspects of spinel ABi2O4 (A=Zn, Cd) oxides via ab-initio calculations

This present study aims to unravel physical properties of spinel oxides in cubic phase represented by general empirical formula of ABi2O4 (A=Zn, Cd) using full potential lineralized augmented plane plus local orbital (LAPW+lo) method. The structural aspect of spinel oxides in cubic phase has been investigated by Perdew-Burke-Ernzerhof generalized gradient approximation (PBEsol-GGA). The thermodynamic stability of ABi2O4 is established by computing the cohesive energies. On the other hand, born stability standard which is based on Chapin's tensor analysis method revealed that the mechanical stability of the oxide compounds under considerations gives a stable cubic phase. For a better prediction of electronic and thermoelectric properties of these compounds, the modified Tran-Bhala Becke and Johnson (TB-mBJ) potential is used which revels very precise band gap. Other than these investigations, thermoelectric characteristics i.e., Wiedman-Tranz constant, Seebeck coefficient and power factor are calculated and it provides essential data for fabrication of thermoelectric devices.

A new method for establishing motion equations in nonholonomic systems

In this paper, we present a new method of establishing the fundamental motion equations of nonholonomic systems without using any variational principles. According to the invariance of motion equations under the generalized coordinates transformation and the nonholonomic constraint function groups transformation, the double index tensor analysis method is proposed cooperating with the product rules of matrix. Then we let first integrals equivalent to the corresponding nonholonomic constraints imposed upon the system to explain the self consistency of nonholonomic systems, it is shown that the self consistency is the core of nonholonomic mechanics and can verify which model is appropriate for describing nonholonomic systems. Therefore, the form of nonholonomic constraint force is determined only by three qualities: the invariance of the motion equations under the constraint of first integrals, the invariance of nonholonomic constraint force under the generalized coordinates transformation and the nonholonomic constraint function groups transformation, to establish the fundamental motion equation of nonholonomic systems. Using the double index tensor analysis method, the three qualities and the Moore-Penrose generalized inverse of matrix theory, the equation of motion of nonholonomic systems are derived. Some classical equations in nonholonomic systems, such as the Routh equation, the Nielsen equation and the Chaplygin equation are also derived to prove our method. The method is totally based on the self consistency of nonholonomic systems and the covariation of motion equations, these two characters are naturally derived from mathematical and mechanical requirements of nonholonomic systems. Not only does not use any transcendental variational principles, such as D’Alembert-Lagrange principle, Gauss principle or Jourdian principle, but also illustrate that the validity of the three principles are attributed to the two characters. Further more, this method even provides a reasonable explanation for Chetaev conditions in nonholonomic systems, and shows that the vakonomic mechanics derived by Hamilton’s principle is not an appropriate model for nonholonomic systems.

Helical symmetric solution of 3d Navier-Stokes equations arising from geometric shape of the boundary

In this article, we investigate three-dimensional solution with helical symmetry in a gap between two concentric rotating cylinders, inside is a helicoidal surface (screw propeller) while outside is a cylindrical surface. Establish the partial differential equations and its variational formulation satisfied by a helical solution in a helical coordinate system using tensor analysis method, we provide a computational method for the power and propulsion of the screw. The existence and uniqueness of weak helical solutions are proved.

TDRM: tensor-based data representation and mining for healthcare data in cloud computing environments

Big data analytics proved to be one of the most influential forces in today’s competitive business environments due to its ability to generate new insights by processing a large volume and variety of data. Storing as well as mining these datasets is one of the primary challenges of the big data era. If data are stored in a well-defined pattern, then its updation mining and deletion processes become easy. In this paper, granular computing concept is used to store heterogeneous data in the format of tensor. A multi-dimensional matrix, also known as tensor, stores data in the raw format, and then, raw tensor is replicated to multiple tensors of different abstraction levels based on concept hierarchy of each attribute. Mathematical foundation of tensor formation and query processing are developed. The proposed method is successful in creating tensors of a diabetes dataset proving its applicability. The proposed system provides faster computation, low response time, better privacy and high relevancy as compared to baseline PARAFAC2 and CANDELINC tensor analysis method when run on Microsoft Azure cloud infrastructure. Different levels of information granules in the form of tensors make data storage and its query processing effective.

Tensor-Based Shot Boundary Detection in Video Streams

This paper presents a method for content change detection in multidimensional video signals. Video frames are represented as tensors of order consistent with signal dimensions. The method operates on unprocessed signals and no special feature extraction is assumed. The dynamic tensor analysis method is used to build a tensor model from the stream. Each new datum in the stream is then compared to the model with the proposed concept drift detector. If it fits, then a model is updated. Otherwise, a model is rebuilt, starting from that datum, and the signal shot is recorded. The proposed fast tensor decomposition algorithm allows efficient operation compared to the standard tensor decomposition method. Experimental results show many useful properties of the method, as well as its potential further extensions and applications.

A QTAIM and stress tensor investigation of the torsion path of a light-driven fluorene molecular rotary motor.

The utility of the QTAIM/stress tensor analysis method for characterizing the photoisomerization of light driven molecular rotary machines is investigated on the example of the torsion path in fluorene molecular motor. The scalar and vector descriptors of QTAIM/stress tensor reveal additional information on the bonding interactions between the rotating units of the motor, which cannot be obtained from the analysis of the ground and excited state potential energy surfaces. The topological features of the fluorene motor molecular graph display that, upon the photoexcitation a certain increase in the torsional stiffness of the rotating bond can be attributed to the increasing topological stability of the rotor carbon atom attached to the rotation axle. The established variations in the torsional stiffness of the rotating bond may cause transfer of certain fraction of the torsional energy to other internal degrees of freedom, such as the pyramidalization distortion. © 2016 Wiley Periodicals, Inc.

3-D Elastic-Plastic Constitutive Relationship of Mixed Hardening

In finite element calculation of plastic mechanics, isotropic hardening model, kinematic hardening model and mixed hardening model have their advantages and disadvantages as well as applicability area. In this paper, by use of the tensor analysis method and mixed hardening theory in plastic mechanics, the constitutive relation of 3-D mixed hardening problem is derived in detail based on the plane mixed hardening. Numerical results show that, the proposed 3-D mixed hardening constitutive relation agrees well with the test results in existing references, and can be used in the 3-D elastic-plastic finite element analysis.

Feature fusion of palmprint and face via tensor analysis and curvelet transform

AbstractIn order to improve the recognition accuracy of the unimodal biometric system and to address the problem of the small samples recognition, a multimodal biometric recognition approach based on feature fusion level and curve tensor is proposed in this paper. The curve tensor approach is an extension of the tensor analysis method based on curvelet coefficients space. We use two kinds of biometrics: palmprint recognition and face recognition. All image features are extracted by using the curve tensor algorithm and then the normalized features are combined at the feature fusion level by using several fusion strategies. The k-nearest neighbour (KNN) classifier is used to determine the final biometric classification. The experimental results demonstrate that the proposed approach outperforms the unimodal solution and the proposed nearly Gaussian fusion (NGF) strategy has a better performance than other fusion rules.

Constitutive Model of Viscous-Elastic Polymer Solution in Porous Media

The rheological behavior of viscous-elastic polymer solution in porous media of an oil reservoir is different from that in the shearing rheometer. Its flowing complexity lies in not only the complication of polymer's molecular structure and character but also in the change of the physicochemical effect between formation and polymer in space and time, which make it difficult to describe rheological behavior of viscous-elastic polymer solution in porous media. Based on the analysis of viscous-elastic polymer solution flowing in a throat of porous media, the flowing process is divided into three stages as entrance constriction, pore passage, and extrusion. Accordingly, the pressure drop in every stage is separated into viscous drop and elastic drop. Pressure expressions of every stage are established with a tensor analysis method in consideration of such factors as pseudoplasticity, elastic properties, elastic recovery characteristics, pore throat ratio, porosity, and other characteristics. As a result, the constitutive model of viscous-elastic solution in the porous media is established, which is examined and analyzed by a shearing and rheological experiment and a displacement experiment.

Estimation of Entry Pressure Drop during Conical Die Flow of Carbon Black-Filled Rubber Compound

The flow behavior of polymer melts in a conical die extrusion was discussed in the present paper. On the basis of simplified suppositions, a mathematical model for estimation of entry pressure drop was established by using a tensor analysis method. The rheological properties of rubber compound, such as flow curves, viscosity, entry pressure drop, and extrudate swell, were measured by employing a capillary rheometer in a temperature range of 90–130° C and apparent shear rates varied from 50 to 103 s-1. It was found that the shear flow for the sample obeyed the Power law, and the first normal stress difference increased with increasing shear rates at the channel wall as an exponential function. Furthermore, the entry pressure drop during extrusion of the samples was estimated by using this model. The results showed that the predictions of entry pressure drop were basically consistent with the measured data from the experiments of the sample.

Fractional Fourier transform for partially coherent beam in spatial-frequency domain

By using Fourier transform and the tensor analysis method, the fractional Fourier transform (FRT) in the spatial-frequency domain for partially coherent beams is derived. Based on the FRT in the spatial-frequency domain, an analytical transform formula is derived for a partially coherent twisted anisotropic Gaussian–Schell model (GSM) beam passing through the FRT system. The connections between the FRT formula and the generalized diffraction integral formulae for partially coherent beams through an aligned optical system and a misaligned optical system in the spatial-frequency domain are discussed, separately. By using the derived formula, the intensity distribution of partially coherent twisted anisotropic GSM beams in the FRT plane are studied in detail. The formula derived provide a convenient tool for analysing and calculating the FRTs of the partially coherent beams in spatial-frequency domain.

Predication of critical distance of wall‐slip phenomenon during extrusion of carbon black‐filled natural rubber/cis‐polybutadiene rubber compound

AbstractThe wall‐slip phenomenon during extrusion of polymer fluids is an important characteristic of viscoelasticity. The wall‐slip behavior and the factors affecting it for natural rubber (NR)/cis‐polybutadiene rubber (BR) filled with carbon black compound were investigated by using a Monsanto processability tester in a temperature range of 90–130°C and at shear rates that varied from 50 to 103 s−1. Under simplified supposition conditions, a mathematical model for description of the relationship between pressure variation, polymeric properties, and extrusion operation parameters when wall‐slip phenomenon occurs was established by using a tensor analysis method. On the basis of this model, an equation for estimation of critical slip distance (or position) was derived. The results showed that the measured critical pressure drop, when wall‐slip begins to occur, was consistent with the theoretical predictions. The wall‐slip phenomenon of the sample happened near the exit of the die. © 2004 Wiley Periodicals, Inc. J Appl Polym Sci 91: 3239–3243, 2004

Pressure losses during the annular conical die flow of a rubber compound

The flow behavior of polymer melts in an annular conical extrusion die is discussed in the present paper. Annular die extrusion is a common way of producing tube-like products in polymer processing but the rheological behavior of polymer fluids during extrusion is relatively complex. On the basis of simplified suppositions, a mathematical model for estimation of the pressure drop during the die flow of polymer melts was established by a using tensor analysis method. The flow properties during extrusion of rubber compound were investigated by using a capillary rheometer in a temperature range of 85–110°C and apparent shear rates varied from 50 to 10 3 s −1. It was found that the sample shear flow obeyed roughly the power law. The pressure drop of the sample flowing in an annular conical die installed in an industrial screw-extruder was measured at the same extrusion operation conditions. The results showed that calculations from the mathematical model were approximately consistent with the measured pressure drop data from the experiments.

Propagation of Optical Pulses and Pulsed Beams in theFrequency Domain

The diffraction integral formulae in the temporal andspatial-temporal frequency domains are derived by using a Fourier transformand tensor analysis method. Based on these formulae, the abcd law in thetemporal frequency domain and the tensor ABCD law in the four-dimensionalspatial-temporal frequency domain are derived. An application example of thederived formulae is provided.

Collins formula and tensor ABCD law in spatial-frequency domain

The Collins formula in spatial-frequency domain is generalized into axially nonsymmetrical optical systems by means of tensor analysis method. Based on this formula, the tensor ABCD law in spatial-frequency domain is derived, which governs the transformation of angular spectrum through axially nonsymmetrical optical systems. The spatial-frequency domain tensor ABCD law is a complement to spatial domain tensor ABCD law. An application example is provided.

A tensor analysis method for estimating 3-D motion parameters

By using the center projection image sequence to estimate 3-D motion parameters, one needs to know the corresponding relationship between the feature of motion object in space and the projection coordinate on image plane. In order to avoid using the relationship of feature correspondence, the tensor analysis method in the affine transformation system is presented, and the simulation data of experimental results are given.