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The missing travel time data for roads is a common problem encountered by traffic management departments. Tensor decomposition, as one of the most widely used method for completing missing traffic data, plays a significant role in the intelligent transportation system (ITS). However, existing methods of tensor decomposition focus on the global data structure, resulting in relatively low accuracy in fibrosis missing scenarios. Therefore, this paper aims to propose a novel tensor decomposition model which further considers the local spatiotemporal similarity for fibrosis missing to improve travel time completion accuracy.

The proposed model can aggregate road sections with similar physical attributes by spatial clustering, and then it calculates the temporal association of road sections by the dynamic longest common subsequence. A similarity relationship matrix in the temporal dimension is constructed and incorporated into the tensor completion model, which can enhance the local spatiotemporal relationship of the missing parts of the fibrosis type.

The experiment shows that this method is superior and robust. Compared with other baseline models, this method has the smallest error and maintains good completion results despite high missing rates.

This model has higher accuracy for the fibrosis missing and performs good convergence effects in the case of the high missing rate.

Understanding the fluid flow through rock masses, which commonly consist of rock matrix and fractures, is a fundamental issue in many application areas of rock engineering. As the equivalent porous medium approach is the dominant approach for engineering applications, it is of great significance to estimate the equivalent permeability tensor of rock masses. This study aims to develop a novel numerical approach to estimate the equivalent permeability tensor for fractured porous rock masses.

The radial point interpolation method (RPIM) and finite element method (FEM) are coupled to simulate the seepage flow in fractured porous rock masses. The rock matrix is modeled by the RPIM, and the fractures are modeled explicitly by the FEM. A procedure for numerical experiments is then designed to determinate the equivalent permeability tensor directly on the basis of Darcy’s law.

The coupled RPIM-FEM method is a reliable numerical method to analyze the seepage flow in fractured porous rock masses, which can consider simultaneously the influences of fractures and rock matrix. As the meshes of rock matrix and fracture network are generated separately without considering the topology relationship between them, the mesh generation process can be greatly facilitated. Using the proposed procedure for numerical experiments, which is designed directly on the basis of Darcy’s law, the representative elementary volume and equivalent permeability tensor of fractured porous rock masses can be identified conveniently.

A novel numerical approach to estimate the equivalent permeability tensor for fractured porous rock masses is proposed. In the approach, the RPIM and FEM are coupled to simulate the seepage flow in fractured porous rock masses, and then a numerical experiment procedure directly based on Darcy’s law is introduced to estimate the equivalent permeability tensor.

In recent years, the partially averaged Navier–Stokes (PANS) methodology has earned acceptability as a viable scale-resolving bridging method of turbulence. To further enhance its capabilities, especially for simulating separated flows past bluff bodies, this paper aims to combine PANS with a non-linear eddy viscosity model (NLEVM).

The authors first extract a PANS closure model using the Shih’s quadratic eddy viscosity closure model [originally proposed for Reynolds-averaged Navier–Stokes (RANS) paradigm (Shih et al., 1993)]. Subsequently, they perform an extensive evaluation of the combination (PANS + NLEVM).

The NLEVM + PANS combination shows promising result in terms of reduction of the anisotropy tensor when the filter parameter (f_k) is reduced. Further, the influence of PANS filter parameter f on the magnitude and orientation of the non-linear part of the stress tensor is closely scrutinized. Evaluation of the NLEVM + PANS combination is subsequently performed for flow past a square cylinder at Reynolds number of 22,000. The results show that for the same level of reduction in f_k, the PANS + NLEVM methodology releases significantly more scales of motion and unsteadiness as compared to the traditional linear eddy viscosity model (LEVM) of Boussinesq (PANS + LEVM). The authors further demonstrate that with this enhanced ability the NLEVM + PANS combination shows much-improved predictions of almost all the mean quantities compared to those observed in simulations using LEVM + PANS.

Based on these results, the authors propose the NLEVM + PANS combination as a more potent methodology for reliable prediction of highly separated flow fields.

Combination of a quadratic eddy viscosity closure model with PANS framework for simulating flow past bluff bodies.

The purpose of this paper is to continue the path opened by previous researches that focused on the stress and deformation behaviour of discrete particle models, along with mechanical and morphological analyses.

This work presents a formulation that allows the study of discrete particle models as if they were continuum. By knowing forces, torques, displacements and rotations that occur inside a particle media whenever a force is loading it, this formulation permits to obtain the stress, the torque, strain and rotation tensors of the media.

These tensors are equivalent to the ones that would have been obtained by treating a discrete media as if it were a continuum. In addition, a procedure to apply the formulas to a numerical model has been detailed in the text. Finally, these formulas are compared to the one obtained from an energy balance approach to establish a connection between the forces and the increase of the energy produced inside the media.

This paper presents a proposal of formulation to calculate the stress, torque, deformation and curvature tensor for discrete particle medias, welded or non‐welded, in order to study them as if they were continuous.

The purpose of this paper is to present a novel registration method for augmented reality (AR) systems based on robust estimation of trifocal tensor using point and line correspondence simultaneously.

The proposed method distinguishes itself in following three ways: first, to establish the world coordinate system, the restriction that the four specified points must form an approximate square is relaxed, the only requirement is that these four points should not be collinear. Second, besides feature points, line segments are also used to calculate the needed trifocal tensors. The registration process can still be achieved even without the use of feature points. Third, to estimate trifocal tensors precisely, progressive sample consensus (PROSAC) is used instead of random sample consensus to remove outliers.

As shown in the experiments, the proposed method really enhances the usability of this system. To calculate trifocal tensor, a PROSAC based algebraic minimization algorithm is put forward which improves the accuracy and reduces the computation complexity.

In current system, it is stipulated that there is no large rotation of the user's head relative to the registration scenes, because the NCC will degrade when there is a large rotation between images.

A more robust feature matching strategy is needed. Treating feature matching as a classification problem may be a good choice.

This paper presents a novel registration approach for AR system.

Non‐linear reaction‐diffusion processes with cross‐diffusion in two‐dimensional, anisotropic media are analyzed by means of an implicit, iterative, time‐linearized approximate factorization technique as functions of the anisotropy of the heat and species diffusivity tensors, the Soret and Dufour cross‐diffusion effects, and five types of boundary conditions. It is shown that anisotropy and cross‐diffusion deform the reaction front and affect the front velocity, and the magnitude of these effects increases as the magnitude of the off‐diagonal components of the heat and species diffusivity tensors is increased. It is also shown that the five types of boundary conditions employed in this study produce similar results except when there is either strong anisotropy in the species or heat diffusivity tensors and there are no Soret and Dufour effects, or the species and heat diffusivity tensors are isotropic, but the anisotropy of the Soret and Dufour effects is important. If the species and heat diffusivity tensors are isotropic, the effects of either the Soret or the Dufour cross‐diffusion effects are small for the cases considered in this study. The time required to achieve steady state depends on the anisotropy of the heat and diffusivity tensors, the cross‐diffusion effects, and the boundary conditions.

The purpose of this paper is to study the Bertotti–Kasner space-time and its geometric properties.

This paper is based on the features of λ-tensor and the technique of six-dimensional formalism introduced by Pirani and followed by W. Borgiel, Z. Ahsan et al. and H.M. Manjunatha et al. This technique helps to describe both the geometric properties and the nature of the gravitational field of the space-times in the Segre characteristic.

The Gaussian curvature quantities specify the curvature of Bertotti–Kasner space-time. They are expressed in terms of invariants of the curvature tensor. The Petrov canonical form and the Weyl invariants have also been obtained.

The findings are revealed to be both physically and geometrically interesting for the description of the gravitational field of the cylindrical universe of Bertotti–Kasner type as far as the literature is concerned. Given the technique of six-dimensional formalism, the authors have defined the Weyl conformal λW-tensor and discussed the canonical form of the Weyl tensor and the Petrov scalars. To the best of the literature survey, this idea is found to be modern. The results deliver new insight into the geometry of the nonstatic cylindrical vacuum solution of Einstein's field equations.

The purposes of this research are to study the theory and method of multi-attribute index system design and establish a set of systematic, standardized, scientific index systems for the design optimization and inspection process. The research may form the basis for a rational, comprehensive evaluation and provide the most effective way of improving the quality of management decision-making. It is of practical significance to improve the rationality and reliability of the index system and provide standardized, scientific reference standards and theoretical guidance for the design and construction of the index system.

Using modern methods such as complex networks and machine learning, a system for the quality diagnosis of index data and the classification and stratification of index systems is designed. This guarantees the quality of the index data, realizes the scientific classification and stratification of the index system, reduces the subjectivity and randomness of the design of the index system, enhances its objectivity and rationality and lays a solid foundation for the optimal design of the index system.

Based on the ideas of statistics, system theory, machine learning and data mining, the focus in the present research is on “data quality diagnosis” and “index classification and stratification” and clarifying the classification standards and data quality characteristics of index data; a data-quality diagnosis system of “data review – data cleaning – data conversion – data inspection” is established. Using a decision tree, explanatory structural model, cluster analysis, K-means clustering and other methods, classification and hierarchical method system of indicators is designed to reduce the redundancy of indicator data and improve the quality of the data used. Finally, the scientific and standardized classification and hierarchical design of the index system can be realized.

The innovative contributions and research value of the paper are reflected in three aspects. First, a method system for index data quality diagnosis is designed, and multi-source data fusion technology is adopted to ensure the quality of multi-source, heterogeneous and mixed-frequency data of the index system. The second is to design a systematic quality-inspection process for missing data based on the systematic thinking of the whole and the individual. Aiming at the accuracy, reliability, and feasibility of the patched data, a quality-inspection method of patched data based on inversion thought and a unified representation method of data fusion based on a tensor model are proposed. The third is to use the modern method of unsupervised learning to classify and stratify the index system, which reduces the subjectivity and randomness of the design of the index system and enhances its objectivity and rationality.

In this paper, a new rate type endochronic constitutive model is introduced to describe deformations in the finite strain range. A new material dependent objective rate of Cauchy stress is suggested based on the general form of spin tensors, defining objective stress rates. The endochronic constitutive equations are extended using the concept of corotational stress rates and additive decomposition of deformation rate. The constitutive relations are specialized for thin‐walled tubes under torsion and a procedure for solving the ordinary differential equations for cases of simple and pure torsion is developed. The axial effects for various materials, subjected to simple and pure torsion, are simulated and compared with experimental data. The results clearly indicate that the new combined rate endochronic model can be effectively used to describe the behavior of material in the finite strain range.

The purpose of this paper is to study the statistics of thermal conductivity and resistivity tensors in two-phase random checkerboard microstructures at finite mesoscales.

Microstructures at finite scales are generated by randomly sampling an infinite checkerboard at 50 percent nominal fraction. Boundary conditions that stem from the Hill-Mandel homogenization condition are then applied as thermal loadings on these microstructures.

It is observed that the thermal response of the sampled microstructures is in general anisotropic at finite mesoscales. Based on 1,728 boundary value problems, the statistics of the tensor invariants (trace and determinant) are obtained as a function of material contrast, mesoscale and applied boundary conditions. The histograms as well as the moments (mean, variance, skewness and kurtosis) of the invariants are computed and discussed. A simple analytical form for the variance of the trace of mesoscale conductivity tensor is proposed as a function of individual phase conductivities and the mesoscale.

A rigorous methodology to determine the evolution of the invariants of thermal conductivity (and resistivity) tensors across a variety of length scales (microscale to macroscale) is presented. The objective is to enable setting up of constitutive equations applicable to heat conduction that are valid across all length scales.