Tensor Form Research Articles

On the magneto-mechanical response of piezomagnetic microbeam with size effects

Classical piezomagnetic elasticity theory fails to explain the size-dependent magneto-mechanical behaviour. The extended piezomagnetic elasticity theory incorporating the strain gradient elasticity and flexomagneticity is developed to describe the size effects phenomenon. Compared with the flexomagneticity whose contribution is explicit, the influence mechanism of strain gradient elasticity on the magneto-mechanical response is not clarified. In this paper, we clarify the relation and difference among the extended piezomagnetic elasticity theory considering different strain gradient elasticity. For the relation analysis, according to the orthogonal decomposition of the general strain gradient elasticity, we express the extended piezomagnetic elasticity theory in form of strain gradient tensor and its components of symmetric/anti-symmetric splitting, respectively. By ignoring some strain gradients, the extended piezomagnetic elasticity theory with the general strain gradient elasticity can reduce to that with the reduced strain gradient elasticity. For the difference analysis, we perform the magneto-mechanical analysis of the Terfenol-D/Silicon bilayer microbeam. The flexomagnetic coefficient of Terfenol-D is obtained by fitting deflection solution with experiment results. Then, the size-dependent direct/inverse magneto-mechanical behaviour is revealed. Results reveal that the strain gradient effects and flexomagnetic effects significantly affect the magnetic potential and bending defection when the beam thickness is comparable to the material length-scale parameters. Moreover, compared with the extended piezomagnetic elasticity theory with the reduced strain gradient elasticity, the extended piezomagnetic elasticity theory with the general strain gradient elasticity predicts smaller magnetic potential, bending deflection, and thus can describe the magneto-mechanical behaviour more appropriately.

Nonequilibrium thermodynamic modeling of case II diffusion in glassy polymers

In this article, we formulate a nonequilibrium thermodynamic theory for case II diffusion in a glassy polymer. In the model, we integrate the three-dimensional elasto-visco-plasticity of a glassy polymer, the Flory-Rehner theory for polymer network swelling, and the kinetics law for solvent migration with the concentration-dependent diffusivity. Our theory is given in a general 3D tensorial form, which, therefore, can be used to model case II diffusion in glassy polymers with arbitrary geometries and under different mechano-chemical loading conditions. An intrinsic length determined by the combination of the polymer viscosity and solvent diffusivity arises from the theory, which dictates the size-dependent case II diffusion in glassy polymers. The theory developed in the article may provide important guidance for designing semi-permeable membranes, waterproof coating, and drug-delivery systems, where case II diffusion can commonly occur.

UNMF: a unified nonnegative matrix factorization for multi-dimensional omics data.

Factor analysis, ranging from principal component analysis to nonnegative matrix factorization, represents a foremost approach in analyzing multi-dimensional data to extract valuable patterns, and is increasingly being applied in the context of multi-dimensional omics datasets represented in tensor form. However, traditional analytical methods are heavily dependent on the format and structure of the data itself, and if these change even slightly, the analyst must change their data analysis strategy and techniques and spend a considerable amount of time on data preprocessing. Additionally, many traditional methods cannot be applied as-is in the presence of missing values in the data. We present a new statistical framework, unified nonnegative matrix factorization (UNMF), for finding informative patterns in messy biological data sets. UNMF is designed for tidy data format and structure, making data analysis easier and simplifying the development of data analysis tools. UNMF can handle a wide range of data structures and formats, and works seamlessly with tensor data including missing observations and repeated measurements. The usefulness of UNMF is demonstrated through its application to several multi-dimensional omics data, offering user-friendly and unified features for analysis and integration. Its application holds great potential for the life science community. UNMF is implemented with R and is available from GitHub (https://github.com/abikoushi/moltenNMF).

A tensor formalism for multilayer network centrality measures using the Einstein product

Complex systems that consist of diverse kinds of entities that interact in different ways can be modeled by multilayer networks. This paper uses the tensor formalism with the Einstein product to model this type of networks. Several centrality measures, that are well known for single-layer networks, are extended to multilayer networks using tensors and their properties are investigated. In particular, subgraph centrality based on the exponential and resolvent of a tensor are considered. Krylov subspace methods based on the tensor format are introduced for computing approximations of different measures for large multilayer networks.

Comparative analysis of dynamic stability of cylindrical and conical shells under periodic axial compression

A comparative analysis of the dynamic stability of cylindrical and conical shells with the same geometric and mechanical characteristics under periodic uniformly distributed axial compression was presented. The study of the stability of steady periodic vibrations of thin elastic shells was based on the joint use of the method of curvilinear grids, the projection method and the parameter continuation method combined with the Newton–Kantorovich method. Geometrically nonlinear relations of the thin elastic shells theory are formulated on the basis of the vector approximation of the displacements function in the general curvilinear coordinate system in tensor form and satisfy the Kirchhoff-Love hypothesis. The discretization of the differential equations of the steady forced vibrations in the direction of the generating shells using the method of curvilinear grids was carried out. The components of the elements displacement vectors of the shells middle surface in the circular directionare approximated by trigonometric series. Reduction of the number of generalized coordinates of the discrete dynamic model of shells steady forced vibrations was performed by the Bubnov-Galerkin basis reduction method. A transition from vector ordinary differential equations to a nonlinear system of algebraic equations was made. The construction of a mathematical model of the dynamic stability of steady forced nonlinear vibrations of thin elastic shells was performed according to Floquet's theory using the projection method. The criterion for the loss of stability was the equality to zero of the determinant of the matrix of linearized equations of steady forced nonlinear vibrations of shells according to the Lyapunov theorem. A comparative analysis of frequencies and modes of natural vibrations of cylindrical and conical shells with the same geometric and mechanical characteristics and boundary conditions was performed. Nonlinear steady vibrations of the shells due to periodic axial compression were studied. The critical values of the dynamic load and the corresponding forms of loss of shell stability in the range of lower frequencies of their natural vibrations were obtained.

Parity-odd 3-point functions from CFT in momentum space and the chiral anomaly

We illustrate how the Conformal Ward Identities (CWI) in momentum space for parity-odd correlators determine the structure of a chiral anomaly interaction, taking the example of the VVA (vector/vector/axial-vector) and AAA correlators in momentum space. Only the conservation and the anomalous WIs, together with the Bose symmetry, are imposed from the outset for the determination of the correlators. We use a longitudinal/transverse decomposition of tensor structures and form factors. The longitudinal (L) component is fixed by the anomaly content and the anomaly pole, while in the transverse (T) sector we define a new parameterization. We relate the latter both to the Rosenberg original representation of the VVA and to the longitudinal/transverse (L/T) one, first introduced in the analysis of g-2 of the muon in the investigation of the diagram in the chiral limit of QCD. The correlators are completely identified by the conformal constraints whose solutions are fixed only by the anomaly coefficient, the residue of the anomaly pole. In both cases, our CFT result matches the one-loop perturbative expression, as expected. The CWIs for correlators of mixed chirality J_L J J_R generate solutions in agreement with the all-orders nonrenormalization theorems of perturbative QCD and in the chiral limit.

Computation of minimal covariants bases for 2D coupled constitutive laws

We produce minimal integrity bases for both isotropic and hemitropic invariant algebras (and more generally covariant algebras) of most common bidimensional constitutive tensors and — possibly coupled — laws, including piezoelectricity law, photoelasticity, Eshelby and elasticity tensors, complex viscoelasticity tensor, Hill elasto-plasticity, and (totally symmetric) fabric tensors up to twelfth-order. The concept of covariant, which extends that of invariant is explained and motivated. It appears to be much more useful for applications. All the tools required to obtain these results are explained in detail and a cleaning algorithm is formulated to achieve minimality in the isotropic case. The invariants and covariants are first expressed in complex forms and then in tensorial forms, thanks to explicit translation formulas which are provided. The proposed approach also applies to any n-uplet of bidimensional constitutive tensors.

Methodological platform for determining energy efficiency indicators of a complex system

The correct determination of the energy efficiency (EE) of a complex system is a problematic task that requires the use of specialized methods and approaches. Most often, EE is considered as an indicator of the quality-of-service provision, which most fully corresponds to the technical and economic essence of this indicator. The structural and functional organization of the system of such indicators is carried out either on a bottom-up approach or a top-down approach, gradually deploying macroeconomic indicators defined at the system levels. This paper considers the tensor form of organization of the system of such indicators, which allows combining within a single model not only their organizational levels (economy as a whole, economic sectors, enterprises, technologies and equipment), but also the types of activities that reflect these indicators (energy, financial, economic, institutional, environmental, social, etc.), and the factors of changes in energy use (structural, technological, resource, managerial, regulatory, etc.). The paper presents the mapping of this model on the plane of structural and functional factors in the form of classification tables (matrices) of these factors (system elements). The paper describes the procedure for optimizing indicators, which can be carried out for each of these factors separately, their aggregate at each level and for the system as a whole, taking into account the need to implement iterative procedures for coordinating the global (system-wide) goal and local objective functions. Given the use of optimization variables measured in energy and monetary units, this problem is formalized within the framework of the set-theoretic approach. For the purpose of comparing the results, the paper examines the relevant provisions of the International Energy Agency methodology, which uses the direct method of three-factor Laspeyres decomposition analysis, and the Sectoral Methodology for Calculating Harmful Emissions of the Ministry for Communities and Territories Development of Ukraine. Keywords: Energy efficiency, energy efficiency indicators, system analysis, tensor approach.

Quantum field corrections of the equation of state in cosmological space-time

A proper quantum statistical field theory framework for the decoupling of the cosmological plasma in curved space-time implies the appearance of corrections to the classical kinetic form of the stress-energy tensor of freely streaming particles. Such quantum corrections can become relevant even at long times after the decoupling and can significantly modify the relation between energy density and pressure, that is the equation of state.

Elastic degradation models for the micromorphic continuum

Numerous applications of generalized continua theories have been proposed mainly due to their regularization properties when applied to strain localization problems. This characteristic is directly correlated to the nonlocal feature of generalized media, wherein the material microstructural behavior is incorporated into the continuum formulation. The micromorphic theory poses as the most general theory in this class of generalized theories through the consideration of nine additional degrees of freedom embedded in each material particle. In order to allow the application of the micromorphic theory associated to damage models, extending its regularization properties to different constitutive models, this work presents an extension of classical elastic-degrading damage models for the micromorphic theory focused on scalar-isotropic models. To guarantee conformity to a constitutive models framework implemented for the classical continuum, a compact tensorial formulation is proposed, allowing the application, for the micromorphic theory, of theoretical and numerical resources already defined for the classical theory. A homogenization strategy is also employed to obtain the micromorphic constitutive relations through the consideration of a Cauchy continuum in the microscale, allowing nonlinear analysis of micromorphic media with only the definition of the material parameters of the classical continuum.

Symmetry analysis of charmonium two-body decay

In the light of SU(3) flavor symmetry, the effective interaction Hamiltonian in tensor form is obtained by virtue of group representation theory. The strong and electromagnetic breaking effects are treated as a spurion octet so that the flavor singlet principle can be utilized as the criterion to determine the form of effective Hamiltonian. Two body decays of both baryonic and mesonic final states are parameterized in the uniform scheme, based on which the relative phase between the strong and electromagnetic amplitudes is studied for various charmonium decay modes, including psi' and/or J/jpsi decay to octet baryon pair, decuplet baryon pair, decuplet-octet baryon final state, and pseudoscalar-pseudoscalar meson final state. In data analysis of samples taken in $e^+e^-$ collider, the details of experimental effects, such as energy spread and initial state radiative correction are taken into consideration in order to make full use of experimental information and acquire the accurate and delicate results.

Dielectrophoretic Colloidal Levitation by Electrode Polarization in Oscillating Electric Fields

Controlled colloidal levitation is key to many applications. Recently, it was discovered that polymer microspheres were levitated to a few micrometers in aqueous solutions in alternating current (AC) electric fields. A few mechanisms have been proposed to explain this AC levitation such as electrohydrodynamic flows, asymmetric rectified electric fields, and aperiodic electrodiffusiophoresis. Here, we propose an alternative mechanism based on dielectrophoresis in a spatially inhomogeneous electric field gradient extending from the electrode surface micrometers into the bulk. This field gradient is derived from electrode polarization, where counterions accumulate near electrode surfaces. A dielectric microparticle is then levitated from the electrode surface to a height where the dielectrophoretic lift balances gravity. The dielectrophoretic levitation mechanism is supported by two numerical models. One model assumes point dipoles and solves for the Poisson-Nernst-Planck equations, while the second model incorporates a dielectric sphere of a realistic size and permittivity and uses the Maxwell-stress tensor formulation to solve for the electrical body force. In addition to proposing a plausible levitation mechanism, we further demonstrate that AC colloidal levitation can be used to move synthetic microswimmers to controlled heights. This study sheds light on understanding the dynamics of colloidal particles near an electrode and paves the way to using AC levitation to manipulate colloidal particles, active or passive.

On conformally flat affine hypersurfaces with pseudo-parallel cubic form

In this paper, we study locally strongly convex affine hypersurfaces with vanishing Weyl curvature tensor and semi-parallel cubic form relative to the Levi-Civita connection of affine metric. As the main result, we classify such hypersurfaces being not of flat affine metric. In particular, $2, 3$-dimensional locally strongly convex affine hypersurfaces with semi-parallel cubic form are completely determined.

Dispersion‐type Anisotropic Viscoelasticity: Model Validation for Myocardium

AbstractThis contribution presents a novel constitutive model for rate‐dependent response of the passive myocardium. As a first step, we performed a comparative study on dispersion‐type anisotropic hyperelastic constitutive models [1–3] and assessed performance of various density distribution functions by fitting to experiments conducted on three distinct tissues [4]. Next, we proposed an angular integration type anisotropic viscoelastic constitutive model that uses bivariate von‐Mises distribution function to capture fiber dispersion in passive myocardium. The baseline hyperelasticity is described by a generalized structure tensor formulation proposed by GASSER ET AL. [1]. The non‐equilibrium part of the model utilizes a quadratic free energy function in the logarithmic strain space and a power‐type nonlinear evolution equation in orientation directions. The overstress response is then obtained by the numerical integration over the unit sphere by making use of 21 quadrature points. The proposed model parameters are obtained from cyclic triaxial shear and triaxial shear relaxation experiments on human passive myocardium [5].

On the Geometry of Tangent Bundle and Unit Tangent Bundle with Deformed-Sasaki Metric

Let $(M^{m}, g)$ be a Riemannian manifold and $TM$ its tangent bundle equipped with a deformed Sasaki metric. In this paper, firstly we investigate all forms of Riemannian curvature tensors of $TM$ (Riemannian curvature tensor, Ricci curvature, sectional curvature and scalar curvature). Secondly, we study the geometry of unit tangent bundle equipped with a deformed Sasaki metric, where we presented the formulas of the Levi-Civita connection and also all formulas of the Riemannian curvature tensors of this metric.

ShipHullGAN: A generic parametric modeller for ship hull design using deep convolutional generative model

In this work, we introduce ShipHullGAN, a generic parametric modeller built using deep convolutional generative adversarial networks (GANs) for the versatile representation and generation of ship hulls. At a high level, the new model intends to address the current conservatism in the parametric ship design paradigm, where parametric modellers can only handle a particular ship type. We trained ShipHullGAN on a large dataset of 52,591 physically validated designs from a wide range of existing ship types, including container ships, tankers, bulk carriers, tugboats, and crew supply vessels. We developed a new shape extraction and representation strategy to convert all training designs into a common geometric representation of the same resolution, as typically GANs can only accept vectors of fixed dimension as input. A space-filling layer is placed right after the generator component to ensure that the trained generator can cover all design classes. During training, designs are provided in the form of a shape-signature tensor (SST) which harnesses the compact geometric representation using geometric moments that further enable the inexpensive incorporation of physics-informed elements in ship design. We have shown through extensive comparative studies and optimisation cases that ShipHullGAN can generate designs with augmented features resulting in versatile design spaces that produce traditional and novel designs with geometrically valid and practically feasible shapes.Video abstract: https://youtu.be/LT9Z52vBgzI

TR-ReFloc: A TR-based Framework for Recovering Missed RSS for WiFi indoor positioning in the offline and online phase

The research on WiFi-based fingerprint positioning has become an important topic in the field of indoor positioning due to its low-cost deployment and widespread applications. However, received signal strength (RSS) from access points (APs) may be missed due to factors such as Green WiFi or AP malfunctions. Traditional approach often set the missed RSS to a predetermined default value, which may not be accurate. We propose a fingerprint recovery framework based on tensor-ring nuclear norm minimization (TRNNM) algorithm which uses the correlation of RSS to recover missed fingerprints in both offline and online phases, called TR-ReFloc. In the offline phase, the radio map in tensor form is recovered by tensor ring (TR) decomposition. In the online phase, depending on different user requirements, there are two stages to generate the positioning results. First, rapid results are generated in coarse positioning stage. Next, high-precision results generated in fine positioning stage by recovering the missed fingerprints using the correlation of test points (TPs) are closed to the current TP. Experiments demonstrate that the proposed framework is robust for recovering missed RSS and can maintain localization accuracy within 2 m even in cases of high missing rate, demonstrating significant improvement over traditional methods.

Tensor form of GPBiCG algorithm for solving the generalized Sylvester quaternion tensor equations

Sylvester quaternion tensor equations have a wide range of applications in image processing and system and control theory. In this paper, by the Kronecker product and vectorization operator and the properties of quaternion tensors, we focus mainly on proposing the tensor form of the generalized product-type biconjugate gradient method for solving generalized Sylvester quaternion tensor equations. As an application, we apply the proposed method to restore a blurred and noisy-free color video. The obtained numerical results illustrate the effectiveness of our method compared with some existing methods.

An artificial neural network based system for wave height prediction

ABSTRACT We present a system for predicting the hourly significant wave height at a specific wave measurement station in the middle of Israel’s Mediterranean coast (Hadera). Our system uses an artificial neural network (ANN) composed of two sub-networks. We evaluate the importance of different inputs to the system. The input includes wind forecast data from the SKIRON atmospheric modeling system, wave forecast for the station’s location given by the SWAN wave model, and observed wave data. Our system pre-processes the wind data using a spatial filtering scheme and then enters it into the first sub-network in the form of a multidimensional tensor. We take special care to interconnect the tensor elements through a dimensional permutation that leads the ANN to sum elements along all the tensor’s dimensions. Our system groups the output of the first sub-network with the rest of the input and feeds it to the second sub-network that gives the prediction. Our ANN system outperforms the SWAN wave model in estimating wave heights over 1.5 meters. We obtain the best performance when either all input components are used or just wind and observations. Reimplementation of the system at Ashkelon yields smaller improvements due to insufficient training data.

Codazzi tensors and their space-times and Cotton gravity

We study the geometric properties of certain Codazzi tensors for their own sake, and for their appearance in the recent theory of Cotton gravity. We prove that a perfect-fluid tensor is Codazzi if and only if the metric is a generalized Stephani universe. A trace condition restricts it to a warped space-time, as proven by Merton and Derdziński. We also give necessary and sufficient conditions for a space-time to host a current-flow Codazzi tensor. In particular, we study the static and spherically symmetric cases, which include the Nariai and Bertotti-Robinson metrics. The latter are a special case of Yang Pure space-times, together with spatially flat FRW space-times with constant curvature scalar. We apply these results to the recent Cotton gravity by Harada. We show that the equation of Cotton gravity is Einstein’s equation modified by the presence of a Codazzi tensor, which can be chosen freely and constrains the space-time where the theory is staged. In doing so, the tensor (chosen in forms appropriate for physics) implies the form of the Ricci tensor. The two tensors specify the energy-momentum tensor, which is the source in the equation of Cotton gravity for the metric implied by the Codazzi tensor. For example, we show that the Stephani, Nariai and Bertotti-Robinson space-times are characterized by a “current flow” Codazzi tensor. Because of it, they solve Cotton gravity with physically sensible energy-momentum tensors. Finally, we discuss Cotton gravity in constant curvature space-times.