scholarly journals Decomposition of third-order constitutive tensors

2021 ◽  
pp. 108128652110165
Author(s):  
Yakov Itin ◽  
Shulamit Reches
Keyword(s):  
Tensor Decomposition ◽  
Physical Parameters ◽  
Mathematical Tool ◽  
Solid State Physics ◽  
Third Order ◽  
Order Tensor ◽  
Algebraic Properties ◽  
Complete Set ◽  
Physical Quantities ◽  
Constitutive Tensor

Third-order tensors are widely used as a mathematical tool for modeling the physical properties of media in solid-state physics. In most cases, they arise as constitutive tensors of proportionality between basic physical quantities. The constitutive tensor can be considered the complete set of physical parameters of a medium. The algebraic features of the constitutive tensor can be used as a tool for proper identification of natural materials, such as crystals, and for designing artificial nanomaterials with prescribed properties. In this paper, we study the algebraic properties of a general asymmetric third-order tensor relative to its invariant decomposition. In correspondence with different groups acting on the basic vector space, we present the hierarchy of different types of tensor decomposition into invariant subtensors. In particular, we discuss the problem of non-uniqueness and reducibility of high-order tensor decomposition. For a general asymmetric third-order tensor, these features are described explicitly. In the case of special tensors with a prescribed symmetry, the decomposition is demonstrated to be irreducible and unique. We present the explicit results for two physically interesting models: the piezoelectric tensor as an example of pair symmetry and the Hall tensor as an example of pair skew-symmetry.

scholarly journals Tensor Decomposition of KUKA Industrial Robot (KR16-2) in Rotational System

2020 ◽  
Vol 9 (2) ◽  
pp. 688-690
Keyword(s):  
Rotational Motion ◽  
Industrial Robot ◽  
Matrix Decomposition ◽  
Tensor Decomposition ◽  
Tensor Model ◽  
Third Order ◽  
Order Tensor ◽  
The Third ◽  
Decomposition Model ◽  
The Matrix

This paper refers to study of industrial robot (KUKA KR16-2), in which we have considered the matrix decomposition and tensor decomposition model in rotational motion. We have considered robotic matrix & Tensor and defined a modal product between robot rotation matrix and a tensor Further we have proposed the third order tensor for the motion of Industrial robot and tried to find out the useful result. At last we have shown that the tensor model is providing alternate way to find the solution.

scholarly journals A Watermarking Scheme for Color Image Using Quaternion Discrete Fourier Transform and Tensor Decomposition

2021 ◽  
Vol 11 (11) ◽  
pp. 5006
Author(s):  
Li Li ◽  
Rui Bai ◽  
Jianfeng Lu ◽  
Shanqing Zhang ◽  
Ching-Chun Chang
Keyword(s):  
Fourier Transform ◽  
Discrete Fourier Transform ◽  
Color Image ◽  
Image Watermarking ◽  
Tensor Decomposition ◽  
Geometric Distortion ◽  
Support Vector ◽  
Third Order ◽  
Order Tensor ◽  
Watermarking Scheme

To protect the copyright of the color image, a color image watermarking scheme based on quaternion discrete Fourier transform (QDFT) and tensor decomposition (TD) is presented. Specifically, the cover image is partitioned into non-overlapping blocks, and then QDFT is performed on each image block. Then, the three imaginary frequency components of QDFT are used to construct a third-order tensor. The third-order tensor is decomposed by Tucker decomposition and generates a core tensor. Finally, an improved odd–even quantization technique is employed to embed a watermark in the core tensor. Moreover, pseudo-Zernike moments and multiple output least squares support vector regression (MLS–SVR) network model are used for geometric distortion correction in the watermark extraction stage. The scheme utilizes the inherent correlations among the three RGB channels of a color image, and spreads the watermark into the three channels. The experimental results indicate that the proposed scheme has better fidelity and stronger robustness for common image-processing and geometric attacks, can effectively resist each color channel exchange attack. Compared with the existing schemes, the presented scheme achieves better performance

scholarly journals Denoising of series electron holograms using tensor decomposition

Microscopy ◽  
2020 ◽  
Author(s):  
Yuki Nomura ◽  
Kazuo Yamamoto ◽  
Satoshi Anada ◽  
Tsukasa Hirayama ◽  
Emiko Igaki ◽  
...  
Keyword(s):  
Low Dose ◽  
Tensor Decomposition ◽  
Electron Holography ◽  
Third Order ◽  
Order Tensor ◽  
Fringe Contrast ◽  
Time Resolved ◽  
Accuracy And Precision ◽  
In Situ Experiments

Abstract In this study, a noise-reduction technique for series low-dose electron holograms using tensor decomposition is demonstrated through simulation. We treated an entire dataset of the series holograms with Poisson noise as a third-order tensor, which is a stack of 2D holograms. The third-order tensor, which is decomposed into a core tensor and three factor matrices, is approximated as a lower-rank tensor using only noise-free principal components. This technique is applied to simulated holograms by assuming a p-n junction in a semiconductor sample. The peak signal-to-noise ratios of the holograms and the reconstructed phase maps have been improved significantly using tensor decomposition. Moreover, the proposed method was applied to a more practical situation of time-resolved in situ electron holography by considering a nonuniform fringe contrast and fringe drift relative to the sample. The accuracy and precision of the reconstructed phase maps were quantitatively evaluated to demonstrate its effectiveness for in situ experiments and low-dose experiments on beam-sensitive materials.

Investigation of zirconium nanowire by elastic, thermal and ultrasonic analysis

2020 ◽  
Vol 75 (12) ◽  
pp. 1077-1084
Author(s):  
Bhawan Jyoti ◽  
Shakti Pratap Singh ◽  
Mohit Gupta ◽  
Sudhanshu Tripathi ◽  
Devraj Singh ◽  
...  
Keyword(s):  
Ultrasonic Attenuation ◽  
Thermal Relaxation ◽  
Coupling Constants ◽  
Physical Parameters ◽  
Third Order ◽  
Jones Potential ◽  
Acoustic Coupling ◽  
Anisotropic Factor ◽  
Third Order Elastic Constants ◽  
Ultrasonic Analysis

AbstractThe elastic, thermal and ultrasonic properties of zirconium nanowire (Zr-NW) have been investigated at room temperature. The second and third order elastic constants (SOECs and TOECs) of Zr-NW have been figured out using the Lennard–Jones Potential model. SOECs have been used to find out the Young’s modulus, bulk modulus, shear modulus, Poisson’s ratio, Pugh’s ratio, Zener anisotropic factor and ultrasonic velocities. Further these associated parameters of Zr-NW have been utilized for the evaluation of the Grüneisen parameters, thermal conductivity, thermal relaxation time, acoustic coupling constants and ultrasonic attenuation. On the basis of the above analyzed properties of Zr-NW, some characteristics features of the chosen nanowire connected with ultrasonic and thermo-physical parameters have been discussed.

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