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Journal articles on the topic 'Eigentensor'

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Author: Grafiati

Published: 10 March 2023

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1

Nikabadze, M. U. "Construction of eigentensor columns in the linear micropolar theory of elasticity." Moscow University Mechanics Bulletin 69, no. 1 (January 2014): 1–9. http://dx.doi.org/10.3103/s0027133014010014.

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2

Nikabadze, M. U. "On the eigenvalue and eigentensor problem for a tensor of even rank." Mechanics of Solids 43, no. 4 (August 2008): 586–99. http://dx.doi.org/10.3103/s0025654408040079.

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3

MARTÍNEZ-MORALES, JOSÉ L. "THE MASTER EQUATIONS IN THE EUCLIDEAN SCHWARZSCHILD–TANGHERLINI METRIC OF A SMALL STATIC PERTURBATION." International Journal of Modern Physics A 22, no. 06 (March 10, 2007): 1239–64. http://dx.doi.org/10.1142/s0217751x07036208.

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The master equations in the Euclidean Schwarzschild–Tangherlini space–time of a small static perturbation are studied. For each harmonic mode on the sphere there are two solutions that behave differently at infinity. One solution goes like the power 2-l-n of the radial variable, the other solution goes like the power l. These solutions occur in power series. The second main statement of the paper is that any eigentensor of the Lichnerowicz operator in a Euclidean Schwarzschild space–time with an eigenvalue different from zero is essentially singular at infinity. Possible applications of the stability of instantons are discussed. We present the analysis of a small static perturbation of the Euclidean Schwarzschild–Tangherlini metric tensor. The higher order perturbations will appear later. We determine independently the static perturbations of the Schwarzschild quantum black hole in dimension 1+n≥4, where the system of equations is reduced to master equations — ordinary differential equations. The solutions are hypergeometric functions which in some cases can be reduced to polynomials. In the same Schwarzschild background, we analyze static perturbations of the scalar mode and show that there does not exist any static perturbation that is regular everywhere outside the event horizon and is well-behaved at the spatial infinity. This confirms the uniqueness of the spherically symmetric static empty quantum black hole, within the perturbation framework. Our strategy for treating the stability problem is also applicable to other symmetric quantum black holes with a nonzero cosmological constant.

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4

Douglas, Stephen R. "Letter: Eigentensors of the Bel Tensor." General Relativity and Gravitation 31, no. 10 (October 1999): 1605–7. http://dx.doi.org/10.1023/a:1026738622165.

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5

MEHRABADI, MORTEZA M., and STEPHEN C. COWIN. "EIGENTENSORS OF LINEAR ANISOTROPIC ELASTIC MATERIALS." Quarterly Journal of Mechanics and Applied Mathematics 43, no. 1 (1990): 15–41. http://dx.doi.org/10.1093/qjmam/43.1.15.

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6

MEHRABADI, MORTEZA M., and STEPHEN C. COWIN. "EIGENTENSORS OF LINEAR ANISOTROPIC ELASTIC MATERIALS." Quarterly Journal of Mechanics and Applied Mathematics 44, no. 2 (1991): 331. http://dx.doi.org/10.1093/qjmam/44.2.331.

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7

Theocaris, Pericles S., and Dimitrios P. Sokolis. "Spectral decomposition of the linear elastic tensor for monoclinic symmetry." Acta Crystallographica Section A Foundations of Crystallography 55, no. 4 (July 1, 1999): 635–47. http://dx.doi.org/10.1107/s0108767398016766.

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The compliance fourth-rank tensor related to crystalline or other anisotropic media belonging to the monoclinic crystal system is spectrally decomposed for the first time, and its characteristic values and idempotent fourth-rank tensors are established. Further, it is proven that the idempotent tensors resolve the stress and strain second-rank tensors into eigentensors, thus giving rise to a decomposition of the total elastic strain-energy density into non-interacting strain-energy parts. Several examples of representative inorganic crystals of the monoclinic system illustrate the results of the theoretical analysis. It is also proven that the essential parameters required for a coordinate-invariant characterization of the elastic properties of a crystal exhibiting monoclinic symmetry are both the six characteristic values of the compliance tensor and seven dimensionless parameters. These material constants, referred to as the eigenangles, are shown to be accountable for the orientation of the stress and strain eigentensors, when represented in a stress coordinate system. Finally, the restrictions dictated by the classical thermodynamical argument on the elements of the compliance tensor, which are necessary and sufficient for the elastic strain-energy density to be positive definite, are investigated for the monoclinic symmetry.

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8

Martínez-Morales, J. L. "Eigentensors of the Lichnerowicz operator in Euclidean Schwarzschild metrics." Annalen der Physik 15, no. 9 (September 1, 2006): 653–62. http://dx.doi.org/10.1002/andp.200510184.

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9

François, Marc L. M. "A damage model based on Kelvin eigentensors and Curie principle." Mechanics of Materials 44 (January 2012): 23–34. http://dx.doi.org/10.1016/j.mechmat.2011.07.017.

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10

Martínez‐Morales, J. L. "Eigentensors of the Lichnerowicz operator in Euclidean Schwarzschild metrics ^*." Annalen der Physik 518, no. 9 (July 24, 2006): 653–62. http://dx.doi.org/10.1002/andp.20065180903.

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11

Boucetta, Mohamed. "Spectra and symmetric eigentensors of the Lichnerowicz Laplacian on Pn(C)." Journal of Geometry and Physics 60, no. 10 (October 2010): 1352–69. http://dx.doi.org/10.1016/j.geomphys.2010.04.013.

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12

Jiang, Huiyan, Di Zhao, Tianjiao Feng, Shiyang Liao, and Yenwei Chen. "Construction of Classifier Based on MPCA and QSA and Its Application on Classification of Pancreatic Diseases." Computational and Mathematical Methods in Medicine 2013 (2013): 1–7. http://dx.doi.org/10.1155/2013/713174.

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A novel method is proposed to establish the classifier which can classify the pancreatic images into normal or abnormal. Firstly, the brightness feature is used to construct high-order tensors, then using multilinear principal component analysis (MPCA) extracts the eigentensors, and finally, the classifier is constructed based on support vector machine (SVM) and the classifier parameters are optimized with quantum simulated annealing algorithm (QSA). In order to verify the effectiveness of the proposed algorithm, the normal SVM method has been chosen as comparing algorithm. The experimental results show that the proposed method can effectively extract the eigenfeatures and improve the classification accuracy of pancreatic images.

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13

Huang, Yong-nian. "The eigentensors of an arbitrary second-order tensor and their quality analyses." Applied Mathematics and Mechanics 22, no. 7 (July 2001): 776–80. http://dx.doi.org/10.1007/bf02438220.

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14

Theocaris, P. S., and D. P. Sokolis. "Linear elastic eigenstates of the compliance tensor for trigonal crystals." Zeitschrift für Kristallographie - Crystalline Materials 215, no. 1 (January 1, 2000): 1–9. http://dx.doi.org/10.1524/zkri.2000.215.1.01.

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The spectral decomposition of the compliance fourth-rank tensor, representative of a trigonal crystalline or other anisotropic medium, is offered in this paper, and its characteristic values and idempotent fourth-rank tensors are established, with respect to the Cartesian tensor components. Consequently, it is proven that the idempotent tensors serve to analyse the second-rank symmetric tensor space into orthogonal subspaces, resolving the stress and strain tensors for the trigonal medium into their eigentensors, and, finally, decomposing the total elastic strain energy density into distinct, autonomous components. Finally, bounds on the values of the compliance tensor components for the trigonal system, dictated by the classical thermodynamical argument for the elastic potential to be positive definite, are estimated by imposing the characteristic values of the compliance tensor to be strictly positive.

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15

Theocaris, Pericles S., and Dimitrios P. Sokolis. "Invariant elastic constants and eigentensors of orthorhombic, tetragonal, hexagonal and cubic crystalline media." Acta Crystallographica Section A Foundations of Crystallography 56, no. 4 (July 1, 2000): 319–31. http://dx.doi.org/10.1107/s0108767300001926.

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16

Delay, Erwann. "TT-eigentensors for the Lichnerowicz Laplacian on some asymptotically hyperbolic manifolds with warped products metrics." manuscripta mathematica 123, no. 2 (April 28, 2007): 147–65. http://dx.doi.org/10.1007/s00229-007-0089-z.

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17

Lemos, P., M. Raveri, A. Campos, Y. Park, C. Chang, N. Weaverdyck, D. Huterer, et al. "Assessing tension metrics with dark energy survey and Planck data." Monthly Notices of the Royal Astronomical Society 505, no. 4 (June 14, 2021): 6179–94. http://dx.doi.org/10.1093/mnras/stab1670.

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ABSTRACT Quantifying tensions – inconsistencies amongst measurements of cosmological parameters by different experiments – has emerged as a crucial part of modern cosmological data analysis. Statistically significant tensions between two experiments or cosmological probes may indicate new physics extending beyond the standard cosmological model and need to be promptly identified. We apply several tension estimators proposed in the literature to the dark energy survey (DES) large-scale structure measurement and Planck cosmic microwave background data. We first evaluate the responsiveness of these metrics to an input tension artificially introduced between the two, using synthetic DES data. We then apply the metrics to the comparison of Planck and actual DES Year 1 data. We find that the parameter differences, Eigentension, and Suspiciousness metrics all yield similar results on both simulated and real data, while the Bayes ratio is inconsistent with the rest due to its dependence on the prior volume. Using these metrics, we calculate the tension between DES Year 1 3 × 2pt and Planck, finding the surveys to be in ∼2.3σ tension under the ΛCDM paradigm. This suite of metrics provides a toolset for robustly testing tensions in the DES Year 3 data and beyond.

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18

Feng, Jun, Laurence T. Yang, Qing Zhu, Yang Xiang, Jinjun Chen, and Zheng Yan. "Secure Outsourced Principal Eigentensor Computation for Cyber-Physical-Social Systems." IEEE Transactions on Sustainable Computing, 2018, 1. http://dx.doi.org/10.1109/tsusc.2018.2881241.

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19

Bonifacio, James. "Bootstrap bounds on closed hyperbolic manifolds." Journal of High Energy Physics 2022, no. 2 (February 2022). http://dx.doi.org/10.1007/jhep02(2022)025.

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Abstract The eigenvalues of the Laplace-Beltrami operator and the integrals of products of eigenfunctions must satisfy certain consistency conditions on compact Riemannian manifolds. These consistency conditions are derived by using spectral decompositions to write quadruple overlap integrals in terms of products of triple overlap integrals in multiple ways. In this paper, we show how these consistency conditions imply bounds on the Laplacian eigenvalues and triple overlap integrals of closed hyperbolic manifolds, in analogy to the conformal bootstrap bounds on conformal field theories. We find an upper bound on the gap between two consecutive nonzero eigenvalues of the Laplace-Beltrami operator in terms of the smaller eigenvalue, an upper bound on the smallest eigenvalue of the rough Laplacian on symmetric, transverse-traceless, rank-2 tensors, and bounds on integrals of products of eigenfunctions and eigentensors. Our strongest bounds involve numerically solving semidefinite programs and are presented as exclusion plots. We also prove the analytic bound λi+1 ≤ 1/2 + 3λi + $$ \sqrt{\lambda_i^2+2{\lambda}_i+1/4} $$ λ i 2 + 2 λ i + 1 / 4 for consecutive nonzero eigenvalues of the Laplace-Beltrami operator on closed orientable hyperbolic surfaces. We give examples of genus-2 surfaces that nearly saturate some of these bounds. To derive the consistency conditions, we make use of a transverse-traceless decomposition for symmetric tensors of arbitrary rank.

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