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Journal articles on the topic 'Tensor modes'

Author: Grafiati

Published: 4 June 2021

Last updated: 3 February 2022

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1

Adawi, Tom, Martin Cederwall, Ulf Gran, Bengt E. W. Nilsson, and Behrooz Razaznejad. "Goldstone tensor modes." Journal of High Energy Physics 1999, no. 02 (February 1, 1999): 001. http://dx.doi.org/10.1088/1126-6708/1999/02/001.

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2

SASAKURA, NAOKI. "THE LOWEST MODES AROUND GAUSSIAN SOLUTIONS OF TENSOR MODELS AND THE GENERAL RELATIVITY." International Journal of Modern Physics A 23, no. 24 (September 30, 2008): 3863–90. http://dx.doi.org/10.1142/s0217751x0804130x.

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In the paper arXiv:0706.1618[hep-th], the number distribution of the low-lying spectra around Gaussian solutions representing various dimensional fuzzy tori of a tensor model was numerically shown to be in accordance with the general relativity on tori. In this paper, I perform more detailed numerical analysis of the properties of the modes for two-dimensional fuzzy tori, and obtain conclusive evidences for the agreement. Under a proposed correspondence between the rank-3 tensor in tensor models and the metric tensor in the general relativity, conclusive agreement is obtained between the profiles of the low-lying modes in a tensor model and the metric modes transverse to the general coordinate transformation. Moreover, the low-lying modes are shown to be well on a massless trajectory with quartic momentum dependence in the tensor model. This is in agreement with that the lowest momentum dependence of metric fluctuations in the general relativity will come from the R2-term, since the R-term is topological in two dimensions. These evidences support the idea that the low-lying low-momentum dynamics around the Gaussian solutions of tensor models is described by the general relativity. I also propose a renormalization procedure for tensor models. A classical application of the procedure makes the patterns of the low-lying spectra drastically clearer, and suggests also the existence of massive trajectories.

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3

Van Eeghem, Frederik, Otto Debals, and Lieven De Lathauwer. "Tensor Similarity in Two Modes." IEEE Transactions on Signal Processing 66, no. 5 (March 1, 2018): 1273–85. http://dx.doi.org/10.1109/tsp.2017.2786208.

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4

Sorbo, Lorenzo. "Odd tensor modes from inflation." Modern Physics Letters A 31, no. 21 (July 10, 2016): 1640010. http://dx.doi.org/10.1142/s0217732316400101.

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The existence of a primordial spectrum of gravitational waves is a generic prediction of inflation. Here, I will discuss under what conditions the coupling of a pseudoscalar inflaton to a U(1) gauge field can induce, in a two-step process, gravitational waves with unusual properties such as: (i) a net chirality, (ii) a blue spectrum, (iii) large non-Gaussianities even if the scalar perturbations are approximately Gaussian and (iv) being detectable in the (relatively) near future by ground-based gravitational interferometers.

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Baumann, Daniel, and Matias Zaldarriaga. "Causality and primordial tensor modes." Journal of Cosmology and Astroparticle Physics 2009, no. 06 (June 9, 2009): 013. http://dx.doi.org/10.1088/1475-7516/2009/06/013.

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6

Wimalawarne, Kishan, Makoto Yamada, and Hiroshi Mamitsuka. "Scaled Coupled Norms and Coupled Higher-Order Tensor Completion." Neural Computation 32, no. 2 (February 2020): 447–84. http://dx.doi.org/10.1162/neco_a_01254.

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Recently, a set of tensor norms known as coupled norms has been proposed as a convex solution to coupled tensor completion. Coupled norms have been designed by combining low-rank inducing tensor norms with the matrix trace norm. Though coupled norms have shown good performances, they have two major limitations: they do not have a method to control the regularization of coupled modes and uncoupled modes, and they are not optimal for couplings among higher-order tensors. In this letter, we propose a method that scales the regularization of coupled components against uncoupled components to properly induce the low-rankness on the coupled mode. We also propose coupled norms for higher-order tensors by combining the square norm to coupled norms. Using the excess risk-bound analysis, we demonstrate that our proposed methods lead to lower risk bounds compared to existing coupled norms. We demonstrate the robustness of our methods through simulation and real-data experiments.

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7

Nomura, Yasunori, and Masahito Yamazaki. "Tensor modes in pure natural inflation." Physics Letters B 780 (May 2018): 106–10. http://dx.doi.org/10.1016/j.physletb.2018.02.071.

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8

Powell, Brian A. "Tensor tilt from primordial B modes." Monthly Notices of the Royal Astronomical Society 419, no. 1 (October 13, 2011): 566–72. http://dx.doi.org/10.1111/j.1365-2966.2011.19734.x.

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9

Efstathiou, George, and Sirichai Chongchitnan. "The Search for Primordial Tensor Modes." Progress of Theoretical Physics Supplement 163 (2006): 204–19. http://dx.doi.org/10.1143/ptps.163.204.

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10

Fujita, Tomohiro, Ippei Obata, Takahiro Tanaka, and Shuichiro Yokoyama. "Statistically anisotropic tensor modes from inflation." Journal of Cosmology and Astroparticle Physics 2018, no. 07 (July 12, 2018): 023. http://dx.doi.org/10.1088/1475-7516/2018/07/023.

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11

Zeng, Haijin, Yongyong Chen, Xiaozhen Xie, and Jifeng Ning. "Enhanced Nonconvex Low-Rank Approximation of Tensor Multi-Modes for Tensor Completion." IEEE Transactions on Computational Imaging 7 (2021): 164–77. http://dx.doi.org/10.1109/tci.2021.3053699.

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12

Cooray, Asantha. "Polarized CMB: Reionization and Primordial Tensor Modes." Symposium - International Astronomical Union 216 (2005): 51–58. http://dx.doi.org/10.1017/s0074180900196494.

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We discuss upcoming opportunities with cosmic microwave background (CMB) observations during the post-WMAP era. The curl-modes of CMB polarization probe inflationary gravitational waves (IGWs). While a significant source of confusion is expected from cosmic shear conversion of polarization related to density perturbations, higher resolution observations of CMB anisotropies can be used for a lensing reconstruction and to separate gravitational-wave polarization signature from that of lensing. Separations based on current lensing reconstruction techniques allow the possibility to probe inflationary energy scales below 1015 GeV in a range that includes grand unified theories. The observational detection of primordial curl-modes is aided by rescattering at late times during the reionized epoch with optical depth to electron scattering at the level of 0.1 and above. An improved measurement of this optical depth is useful to optimize experimental parameters of a post-WMAP mission attempting to target the IGW background.

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13

Brümmer, Felix, Valerie Domcke, and Verónica Sanz. "GUT-scale inflation with sizeable tensor modes." Journal of Cosmology and Astroparticle Physics 2014, no. 08 (August 29, 2014): 066. http://dx.doi.org/10.1088/1475-7516/2014/08/066.

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14

Dong, Le, and Yuan Yuan. "Sparse Constrained Low Tensor Rank Representation Framework for Hyperspectral Unmixing." Remote Sensing 13, no. 8 (April 11, 2021): 1473. http://dx.doi.org/10.3390/rs13081473.

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Recently, non-negative tensor factorization (NTF) as a very powerful tool has attracted the attention of researchers. It is used in the unmixing of hyperspectral images (HSI) due to its excellent expression ability without any information loss when describing data. However, most of the existing unmixing methods based on NTF fail to fully explore the unique properties of data, for example, low rank, that exists in both the spectral and spatial domains. To explore this low-rank structure, in this paper we learn the different low-rank representations of HSI in the spectral, spatial and non-local similarity modes. Firstly, HSI is divided into many patches, and these patches are clustered multiple groups according to the similarity. Each similarity group can constitute a 4-D tensor, including two spatial modes, a spectral mode and a non-local similarity mode, which has strong low-rank properties. Secondly, a low-rank regularization with logarithmic function is designed and embedded in the NTF framework, which simulates the spatial, spectral and non-local similarity modes of these 4-D tensors. In addition, the sparsity of the abundance tensor is also integrated into the unmixing framework to improve the unmixing performance through the L2,1 norm. Experiments on three real data sets illustrate the stability and effectiveness of our algorithm compared with five state-of-the-art methods.

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15

SAVVIDY, GEORGE. "PARTICLE SPECTRUM OF NON-ABELIAN TENSOR GAUGE FIELDS." Modern Physics Letters A 25, no. 14 (May 10, 2010): 1137–61. http://dx.doi.org/10.1142/s0217732310033001.

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We review the non-Abelian tensor gauge field theory and analyze its free field equations for lower rank gauge fields when the interaction coupling constant tends to zero. The free field equations are written in terms of the first-order derivatives of extended field strength tensors similar to the electrodynamics and non-Abelian gauge theories. We determine the particle content of the free field equations and count the propagating modes which they describe. In four-dimensional spacetime the rank-2 gauge field describes propagating modes of helicity two and zero. We show that the rank-3 gauge field describes propagating modes of helicity-three and a doublet of helicity-one gauge bosons. Only four-dimensional spacetime is physically acceptable, because in five- and higher-dimensional spacetime the equation has solutions with negative norm states. We discuss the structure of the particle spectrum for higher rank gauge fields.

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16

Sasaki, Misao, Takahiro Tanaka, and Yoshihiro Yakushige. "Wall fluctuation modes and tensor CMB anisotropy in open inflation models." Physical Review D 56, no. 2 (July 15, 1997): 616–24. http://dx.doi.org/10.1103/physrevd.56.616.

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17

Zhang, Xiao, and Shizhong Liao. "Tensor completion via multi-shared-modes canonical correlation analysis." Neurocomputing 205 (September 2016): 106–15. http://dx.doi.org/10.1016/j.neucom.2016.05.001.

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18

Ashoorioon, Amjad, P. S. Bhupal Dev, and Anupam Mazumdar. "Implications of purely classical gravity for inflationary tensor modes." Modern Physics Letters A 29, no. 30 (September 28, 2014): 1450163. http://dx.doi.org/10.1142/s0217732314501636.

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We discuss the implications of a purely classical (instead of quantum) theory of gravity for the primordial gravitational wave spectrum generated during inflation. We argue that for a scalar field driven inflation in a classical gravity the amplitude of the gravitational wave will be too small, irrespective of its primordial seed, to be detected in any forthcoming experiments. Therefore, a positive detection of the B-mode polarizations in the Cosmic Microwave Background (CMB) spectrum will naturally confirm the quantum nature of gravity itself. Furthermore there will be no upper limit on the scale of inflation in the case of classical gravity, and a high-scale model of inflation can easily bypass the observational constraints.

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19

Bessada, Dennis, and Oswaldo D. Miranda. "CMB anisotropies induced by tensor modes in Massive Gravity." Journal of Cosmology and Astroparticle Physics 2009, no. 08 (August 26, 2009): 033. http://dx.doi.org/10.1088/1475-7516/2009/08/033.

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20

Amendola, Luca, Frank Könnig, Matteo Martinelli, Valeria Pettorino, and Miguel Zumalacarregui. "Surfing gravitational waves: can bigravity survive growing tensor modes?" Journal of Cosmology and Astroparticle Physics 2015, no. 05 (May 26, 2015): 052. http://dx.doi.org/10.1088/1475-7516/2015/05/052.

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21

MARTINEAU, PATRICK, and ROBERT BRANDENBERGER. "A BACK-REACTION INDUCED LOWER BOUND ON THE TENSOR-TO-SCALAR RATIO." Modern Physics Letters A 23, no. 10 (March 28, 2008): 727–35. http://dx.doi.org/10.1142/s0217732308026777.

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There are large classes of inflationary models, particularly popular in the context of string theory and braneworld approaches to inflation, in which the ratio of linearized tensor-to-scalar metric fluctuations is very small. In such models, however, gravitational waves produced by scalar modes cannot be neglected. We derive the lower bound on the tensor-to-scalar ratio by considering the back-reaction of the scalar perturbations as a source of gravitational waves. These results show that no cosmological model that is compatible with a metric scalar amplitude of ≈10-5 can have a ratio of the tensor-to-scalar power spectra less than ≈10-8 at recombination and that higher-order terms leads to logarithmic growth for r during radiation domination. Our lower bound also applies to non-inflationary models which produce an almost scale-invariant spectrum of coherent super-Hubble scale metric fluctuations.

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22

Wimalawarne, Kishan, Makoto Yamada, and Hiroshi Mamitsuka. "Convex Coupled Matrix and Tensor Completion." Neural Computation 30, no. 11 (November 2018): 3095–127. http://dx.doi.org/10.1162/neco_a_01123.

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We propose a set of convex low-rank inducing norms for coupled matrices and tensors (hereafter referred to as coupled tensors), in which information is shared between the matrices and tensors through common modes. More specifically, we first propose a mixture of the overlapped trace norm and the latent norms with the matrix trace norm, and then, propose a completion model regularized using these norms to impute coupled tensors. A key advantage of the proposed norms is that they are convex and can be used to find a globally optimal solution, whereas existing methods for coupled learning are nonconvex. We also analyze the excess risk bounds of the completion model regularized using our proposed norms and show that they can exploit the low-rankness of coupled tensors, leading to better bounds compared to those obtained using uncoupled norms. Through synthetic and real-data experiments, we show that the proposed completion model compares favorably with existing ones.

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23

RYLYUK, V. M., I. M. TKACHENKO, and J. ORTNER. "Dielectric tensor and electromagnetic modes in magnetized non-ideal plasmas." Journal of Plasma Physics 63, no. 3 (April 2000): 239–53. http://dx.doi.org/10.1017/s0022377899008211.

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The effect of Coulomb correlations on the spectrum of electromagnetic waves propagating in a non-ideal magnetized fully ionized hydrogen plasma is studied. We employ the dielectric tensor constructed by means of the classical theory of moments without using perturbation theory.

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24

Пенкин, Юрий Михайлович, and Алина Александровна Федосеева. "СТРУКТУРНЫЕ КОНЕЧНЫЕ АВТОМАТЫ В ВИДЕ ТЕНЗОРОВ ТРЕТЬЕГО РАНГА ТИПА СУДОКУ." RADIOELECTRONIC AND COMPUTER SYSTEMS, no. 4 (December 25, 2019): 79–87. http://dx.doi.org/10.32620/reks.2019.4.09.

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The construction concept and general principles of the operation of a new kind of finite state machine are presented, for which the input and output elements are panels of square matrices, and the transitions between their states are determined by numerical tensors of the third rank. In this case, the structure of the tensors is specified in the form of cubic grids, in whose cells' natural numbers are located according to the principle of Sudoku construction. An algorithm for constructing such tensors of arbitrary size is indicated. The structures of tensors constructed using ranked sets of natural numbers are defined as standard. It is shown that the possibility of determining Sudoku type tensors using a one-dimensional parameter is basic for the manifestation of their functional self-similarity. The property of additive conservation of the structure of numerical tensors of the third rank to the requirements of Sudoku is formulated as a theorem. It is proved that the tensor obtained by summing an arbitrary tensor structure and a constant, taking into account the introduced cyclic ranking rule, satisfies the general requirements of Sudoku. The problems of abstract and structural synthesis of finite state machine based on the analyzed tensor structures are considered. In this case, the task of abstract synthesis has traditionally been defined as the creation of a mathematical model of an automaton, and the task of structural synthesis is just the development of its functional logical scheme. Based on the ambiguity of the function of the output of the finite state machine, the possibility of the simultaneous use of several different output alphabets is substantiated. The modes of functioning of the minimal finite state machine of the proposed type are described by the example of an initial state machine with a distinguished standard initial state. In the general case, it is shown that the finite state machines defined on the group of these requirements can be attributed to generalized first-order finite-state machines (or Mealy machines) with a multi-valued output. The features of network applications of structural automata are presented. Variants of possible applications of the considered finite state machines are analyzed.

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25

Zare, Marzieh, Mohammad Sadegh Helfroush, Kamran Kazemi, and Paul Scheunders. "Hyperspectral and Multispectral Image Fusion Using Coupled Non-Negative Tucker Tensor Decomposition." Remote Sensing 13, no. 15 (July 26, 2021): 2930. http://dx.doi.org/10.3390/rs13152930.

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Fusing a low spatial resolution hyperspectral image (HSI) with a high spatial resolution multispectral image (MSI), aiming to produce a super-resolution hyperspectral image, has recently attracted increasing research interest. In this paper, a novel approach based on coupled non-negative tensor decomposition is proposed. The proposed method performs a tucker tensor factorization of a low resolution hyperspectral image and a high resolution multispectral image under the constraint of non-negative tensor decomposition (NTD). The conventional matrix factorization methods essentially lose spatio-spectral structure information when stacking the 3D data structure of a hyperspectral image into a matrix form. Moreover, the spectral, spatial, or their joint structural features have to be imposed from the outside as a constraint to well pose the matrix factorization problem. The proposed method has the advantage of preserving the spatio-spectral structure of hyperspectral images. In this paper, the NTD is directly imposed on the coupled tensors of the HSI and MSI. Hence, the intrinsic spatio-spectral structure of the HSI is represented without loss, and spatial and spectral information can be interdependently exploited. Furthermore, multilinear interactions of different modes of the HSIs can be exactly modeled with the core tensor of the Tucker tensor decomposition. The proposed method is straightforward and easy to implement. Unlike other state-of-the-art approaches, the complexity of the proposed approach is linear with the size of the HSI cube. Experiments on two well-known datasets give promising results when compared with some recent methods from the literature.

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26

Bree, A., and R. Zwarich. "Raman scattering tensor elements for some ag modes of anthracene." Journal of Raman Spectroscopy 18, no. 1 (February 1987): 37–45. http://dx.doi.org/10.1002/jrs.1250180108.

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27

Litwin, C., and R. N. Sudan. "Renormalization of the diffusion tensor for high-frequency, electromagnetic modes." Physics of Fluids 30, no. 8 (1987): 2577. http://dx.doi.org/10.1063/1.866512.

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28

Saito, Ryo, and Takahiro Kubota. "Heavy particle signatures in cosmological correlation functions with tensor modes." Journal of Cosmology and Astroparticle Physics 2018, no. 06 (June 5, 2018): 009. http://dx.doi.org/10.1088/1475-7516/2018/06/009.

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29

Myung, Yun Soo. "Propagating Degrees of Freedom in f(R) Gravity." Advances in High Energy Physics 2016 (2016): 1–6. http://dx.doi.org/10.1155/2016/3901734.

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We have computed the number of polarization modes of gravitational waves propagating in the Minkowski background in f(R) gravity. These are three of two from transverse-traceless tensor modes and one from a massive trace mode, which confirms the results found in the literature. There is no massless breathing mode and the massive trace mode corresponds to the Ricci scalar. A newly defined metric tensor in f(R) gravity satisfies the transverse-traceless (TT) condition as well as the TT wave equation.

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30

Väliviita, Jussi, Matti Savelainen, Marianne Talvitie, Hannu Kurki-Suonio, and Stanislav Rusak. "CONSTRAINTS ON SCALAR AND TENSOR PERTURBATIONS IN PHENOMENOLOGICAL AND TWO-FIELD INFLATION MODELS: BAYESIAN EVIDENCES FOR PRIMORDIAL ISOCURVATURE AND TENSOR MODES." Astrophysical Journal 753, no. 2 (June 25, 2012): 151. http://dx.doi.org/10.1088/0004-637x/753/2/151.

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31

MASSAR, S. "LOCAL MODES, LOCAL VACUUM, LOCAL BOGOLJUBOV COEFFICIENTS AND THE RENORMALISED STRESS TENSOR." International Journal of Modern Physics D 03, no. 01 (March 1994): 237–40. http://dx.doi.org/10.1142/s0218271894000368.

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Local modes and local particles are defined at any point in curved space time as those that most resemble Minkowsky modes at that point. It is shown that the renormalised stress tensor is the difference of energy between the physical vacuum and that defined by these local modes.

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32

ODA, ICHIRO. "ANTISYMMETRIC TENSOR FIELDS IN THE LOCALLY LOCALIZED GRAVITY MODELS." Modern Physics Letters A 16, no. 15 (May 20, 2001): 1017–26. http://dx.doi.org/10.1142/s0217732301004200.

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We study the localization property of antisymmetric tensor fields in the locally localized gravity models. It is shown that all the antisymmetric tensor fields, including the vector field, in a bulk space–time are trapped on an AdS brane by a gravitational interaction where the presence of the brane cosmological constant plays an important role as in the cases of other bulk fields. The normalized zero-modes spread rather widely in extra space, so small extra dimensions might be needed in order not to conflict with experiment.

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33

Nzioki, Anne Marie, Rituparno Goswami, and Peter K. S. Dunsby. "Covariant perturbations of Schwarzschild black holes in f(R) gravity." International Journal of Modern Physics D 26, no. 06 (November 9, 2016): 1750048. http://dx.doi.org/10.1142/s0218271817500481.

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We consider general perturbations of a Schwarzschild black holes in the context of [Formula: see text] gravity. A reduced set of frame independent master variables are determined, which obey two closed wave equations — one for the transverse, trace-free, tensor perturbations and the other for the additional scalar degree of freedom which characterize fourth-order theories of gravity. We show that for the tensor modes, the underlying dynamics in [Formula: see text] gravity is governed by a modified Regge–Wheeler tensor which obeys the same Regge–Wheeler equation as in General Relativity (GR). We find that the possible sources of scalar quasinormal modes (QNMs) that follow from scalar perturbations for the lower multipoles result from primordial black holes, while higher mass, stellar black holes are associated with extremely high multipoles, which can only be produced in the first stage of black hole formation. Since scalar quasinormal modes are short ranged, this scenario makes their detection beyond the range of current experiments.

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34

VAN DE CRUYS, TIM. "A non-negative tensor factorization model for selectional preference induction." Natural Language Engineering 16, no. 4 (October 2010): 417–37. http://dx.doi.org/10.1017/s1351324910000148.

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AbstractThe distributional similarity methods have proven to be a valuable tool for the induction of semantic similarity. Until now, most algorithms use two-way co-occurrence data to compute the meaning of words. Co-occurrence frequencies, however, need not be pairwise. One can easily imagine situations where it is desirable to investigate co-occurrence frequencies of three modes and beyond. This paper will investigate tensor factorization methods to build a model of three-way co-occurrences. The approach is applied to the problem of selectional preference induction, and automatically evaluated in a pseudo-disambiguation task. The results show that tensor factorization, and non-negative tensor factorization in particular, is a promising tool for Natural Language Processing (nlp).

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35

Idé, Tsuyoshi. "Tensorial Change Analysis Using Probabilistic Tensor Regression." Proceedings of the AAAI Conference on Artificial Intelligence 33 (July 17, 2019): 3902–9. http://dx.doi.org/10.1609/aaai.v33i01.33013902.

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This paper proposes a new method for change detection and analysis using tensor regression. Change detection in our setting is to detect changes in the relationship between the input tensor and the output scalar while change analysis is to compute the responsibility score of individual tensor modes and dimensions for the change detected. We develop a new probabilistic tensor regression method, which can be viewed as a probabilistic generalization of the alternating least squares algorithm. Thanks to the probabilistic formulation, the derived change scores have a clear information-theoretic interpretation. We apply our method to semiconductor manufacturing to demonstrate the utility. To the best of our knowledge, this is the first work of change analysis based on probabilistic tensor regression.

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36

GANGOPADHYAY, DEBASHIS. "GAUGE FIXING FOR LINEARIZED GRAVITY AND ANTISYMMETRIC TENSOR FIELDS." International Journal of Modern Physics A 05, no. 11 (June 10, 1990): 2145–54. http://dx.doi.org/10.1142/s0217751x90000982.

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Using the functional stochastic scheme, the gauge fixing term for linearized gravity is shown to be related to longitudinal modes within the framework of the usual set of momentum projection operators. A similar analysis is done for non-Abelian antisymmetric tensor field by replacing derivatives with covariant derivatives in all relevant equations and by constructing suitable operators for projecting out transverse and longitudinal modes.

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37

Campbell, Charles S. "The stress tensor for simple shear flows of a granular material." Journal of Fluid Mechanics 203 (June 1989): 449–73. http://dx.doi.org/10.1017/s0022112089001540.

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The complete stress tensor has been measured using a computer simulation of an assemblage of rough, inelastic spheres in an imposed simple shear flow. Only five components of the stress tensor were found to be significantly different from zero. These represent the disperssive normal stresses τxx, τyy and τzz and the in-the-shear-plane shear stresses τxy and τyx; furthermore, the two off-diagonal stresses, τxy and τyx, were found to be equal so that the resultant stress tensor is symmetric. Two modes of microscopic momentum transport produce the final macroscopic stress tensor: the streaming or kinetic mode by which particles carry the momentum of their motion as they move through the bulk material, and the collisional mode by which momentum is transported by interparticle collisions. The contribution of each to the final result is examined separately. The friction coefficient, the ratio of shear to normal force, is shown to decrease at dense packings for both the collisional and streaming modes. Also observed were normal stress differences, both in and out of the shear plane, reflecting anisotropies in the granular temperature.

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38

Yunga, S., A. Lutikov, and O. Molchanov. "Non double couple seismic sources, faults interaction and hypothesis of self-organized criticality." Natural Hazards and Earth System Sciences 5, no. 1 (January 3, 2005): 11–15. http://dx.doi.org/10.5194/nhess-5-11-2005.

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Abstract. Non double couple (NDC) sources are considered in framework of the hypothesis that the process of seismic rupture can be viewed as a result of complicated fault geometry and its segmentation. Analytical approach is found to reveal reliability of NDC measure taking into consideration the values of seismic moment tensor errors. The study focuses on the comparison of the deformation modes of the NDC sources with the stress states in its vicinity. The deformation modes of faulting and fracturing at a small scale in NDC earthquake focus and at regional scale in geological unit were investigated using at the last case summation of seismic moment tensors. These local and regional deformation modes in some of geodynamic regimes confirm the self-similarity assumption. For the whole data set scaling relations seem to be more complicated. This feature implies that besides stresses second order factors, as the hydrothermal or magmatic pore fluids in rock, influence source characteristics and bring new complications in scaling relations.

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39

Chen, Kongtao, Jian Han, Xiaoqing Pan, and David J. Srolovitz. "The grain boundary mobility tensor." Proceedings of the National Academy of Sciences 117, no. 9 (February 18, 2020): 4533–38. http://dx.doi.org/10.1073/pnas.1920504117.

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The grain-boundary (GB) mobility relates the GB velocity to the driving force. While the GB velocity is normally associated with motion of the GB normal to the GB plane, there is often a tangential motion of one grain with respect to the other across a GB; i.e., the GB velocity is a vector. GB motion can be driven by a jump in chemical potential across a GB or by shear applied parallel to the GB plane; the driving force has three components. Hence, the GB mobility must be a tensor (the off-diagonal components indicate shear coupling). Performing molecular dynamics (MD) simulations on a symmetric-tilt GB in copper, we demonstrate that all six components of the GB mobility tensor are nonzero (the mobility tensor is symmetric, as required by Onsager). We demonstrate that some of these mobility components increase with temperature, while, surprisingly, others decrease. We develop a disconnection dynamics-based statistical model that suggests that GB mobilities follow an Arrhenius relation with respect to temperature T below a critical temperatureTcand decrease as1/Tabove it.Tcis related to the operative disconnection mode(s) and its (their) energetics. For any GB, which disconnection modes dominate depends on the nature of the driving force and the mobility component of interest. Finally, we examine the impact of the generalization of the mobility for applications in classical capillarity-driven grain growth. We demonstrate that stress generation during GB migration (shear coupling) necessarily slows grain growth and reduces GB mobility in polycrystals.

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40

Stewart, Andrew, and Robert Brandenberger. "Observational constraints on theories with a blue spectrum of tensor modes." Journal of Cosmology and Astroparticle Physics 2008, no. 08 (August 7, 2008): 012. http://dx.doi.org/10.1088/1475-7516/2008/08/012.

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41

Krupka, J., P. Blondy, D. Cros, P. Guillon, and R. G. Geyer. "Whispering-gallery modes and permeability tensor measurements in magnetized ferrite resonators." IEEE Transactions on Microwave Theory and Techniques 44, no. 7 (July 1996): 1097–102. http://dx.doi.org/10.1109/22.508643.

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42

Shchegrov, Andrei V., and P. Scott Carney. "Far-field contribution of evanescent modes to the electromagnetic Green tensor." Journal of the Optical Society of America A 16, no. 10 (October 1, 1999): 2583. http://dx.doi.org/10.1364/josaa.16.002583.

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43

Tattersall, Oliver J. "Quasi-normal modes of hairy scalar tensor black holes: odd parity." Classical and Quantum Gravity 37, no. 11 (May 14, 2020): 115007. http://dx.doi.org/10.1088/1361-6382/ab839b.

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44

Clarkson, Chris, and Bob Osano. "Locally extracting scalar, vector and tensor modes in cosmological perturbation theory." Classical and Quantum Gravity 28, no. 22 (October 14, 2011): 225002. http://dx.doi.org/10.1088/0264-9381/28/22/225002.

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45

Clarkson, Chris, and Bob Osano. "Locally extracting scalar, vector and tensor modes in cosmological perturbation theory." Classical and Quantum Gravity 29, no. 7 (March 20, 2012): 079601. http://dx.doi.org/10.1088/0264-9381/29/7/079601.

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46

Brandenburg, Axel, Grigol Gogoberidze, Tina Kahniashvili, Sayan Mandal, Alberto Roper Pol, and Nakul Shenoy. "The scalar, vector, and tensor modes in gravitational wave turbulence simulations." Classical and Quantum Gravity 38, no. 14 (June 15, 2021): 145002. http://dx.doi.org/10.1088/1361-6382/ac011c.

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47

Chen, Z., and H. E. Fang. "A study on the link between coupled plasticity and damage and decohesion for multiscale modelling." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 215, no. 3 (March 1, 2001): 259–63. http://dx.doi.org/10.1243/0954406011520698.

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To predict the transition from continuous to discontinuous failure modes, a bifurcation analysis is performed based on the continuum tangent stiffness tensor of a coupled plasticity and damage model. As a result, continuum damage and decohesion approaches can be combined for multiscale modelling of material failure.

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48

CYNOLTER, G. "WAVE FUNCTION OF THE RADION WITH BPS BRANES." Modern Physics Letters A 20, no. 07 (March 7, 2005): 519–32. http://dx.doi.org/10.1142/s0217732305016725.

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We investigate coupled gravity and a bulk scalar field on a slice of AdS 5 bulk with special BPS branes at the two ends. With a careful treatment of the general coordinate invariance, the complete tensor–scalar spectrum is presented. There are two massless zero modes in the scalar sector, the radion and a dilatonic zero mode. The four-dimensional effective action is of biscalar–tensor type.

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49

Shoucri, M. "Transverse electromagnetic modes in a hot cylindrical plasma column." Journal of Plasma Physics 52, no. 3 (December 1994): 471–81. http://dx.doi.org/10.1017/s0022377800027276.

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We derive the dielectric tensor of a hot plasma by including the smallgyroradius corrections up to the first harmonic (ω ≈ 2ωcα). We show that these corrections introduce radial wavenumbers associated with transverse electromagnetic modes (TEM). The special case of a cylindrical plasma column is discussed for a hydrogen plasma at the ion-cyclotron frequency and for an electron plasma at the electron-cyclotron frequency and its first harmonic.

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50

Brancus, D. E. N., and A. C. Mocuta. "Anisotropic optical polaron in crystals with complex structure." Canadian Journal of Physics 73, no. 3-4 (March 1, 1995): 126–30. http://dx.doi.org/10.1139/p95-018.

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In the context of intermediate coupling theory, the forms of the self-energy and effective-mass tensor of the optical polaron, in appropriate uniaxial crystals with complex structure, are obtained. These forms contain all sources of anisotropy; the effective-mass tensor of the "bare" electron, the electron – optical-phonon interaction, and the angular dependence of the "true" phonoic modes. A numerical application is developed in the case of the CdS crystal.

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