Topic
Tensor
About: Tensor is a research topic. Over the lifetime, 23487 publications have been published within this topic receiving 544705 citations.
Papers published on a yearly basis
1 / 2
Papers
TL;DR: This survey provides an overview of higher-order tensor decompositions, their applications, and available software.
Abstract: This survey provides an overview of higher-order tensor decompositions, their applications, and available software. A tensor is a multidimensional or $N$-way array. Decompositions of higher-order tensors (i.e., $N$-way arrays with $N \geq 3$) have applications in psycho-metrics, chemometrics, signal processing, numerical linear algebra, computer vision, numerical analysis, data mining, neuroscience, graph analysis, and elsewhere. Two particular tensor decompositions can be considered to be higher-order extensions of the matrix singular value decomposition: CANDECOMP/PARAFAC (CP) decomposes a tensor as a sum of rank-one tensors, and the Tucker decomposition is a higher-order form of principal component analysis. There are many other tensor decompositions, including INDSCAL, PARAFAC2, CANDELINC, DEDICOM, and PARATUCK2 as well as nonnegative variants of all of the above. The N-way Toolbox, Tensor Toolbox, and Multilinear Engine are examples of software packages for working with tensors.
11,513 citations
Book•
1 Jan 1985
TL;DR: In this paper, the physical properties of crystals systematically in tensor notation are presented, presenting tensor properties in terms of their common mathematical basis and the thermodynamic relations between them.
Abstract: First published in 1957, this classic study has been reissued in a paperback version that includes an additional chapter bringing the material up to date. The author formulates the physical properties of crystals systematically in tensor notation, presenting tensor properties in terms of their common mathematical basis and the thermodynamic relations between them. The mathematical groundwork is laid in a discussion of tensors of the first and second ranks. Tensors of higher ranks and matrix methods are then introduced as natural developments of the theory. A similar pattern is followed in discussing thermodynamic and optical aspects.
8,701 citations
TL;DR: Once Deff is estimated from a series of NMR pulsed-gradient, spin-echo experiments, a tissue's three orthotropic axes can be determined and the effective diffusivities along these orthotropic directions are the eigenvalues of Deff.
6,269 citations
1 Jan 1960
TL;DR: In this paper, the angular momentum, one of the most fundamental quantities in all of quantum mechanics, is introduced and a concise introduction to its application in atomic, molecular, and nuclear physics is provided.
Abstract: This book offers a concise introduction to the angular momentum, one of the most fundamental quantities in all of quantum mechanics. Beginning with the quantization of angular momentum, spin angular momentum, and the orbital angular momentum, the author goes on to discuss the Clebsch-Gordan coefficients for a two-component system. After developing the necessary mathematics, specifically spherical tensors and tensor operators, the author then investigates the 3-j, 6-j, and 9-j symbols. Throughout, the author provides practical applications to atomic, molecular, and nuclear physics. These include partial-wave expansions, the emission and absorption of particles, the proton and electron quadrupole moment, matrix element calculation in practice, and the properties of the symmetrical top molecule.
5,085 citations
[...]
TL;DR: In this method, non-linear susceptibility tensors are introduced which relate the induced dipole moment to a power series expansion in field strengths and the various experimental observations are described and interpreted in terms of this formalism.
Abstract: Recent advances in the field of nonlinear optical phenomena are reviewed with particular empphasis placed on such topics as parametric oscillation self-focusing and trapping of laser beams, and stimulated Raman, Rayleigh, and Brillouin scattering. The optical frequency radiation is treated classically in terms of the amplitudes and phases of the electromagnetic fields. The interactions of light waves in a mterial are then formulated in terms of Maxwell's equations and the electric dipole approximation. In this method, non-linear susceptibility tensors are introdueed which relate the induced dipole moment to a power series expansion in field strengths. The tensor nature and the frequency dependence of the nonlinearity coefficients are considered. The various experimental, observations are described and interpreted in terms of this formalism.
4,776 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2022 | 28 |
| 2021 | 1,647 |
| 2020 | 1,536 |
| 2019 | 1,351 |
| 2018 | 1,310 |
| 2017 | 1,147 |