Fabric Tensor Characterization of Tensor-Valued Directional Data: Solution, Accuracy, and Symmetrization
Joint Authors
Source
Journal of Applied Mathematics
Issue
Vol. 2012, Issue 2012 (31 Dec. 2012), pp.1-22, 22 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2012-11-29
Country of Publication
Egypt
No. of Pages
22
Main Subjects
Abstract EN
Fabric tensor has proved to be an effective tool statistically characterizing directional data in a smooth and frame-indifferent form.
Directional data arising from microscopic physics and mechanics can be summed up as tensor-valued orientation distribution functions (ODFs).
Two characterizations of the tensor-valued ODFs are proposed, using the asymmetric and symmetric fabric tensors respectively.
The later proves to be nonconvergent and less accurate but still an available solution for where fabric tensors are required in full symmetry.
Analytic solutions of the two types of fabric tensors characterizing centrosymmetric and anticentrosymmetric tensor-valued ODFs are presented in terms of orthogonal irreducible decompositions in both two- and three-dimensional (2D and 3D) spaces.
Accuracy analysis is performed on normally distributed random ODFs to evaluate the approximation quality of the two characterizations, where fabric tensors of higher orders are employed.
It is shown that the fitness is dominated by the dispersion degree of the original ODFs rather than the orders of fabric tensors.
One application of tensor-valued ODF and fabric tensor in continuum damage mechanics is presented.
American Psychological Association (APA)
Leng, Kuang-dai& Yang, Qiang. 2012. Fabric Tensor Characterization of Tensor-Valued Directional Data: Solution, Accuracy, and Symmetrization. Journal of Applied Mathematics،Vol. 2012, no. 2012, pp.1-22.
https://search.emarefa.net/detail/BIM-993329
Modern Language Association (MLA)
Leng, Kuang-dai& Yang, Qiang. Fabric Tensor Characterization of Tensor-Valued Directional Data: Solution, Accuracy, and Symmetrization. Journal of Applied Mathematics No. 2012 (2012), pp.1-22.
https://search.emarefa.net/detail/BIM-993329
American Medical Association (AMA)
Leng, Kuang-dai& Yang, Qiang. Fabric Tensor Characterization of Tensor-Valued Directional Data: Solution, Accuracy, and Symmetrization. Journal of Applied Mathematics. 2012. Vol. 2012, no. 2012, pp.1-22.
https://search.emarefa.net/detail/BIM-993329
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-993329