scholarly journals Polypolar spherical harmonic decomposition of galaxy correlators in redshift space: Toward testing cosmic rotational symmetry

2017 ◽  
Vol 95 (6) ◽  
Author(s):  
Maresuke Shiraishi ◽  
Naonori S. Sugiyama ◽  
Teppei Okumura
Keyword(s):  
Spherical Harmonic ◽  
Rotational Symmetry ◽  
Harmonic Decomposition ◽  
Spherical Harmonic Decomposition

scholarly journals Mechanical assessment of defects in welded joints: morphological classification and data augmentation

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Hugo Launay ◽  
François Willot ◽  
David Ryckelynck ◽  
Jacques Besson
Keyword(s):  
Welded Joints ◽  
Spherical Harmonic ◽  
Data Augmentation ◽  
Mechanical Response ◽  
Training Data ◽  
Distance Functions ◽  
Elastic Response ◽  
Reduction Techniques ◽  
Harmonic Decomposition ◽  
Spherical Harmonic Decomposition

AbstractWe develop a methodology for classifying defects based on their morphology and induced mechanical response. The proposed approach is fairly general and relies on morphological operators (Angulo and Meyer in 9th international symposium on mathematical morphology and its applications to signal and image processing, pp. 226-237, 2009) and spherical harmonic decomposition as a way to characterize the geometry of the pores, and on the Grassman distance evaluated on FFT-based computations (Willot in C. R., Méc. 343(3):232–245, 2015), for the predicted elastic response. We implement and detail our approach on a set of trapped gas pores observed in X-ray tomography of welded joints, that significantly alter the mechanical reliability of these materials (Lacourt et al. in Int. J. Numer. Methods Eng. 121(11):2581–2599, 2020). The space of morphological and mechanical responses is first partitioned into clusters using the “k-medoids” criterion and associated distance functions. Second, we use multiple-layer perceptron neural networks to associate a defect and corresponding morphological representation to its mechanical response. It is found that the method provides accurate mechanical predictions if the training data contains a sufficient number of defects representing each mechanical class. To do so, we supplement the original set of defects by data augmentation techniques. Artificially-generated pore shapes are obtained using the spherical harmonic decomposition and a singular value decomposition performed on the pores signed distance transform. We discuss possible applications of the present method, and how medoids and their associated mechanical response may be used to provide a natural basis for reduced-order models and hyper-reduction techniques, in which the mechanical effects of defects and structures are decorrelated (Ryckelynck et al. in C. R., Méc. 348(10–11):911–935, 2020).

scholarly journals Three-dimensional reconstruction of neutron, gamma-ray, and x-ray sources using spherical harmonic decomposition

2017 ◽  
Vol 122 (17) ◽  
pp. 175901 ◽  
Author(s):  
P. L. Volegov ◽  
C. R. Danly ◽  
D. Fittinghoff ◽  
V. Geppert-Kleinrath ◽  
G. Grim ◽  
...  
Keyword(s):  
Spherical Harmonic ◽  
Gamma Ray ◽  
Three Dimensional ◽  
Three Dimensional Reconstruction ◽  
X Ray ◽  
Dimensional Reconstruction ◽  
Harmonic Decomposition ◽  
Spherical Harmonic Decomposition
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