Symmetry analysis of the modulated icosahedral phase in AlCuFe

1994 ◽  
Vol 4 (9) ◽  
pp. 1341-1352
Author(s):  
J. M. Perez-Mato ◽  
L. Elcoro
Keyword(s):  
Icosahedral Phase ◽  
Symmetry Analysis

NEUTRON DIFFRACTION STUDIES OF THE ICOSAHEDRAL PHASE OF Al-Mn ALLOYS

1986 ◽  
Vol 47 (C3) ◽  
pp. C3-351-C3-360 ◽  
Author(s):  
B. MOZER ◽  
J. W. CAHN ◽  
D. GRATIAS ◽  
D. SHECHTMAN
Keyword(s):  
Neutron Diffraction ◽  
Icosahedral Phase

Symmetry analysis of differential equations: a primer

2018 ◽  
Author(s):  
Eric Jason Albright ◽  
James D. McHardy ◽  
Scott D. Ramsey ◽  
Joseph H. Schmidt
Keyword(s):  
Differential Equations ◽  
Symmetry Analysis

scholarly journals Symmetry Analysis of Oriental Polygonal Pagodas Using 3D Point Clouds for Cultural Heritage

Sensors ◽  
2021 ◽  
Vol 21 (4) ◽  
pp. 1228
Author(s):  
Ting On Chan ◽  
Linyuan Xia ◽  
Yimin Chen ◽  
Wei Lang ◽  
Tingting Chen ◽  
...  
Keyword(s):  
Cultural Heritage ◽  
Unmanned Aerial Vehicle ◽  
Point Cloud ◽  
Geometric Model ◽  
Digital Camera ◽  
Point Clouds ◽  
Symmetry Analysis ◽  
3D Point Clouds ◽  
Transmission Towers ◽  
Aerial Vehicle

Ancient pagodas are usually parts of hot tourist spots in many oriental countries due to their unique historical backgrounds. They are usually polygonal structures comprised by multiple floors, which are separated by eaves. In this paper, we propose a new method to investigate both the rotational and reflectional symmetry of such polygonal pagodas through developing novel geometric models to fit to the 3D point clouds obtained from photogrammetric reconstruction. The geometric model consists of multiple polygonal pyramid/prism models but has a common central axis. The method was verified by four datasets collected by an unmanned aerial vehicle (UAV) and a hand-held digital camera. The results indicate that the models fit accurately to the pagodas’ point clouds. The symmetry was realized by rotating and reflecting the pagodas’ point clouds after a complete leveling of the point cloud was achieved using the estimated central axes. The results show that there are RMSEs of 5.04 cm and 5.20 cm deviated from the perfect (theoretical) rotational and reflectional symmetries, respectively. This concludes that the examined pagodas are highly symmetric, both rotationally and reflectionally. The concept presented in the paper not only work for polygonal pagodas, but it can also be readily transformed and implemented for other applications for other pagoda-like objects such as transmission towers.

scholarly journals Two-dimensional Weyl points and nodal lines in pentagonal materials and their optical response

Nanoscale ◽  
2021 ◽  
Author(s):  
Sergio Bravo ◽  
M. Pacheco ◽  
V. Nuñez ◽  
J. D. Correa ◽  
Leonor Chico
Keyword(s):  
First Principles ◽  
Optical Response ◽  
Symmetry Analysis ◽  
Two Dimensional ◽  
First Principles Calculations ◽  
Nodal Lines

A symmetry analysis combined with first-principles calculations of two-dimensional pentagonal materials (PdSeTe, PdSeS, InP5 and GeBi2) based on the Cairo tiling reveal nontrivial spin textures, nodal lines and Weyl points.

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