Restricted Correlation Space B-Spline ADC Approach to Molecular Ionization: Theory and Applications to Total Photoionization Cross-Sections

2019 ◽  
Vol 15 (6) ◽  
pp. 3635-3653 ◽  
Author(s):  
M. Ruberti
Keyword(s):  
Cross Sections ◽  
B Spline ◽  
Correlation Space ◽  
Molecular Ionization

scholarly journals Relativistic B-Spline R-Matrix Calculations for Electron Collisions with Ytterbium

Atoms ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 47
Author(s):  
Kathryn R. Hamilton ◽  
Klaus Bartschat ◽  
Oleg Zatsarinny
Keyword(s):  
Experimental Data ◽  
Electron Scattering ◽  
Cross Sections ◽  
Matrix Method ◽  
Model Potential ◽  
Electron Collisions ◽  
R Matrix ◽  
B Spline ◽  
Potential Approach

We have applied the full-relativistic Dirac B-Spline R-matrix method to obtain cross sections for electron scattering from ytterbium atoms. The results are compared with those obtained from a semi-relativistic (Breit-Pauli) model-potential approach and the few available experimental data.

The quadratic B-spline curve fitting for the shape of log cross sections

2006 ◽  
Vol 17 (2) ◽  
pp. 150-152 ◽  
Author(s):  
Hong’e Ren ◽  
Yan Wu ◽  
Xiao-ming Zhu
Keyword(s):  
Cross Sections ◽  
Curve Fitting ◽  
B Spline ◽  
Spline Curve

scholarly journals Tunnel Deformation Inspection via Global Spatial Axis Extraction from 3D Raw Point Cloud

Sensors ◽  
2020 ◽  
Vol 20 (23) ◽  
pp. 6815
Author(s):  
Cheng Yi ◽  
Dening Lu ◽  
Qian Xie ◽  
Jinxuan Xu ◽  
Jun Wang
Keyword(s):  
Cross Sections ◽  
Point Cloud ◽  
Large Scale ◽  
Spline Approximation ◽  
Point Clouds ◽  
Driving Safety ◽  
Inspection Method ◽  
B Spline ◽  
3D Point Clouds ◽  
Spatial Axis

Global inspection of large-scale tunnels is a fundamental yet challenging task to ensure the structural stability of tunnels and driving safety. Advanced LiDAR scanners, which sample tunnels into 3D point clouds, are making their debut in the Tunnel Deformation Inspection (TDI). However, the acquired raw point clouds inevitably possess noticeable occlusions, missing areas, and noise/outliers. Considering the tunnel as a geometrical sweeping feature, we propose an effective tunnel deformation inspection algorithm by extracting the global spatial axis from the poor-quality raw point cloud. Essentially, we convert tunnel axis extraction into an iterative fitting optimization problem. Specifically, given the scanned raw point cloud of a tunnel, the initial design axis is sampled to generate a series of normal planes within the corresponding Frenet frame, followed by intersecting those planes with the tunnel point cloud to yield a sequence of cross sections. By fitting cross sections with circles, the fitted circle centers are approximated with a B-Spline curve, which is considered as an updated axis. The procedure of “circle fitting and B-SPline approximation” repeats iteratively until convergency, that is, the distance of each fitted circle center to the current axis is smaller than a given threshold. By this means, the spatial axis of the tunnel can be accurately obtained. Subsequently, according to the practical mechanism of tunnel deformation, we design a segmentation approach to partition cross sections into meaningful pieces, based on which various inspection parameters can be automatically computed regarding to tunnel deformation. A variety of practical experiments have demonstrated the feasibility and effectiveness of our inspection method.

Geometric model reconstruction through a surface extension algorithm for remanufacturing of twist blades

2017 ◽  
Vol 23 (2) ◽  
pp. 382-390 ◽  
Author(s):  
Jian Gao ◽  
Hao Wen ◽  
Zhiyuan Lin ◽  
Haidong Wu ◽  
Si Li ◽  
...  
Keyword(s):  
Cross Sections ◽  
Reference Model ◽  
Geometric Model ◽  
Repair Process ◽  
Difficult Problem ◽  
Control Points ◽  
Content Type ◽  
B Spline ◽  
Adaptive Machining ◽  
Blade Tip

Purpose Remanufacturing of worn blades with various defects normally requires processes such as scanning, regenerating a geometrical reference model, additive manufacturing (AM) through laser cladding, adaptive machining and polishing and quality inspection. Unlike the manufacturing process of a new part, the most difficult problem for remanufacturing such a complex surface part is that the reference model adaptive to the worn part is no longer available or useful. The worn parts may suffer from geometrical deformation, distortion and other defects because of the effects of harsh operating conditions, thereby making their original computer aided design (CAD) models inadequate for the repair process. This paper aims to regenerate the geometric models for the worn parts, which is a key issue for implementing AM to build up the parts and adaptive machining to reform the parts. Unlike straight blades with similar cross sections, the tip geometry of the worn tip of a twist blade needs to be regenerated by a different method. Design/methodology/approach This paper proposes a surface extension algorithm for the reconstruction of a twist blade tip through the extremum parameterization of a B-spline basis function. Based on the cross sections of the scanned worn blade model, the given control points and knot vectors are firstly reconstructed into a B-spline curve D. After the extremum of each control point is calculated by extremum parameterization of a B-spline basis function, the unknown control points are calculated by substituting the extremum into the curve D. Once all control points are determined, the B-spline surface of the worn blade tip can be regenerated. Finally, the extension algorithm is implemented and validated with several examples. Findings The proposed algorithm was implemented and verified through the exampled blades. Through the extension algorithm, the tip geometry of the worn tip of a twist blade can be regenerated. This method solved a key problem for the repair of a twist blade tip. It provides an appropriate reference model for repairing worn blade tips through AM to build up the blade tip and adaptive machining/polishing processes to reform the blade geometry. Research limitations/implications The extension errors for different repair models are compared and analyzed. The authors found that there are several factors affecting the accuracy of the regenerated model. When the cross-section interval and the extension length are set properly, the restoration accuracy for the blade tip can be improved, which is acceptable for the repairing. Practical implications The lack of a reference geometric model for worn blades is a significant problem when implementing blade repair through AM and adaptive machining processes. Because the geometric reference model is unavailable for the repair process, reconstruction of the geometry of a worn blade tip is the first crucial step. The authors proposed a surface extension algorithm for the reconstruction of a twist blade tip. Through the implementation of the proposed algorithm, the blade tip model can be regenerated. Social implications Remanufacturing of worn blades with various defects is highly demeaned for the aerospace enterprises considering sustainable development. Unlike straight blades, repair of twist blades encountered a very difficult problem because the geometric reference model is unavailable for the repair processes. This paper proposed a different method to generate the reference model for the repair of a twist blade tip. With this model, repair of twist blades can be implemented through AM to build up the blade tip and adaptive machining to subtract the extra material. Originality/value The authors proposed a surface extension algorithm to reconstruct the geometric model for repair of twist blades.

B-Spline Surface Approximation to Cross-Sections Using Distance Maps

1999 ◽  
Vol 15 (12) ◽  
pp. 876-885 ◽  
Author(s):  
J. Jeong ◽  
K. Kim ◽  
H. Park ◽  
H. Cho ◽  
M. Jung
Keyword(s):  
Cross Sections ◽  
Surface Approximation ◽  
B Spline ◽  
Spline Surface
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