Space-filling properties of good lattice point sets

Biometrika ◽  
2015 ◽  
Vol 102 (4) ◽  
pp. 959-966 ◽  
Author(s):  
Yongdao Zhou ◽  
Hongquan Xu
Keyword(s):  
Lattice Point ◽  
Point Sets ◽  
Space Filling ◽  
Good Lattice ◽  
Good Lattice Point

Generalized good lattice point sets

2017 ◽  
Vol 33 (2) ◽  
pp. 887-901 ◽  
Author(s):  
Zong-Feng Qi ◽  
Xue-Ru Zhang ◽  
Yong-Dao Zhou
Keyword(s):  
Lattice Point ◽  
Point Sets ◽  
Good Lattice ◽  
Good Lattice Point

scholarly journals Further research on the good lattice point design

2020 ◽  
Vol 50 (5) ◽  
pp. 585
Author(s):  
Tang Yu ◽  
Chen E
Keyword(s):  
Lattice Point ◽  
Good Lattice ◽  
Good Lattice Point

scholarly journals Optimal maximin $L_{1}$-distance Latin hypercube designs based on good lattice point designs

2018 ◽  
Vol 46 (6B) ◽  
pp. 3741-3766 ◽  
Author(s):  
Lin Wang ◽  
Qian Xiao ◽  
Hongquan Xu
Keyword(s):  
Lattice Point ◽  
Latin Hypercube ◽  
Latin Hypercube Designs ◽  
Good Lattice ◽  
Good Lattice Point

On the forbidden and the optimum crystallographic variant of rutile in garnet

2016 ◽  
Vol 49 (6) ◽  
pp. 1922-1940 ◽  
Author(s):  
Shyh-Lung Hwang ◽  
Pouyan Shen ◽  
Hao-Tsu Chu ◽  
Tzen-Fu Yui
Keyword(s):  
Lattice Point ◽  
Electron Backscatter Diffraction ◽  
Coincidence Site Lattice ◽  
Three Dimensional ◽  
Structural Factors ◽  
Oxygen Sublattices ◽  
Tilt Boundaries ◽  
Good Lattice ◽  
Crystallographic Orientation Relationship ◽  
Selection Of

In many inclusion–host systems with similar oxygen packing schemes, the optimum crystallographic orientation relationship (COR) between the inclusion and the host is mostly determined by matching the similar oxygen sublattices of the two structures. In contrast, the prediction of the optimum COR or even just the rationalization of the observed COR(s) between an inclusion and host with incompatible oxygen sublattices, like rutile–garnet, is not straightforward. The related documentation for such cases is therefore limited. Given the abundant crystallographic data for the rutile–garnet system acquired by transmission electron microscopy and electron backscatter diffraction methods recently, this problem can now be examined in detail for the critical structural factors dictating the selection of optimum COR in such a structurally complicated system. On the basis of the unconstrained three-dimensional lattice point match and structural polyhedron match calculated for the observed CORs, it becomes clear that the prerequisite of optimum COR for rutile (rt) in garnet (grt) is to have most of their octahedra similarly oriented/inclined in space by aligning 〈103〉rtand 〈111〉grtfor needle extension growth. Further rotation along the 〈103〉rt//〈111〉grtdirection then leads to the energetically most favorable COR-2 variant with a good lattice point match defined by the coincidence site lattice (CSL) and a good topotaxial match of the constituent polyhedra at the CSL points, leaving unfavorable COR-1′ in the forbidden zones. This understanding sheds light not only on hierarchical energetics for the selection of inclusion variants in a complicated inclusion–host system, but also on yet-to-be-explored [UVW]-specific CORs and hetero-tilt boundaries for composite materials in general.

Lattice point sets for efficient kernel smoothing models

2015 ◽  
Author(s):  
Cristiano Cervellera ◽  
Mauro Gaggero ◽  
Danilo Maccio ◽  
Roberto Marcialis
Keyword(s):  
Lattice Point ◽  
Kernel Smoothing ◽  
Point Sets

Method for Estimating Failure Probability of Mechanical Structures Using Number Theoretical Net (NT-net) Simulation

2009 ◽  
Vol 628-629 ◽  
pp. 239-244
Author(s):  
Z.J. Wen ◽  
De Shun Liu ◽  
Shu Yi Yang
Keyword(s):  
Failure Probability ◽  
Simulation Method ◽  
Computational Effort ◽  
Side Impact ◽  
Computational Accuracy ◽  
Simulation Techniques ◽  
Net Method ◽  
Good Lattice ◽  
Good Lattice Point ◽  
Point Set

According to poor computational accuracy at small to median sample sizes of Monte Carlo ( MC ) simulation techniques in estimating the probability failure of mechanical structures, the number theoretical net ( NT-net ) simulation method is proposed to reduce computing effort. Several key concepts, such as good point set, good-lattice point ( glp ), discrepancy and NT-net method, are defined. The sampling stategy is improved by introducing NT-net that can provide better convergent rate over MC. The new method is used to estimate failure probability of the side impact bar on the car door. Results indicate the computational effort needed by NT-net for the same accuracy is about 1/12 of that needed by the MC-based method, and the obtained results are more stable.

scholarly journals A note on isotropic discrepancy and spectral test of lattice point sets

2020 ◽  
Vol 58 ◽  
pp. 101441
Author(s):  
Friedrich Pillichshammer ◽  
Mathias Sonnleitner
Keyword(s):  
Lattice Point ◽  
Point Sets ◽  
Spectral Test
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