Discrete Linear Geometry on Non-square Grid

2021 ◽  
pp. 219-232
Author(s):  
Troung Kieu Linh ◽  
Atsushi Imiya
Keyword(s):  
Square Grid ◽  
Linear Geometry

On the Linear Geometry of Lanthanide Hydroxide (Ln—OH, Ln=La-Lu)

2019 ◽  
Author(s):  
Hassan Harb ◽  
Lee Thompson ◽  
Hrant Hratchian
Keyword(s):  
Triple Bond ◽  
Density Functional ◽  
Valence Electron ◽  
Density Functional Theory Calculations ◽  
Electron Configuration ◽  
Functional Theory ◽  
Key Species ◽  
Pi Orbitals ◽  
Lanthanide Hydroxide ◽  
Linear Geometry

Lanthanide hydroxides are key species in a variety of catalytic processes and in the preparation of corresponding oxides. This work explores the fundamental structure and bonding of the simplest lanthanide hydroxide, LnOH (Ln=La-Lu), using density functional theory calculations. Interestingly, the calculations predict that all structures of this series will be linear. Furthermore, these results indicate a valence electron configuration featuring an occupied sigma orbital and two occupied pi orbitals for all LnOH compounds, suggesting that the lanthanide-hydroxide bond is best characterized as a covalent triple bond.

On the Linear Geometry of Lanthanide Hydroxide (Ln—OH, Ln=La-Lu)

2019 ◽  
Author(s):  
Hassan Harb ◽  
Lee Thompson ◽  
Hrant Hratchian
Keyword(s):  
Triple Bond ◽  
Density Functional ◽  
Valence Electron ◽  
Density Functional Theory Calculations ◽  
Electron Configuration ◽  
Functional Theory ◽  
Key Species ◽  
Pi Orbitals ◽  
Lanthanide Hydroxide ◽  
Linear Geometry

Lanthanide hydroxides are key species in a variety of catalytic processes and in the preparation of corresponding oxides. This work explores the fundamental structure and bonding of the simplest lanthanide hydroxide, LnOH (Ln=La-Lu), using density functional theory calculations. Interestingly, the calculations predict that all structures of this series will be linear. Furthermore, these results indicate a valence electron configuration featuring an occupied sigma orbital and two occupied pi orbitals for all LnOH compounds, suggesting that the lanthanide-hydroxide bond is best characterized as a covalent triple bond.

scholarly journals Fractal-induced 2D flexible net undulation

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Michael Joon Seng Goh ◽  
Yeong Shiong Chiew ◽  
Ji Jinn Foo
Keyword(s):  
3D Reconstruction ◽  
Cross Section ◽  
Channel Cross Section ◽  
Time Varying ◽  
Blockage Ratio ◽  
Transient Time ◽  
Cross Sectional ◽  
Velocity Fluctuations ◽  
Square Grid ◽  
Multilength Scale

AbstractA net immersed in fractal-induced turbulence exhibit a transient time-varying deformation. The anisotropic, inhomogeneous square fractal grid (SFG) generated flow interacts with the flexible net to manifest as visible cross-sectional undulations. We hypothesize that the net’s response may provide a surrogate in expressing local turbulent strength. This is analysed as root-mean-squared velocity fluctuations in the net, displaying intensity patterns dependent on the grid conformation and grid-net separation. The net’s fluctuation strength is found to increase closer to the turbulator with higher thickness ratio while presenting stronger fluctuations compared to regular-square-grid (RSG) of equivalent blockage-ratio, σ. Our findings demonstrate a novel application where 3D-reconstruction of submerged nets is used to experimentally contrast the turbulence generated by RSG and multilength scale SFGs across the channel cross-section. The net’s response shows the unique turbulence developed from SFGs can induce 9 × higher average excitation to a net when compared against RSG of similar σ.

Chromous carbonates containing a square-grid layer of {Cr2(CO3)4}n4n− based on a dichromium(ii,ii) paddlewheel core

2021 ◽  
Vol 50 (7) ◽  
pp. 2387-2392
Author(s):  
Zhi-Qiang Dong ◽  
Jian-Hui Yang ◽  
Bin Liu
Keyword(s):  
Magnetic Properties ◽  
Layer Structure ◽  
Square Grid

The structural, spectroscopic and magnetic properties of chromous carbonates with a square-grid layer structure constructed from Cr2(CO3)44− paddlewheel units.

scholarly journals ON A FABRIC OF KISSING CIRCLES

2021 ◽  
pp. 1-10
Author(s):  
VIERA ČERŇANOVÁ
Keyword(s):  
Sufficient Condition ◽  
Arithmetic Sequence ◽  
Square Grid ◽  
The Individual

Abstract Applying circle inversion on a square grid filled with circles, we obtain a configuration that we call a fabric of kissing circles. We focus on the curvature inside the individual components of the fabric, which are two orthogonal frames and two orthogonal families of chains. We show that the curvatures of the frame circles form a doubly infinite arithmetic sequence (bi-sequence), whereas the curvatures in each chain are arranged in a quadratic bi-sequence. We also prove a sufficient condition for the fabric to be integral.

scholarly journals Square Grid Metal–Chloranilate Networks as Robust Host Systems for Guest Sorption

2019 ◽  
Vol 25 (20) ◽  
pp. 5222-5234 ◽  
Author(s):  
Christopher J. Kingsbury ◽  
Brendan F. Abrahams ◽  
Josie E. Auckett ◽  
Hubert Chevreau ◽  
A. David Dharma ◽  
...  
Keyword(s):  
Square Grid

Spatiotemporal distribution of surface charges in square-grid state in a dielectric barrier discharge

2018 ◽  
Vol 25 (3) ◽  
pp. 033510
Author(s):  
Fang Hao ◽  
Lifang Dong ◽  
Tian Du ◽  
Ying Liu ◽  
Weili Fan ◽  
...  
Keyword(s):  
Dielectric Barrier Discharge ◽  
Barrier Discharge ◽  
Spatiotemporal Distribution ◽  
Surface Charges ◽  
Dielectric Barrier ◽  
Square Grid

2D metal-organic frameworks with square grid structure: A promising new-generation superlubricating material

Nano Today ◽  
2021 ◽  
Vol 40 ◽  
pp. 101262
Author(s):  
Lei Liu ◽  
Yong Zhang ◽  
Yijun Qiao ◽  
Shanchao Tan ◽  
Shaofei Feng ◽  
...  
Keyword(s):  
Metal Organic Frameworks ◽  
Grid Structure ◽  
Square Grid ◽  
Metal Organic ◽  
New Generation

scholarly journals The non-linear geometry of Banach spaces after Nigel Kalton

2014 ◽  
Vol 44 (5) ◽  
pp. 1529-1583 ◽  
Author(s):  
G. Godefroy ◽  
G. Lancien ◽  
V. Zizler
Keyword(s):  
Banach Spaces ◽  
Non Linear ◽  
Linear Geometry
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