scholarly journals Constructions for the Optimal Pebbling of Grids

2017 ◽  
Vol 61 (2) ◽  
pp. 217 ◽  
Author(s):  
Ervin Győri ◽  
Gyula Y. Katona ◽  
László F. Papp
Keyword(s):  
Square Grid ◽  
Optimal Pebbling

In [6] the authors conjecture that if every vertex of an infinite square grid is reachable from a pebble distribution, then the covering ratio of this distribution is at most 3.25. First we present such a distribution with covering ratio 3.5, disproving the conjecture. The authors in the above paper also claim to prove that the covering ratio of any pebble distribution is at most 6.75. The proof contains some errors. We present a few interesting pebble distributions that this proof does not seem to cover and highlight some other difficulties of this topic.

scholarly journals Optimal Pebbling Number of the Square Grid

2020 ◽  
Vol 36 (3) ◽  
pp. 803-829
Author(s):  
Ervin Győri ◽  
Gyula Y. Katona ◽  
László F. Papp
Keyword(s):  
Square Grid ◽  
Pebbling Number ◽  
Optimal Pebbling

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

Three Supramolecular Isomers of Square Grid Networks from the Assembly of a Flexible Spacer and Co(NCS)2:  Structures and Polymer Transformation

2006 ◽  
Vol 6 (4) ◽  
pp. 994-998 ◽  
Author(s):  
Yan-Fen Peng ◽  
Hai-Yan Ge ◽  
Bao-Zong Li ◽  
Bao-Long Li ◽  
Yong Zhang
Keyword(s):  
Square Grid ◽  
Grid Networks ◽  
Flexible Spacer

Finite‐difference calculation of direct‐arrival traveltimes using the eikonal equation

Geophysics ◽  
2002 ◽  
Vol 67 (4) ◽  
pp. 1270-1274 ◽  
Author(s):  
Le‐Wei Mo ◽  
Jerry M. Harris
Keyword(s):  
Finite Difference ◽  
Ray Tracing ◽  
Finite Differences ◽  
Eikonal Equation ◽  
Velocity Model ◽  
Uniform Grid ◽  
Square Grid ◽  
Kirchhoff Migration ◽  
Difference Calculation

Traveltimes of direct arrivals are obtained by solving the eikonal equation using finite differences. A uniform square grid represents both the velocity model and the traveltime table. Wavefront discontinuities across a velocity interface at postcritical incidence and some insights in direct‐arrival ray tracing are incorporated into the traveltime computation so that the procedure is stable at precritical, critical, and postcritical incidence angles. The traveltimes can be used in Kirchhoff migration, tomography, and NMO corrections that require traveltimes of direct arrivals on a uniform grid.

A square grid model for assessing the effect of alternative land uses on water quality

1976 ◽  
Vol 3 (2) ◽  
pp. 209-218 ◽  
Author(s):  
Thomas W. Constable ◽  
Nicholas Kouwen ◽  
Shully I. Solomon
Keyword(s):  
Water Quality ◽  
Land Use ◽  
Water Quantity ◽  
Preliminary Design ◽  
Land Use Patterns ◽  
Time Intervals ◽  
Square Grid ◽  
Use Patterns ◽  
Grid Technique ◽  
Artificial Ponds

A mathematical model has been developed which can aid in assessing the effect of the modification of land use patterns on the water quantity and water quality regime of a watershed. The basin under study is divided into a number of elements using a square grid technique. The hydrologic and water quality components are evaluated at each element in the basin at successive time intervals, and flows are routed through the elements by use of a streamflow network system. The model can be used to assist in evaluating the effects of alternative land use configurations in a watershed, such as urbanization, the removal or growth of forests, the construction of dams, etc., on water quantity and water quality. It can also be used in the preliminary design of an urbanized area to estimate the size of storm sewers, artificial ponds, etc.

Sign in / Sign up

Export Citation Format

Share Document