Weighted Distances on a Triangular Grid

2014 ◽  
pp. 37-50 ◽  
Author(s):  
Benedek Nagy
Keyword(s):  
Triangular Grid

A Tile-based 8×8 Triangular Grid Array Beamformer for 5.7 GHz Microwave Power Transmission

2021 ◽  
Author(s):  
Kazuki Arai ◽  
Kaili Wang ◽  
Mitomo Toshiya ◽  
Makoto Higaki ◽  
Kohei Onizuka
Keyword(s):  
Microwave Power ◽  
Power Transmission ◽  
Triangular Grid

scholarly journals Vector Arithmetic in the Triangular Grid

Entropy ◽  
2021 ◽  
Vol 23 (3) ◽  
pp. 373
Author(s):  
Khaled Abuhmaidan ◽  
Monther Aldwairi ◽  
Benedek Nagy
Keyword(s):  
Coordinate System ◽  
Triangular Grid ◽  
Vector Addition ◽  
Plane Space ◽  
Physical Simulations ◽  
Rectangular Grids ◽  
Cartesian Coordinate ◽  
Zero Sum ◽  
Coordinate Geometry ◽  
Point Lattice

Vector arithmetic is a base of (coordinate) geometry, physics and various other disciplines. The usual method is based on Cartesian coordinate-system which fits both to continuous plane/space and digital rectangular-grids. The triangular grid is also regular, but it is not a point lattice: it is not closed under vector-addition, which gives a challenge. The points of the triangular grid are represented by zero-sum and one-sum coordinate-triplets keeping the symmetry of the grid and reflecting the orientations of the triangles. This system is expanded to the plane using restrictions like, at least one of the coordinates is an integer and the sum of the three coordinates is in the interval [−1,1]. However, the vector arithmetic is still not straightforward; by purely adding two such vectors the result may not fulfill the above conditions. On the other hand, for various applications of digital grids, e.g., in image processing, cartography and physical simulations, one needs to do vector arithmetic. In this paper, we provide formulae that give the sum, difference and scalar product of vectors of the continuous coordinate system. Our work is essential for applications, e.g., to compute discrete rotations or interpolations of images on the triangular grid.

Deployment Strategy in Distributed Underwater Sensor Networks

2014 ◽  
Vol 602-605 ◽  
pp. 3643-3647
Author(s):  
Li Yan Liu ◽  
Rong Fu ◽  
Yi He ◽  
Ying Qian Zhang
Keyword(s):  
Network Performance ◽  
Heuristic Method ◽  
Grid Method ◽  
Sensor Nodes ◽  
Triangular Grid ◽  
Underwater Sensor Networks ◽  
Network Coverage ◽  
Coverage Ratio ◽  
Initial Node ◽  
Deployment Strategy

Distributed underwater sensor network coverage is divided into two main categories: deterministic coverage and stochastic coverage. A strategy is put forward to deploy determinate area by using a triangular-grid method. When a coverage ratio is known, the distance between nodes can be adjusted to meet the coverage ratio in the monitored area, and the least number of sensor nodes can be calculated. Also a heuristic method is proposed for stochastic area deployment strategy. It is under the premise that the initial node location randomly deployed is given, using Voronoi diagram, the not easiest monitored path is searched, and the network coverage performance is improved by configuring the new nodes in the path. Finally it is proved that network performance is more improved by the simulation experiments, when one to four nodes are configured in the easiest breach path.

scholarly journals An optimal locating-dominating set in the infinite triangular grid

2006 ◽  
Vol 306 (21) ◽  
pp. 2670-2681 ◽  
Author(s):  
Iiro Honkala
Keyword(s):  
Dominating Set ◽  
Triangular Grid

On the Chamfer Polygons on the Triangular Grid

2017 ◽  
pp. 53-65 ◽  
Author(s):  
Hamid Mir-Mohammad-Sadeghi ◽  
Benedek Nagy
Keyword(s):  
Triangular Grid

scholarly journals Stochastic Flips on Dimer Tilings

2010 ◽  
Vol DMTCS Proceedings vol. AM,... (Proceedings) ◽  
Author(s):  
Thomas Fernique ◽  
Damien Regnault
Keyword(s):  
Fixed Point ◽  
Markov Process ◽  
Upper Bound ◽  
Numerical Experiments ◽  
Triangular Grid ◽  
Expected Number ◽  
Worst Case ◽  
Average Case ◽  
International Audience

International audience This paper introduces a Markov process inspired by the problem of quasicrystal growth. It acts over dimer tilings of the triangular grid by randomly performing local transformations, called $\textit{flips}$, which do not increase the number of identical adjacent tiles (this number can be thought as the tiling energy). Fixed-points of such a process play the role of quasicrystals. We are here interested in the worst-case expected number of flips to converge towards a fixed-point. Numerical experiments suggest a $\Theta (n^2)$ bound, where $n$ is the number of tiles of the tiling. We prove a $O(n^{2.5})$ upper bound and discuss the gap between this bound and the previous one. We also briefly discuss the average-case.

scholarly journals Application of the Discontinuous Galerkin Method to the Study of the Dynamics of Temperature and Pressure Changes in a Formation with an Injection Well and a Hydraulic Fracture

2021 ◽  
Vol 31 (1) ◽  
pp. 161-174
Author(s):  
Ruslan V. Zhalnin ◽  
Victor F. Masyagin ◽  
Elizaveta E. Peskova ◽  
Vladimir F. Tishkin
Keyword(s):  
Temperature Distribution ◽  
Galerkin Method ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Method ◽  
Numerical Algorithm ◽  
Hydraulic Fracture ◽  
Injection Well ◽  
Triangular Grid ◽  
Vertical Injection ◽  
Temperature And Pressure

Introduction. In this article, the problem of temperature distribution in an oil-bearing formation with a hydraulic fracture and a vertical injection well is numerically modeled. Materials and Methods. To describe the process of temperature distribution in the formation under the action of the fluid injected into the formation, the Fourier-Kirchhoff equation of convective heat transfer is used. To solve this equation, the discontinuous Galerkin method on staggered unstructured grids is used. To describe the process of pressure change in the formation under the action of the injection well, an equation is used that is obtained based on the continuity equation and Darcy’s law. To solve it, the discontinuous Galerkin method on an unstructured triangular grid is used. To parallelize the numerical algorithm, the MPI library is used. Results. The article presents a numerical algorithm and the results of modeling the dynamics of the temperature fields in an oil reservoir with a hydraulic fracture and a vertical injection well. Discussion and Conclusion. A numerical algorithm based on the discontinuous Galerkin method for math modeling of the temperature and pressure fields in a oil-bearing formation with a hydraulic fracture and injection well was developed and implemented. The results obtained for the distribution of temperature and pressure in the fracture are adequate and in good agreement with the specified initial-boundary conditions. Further work in this direction involves modeling on tetrahedral unstructured meshes for a more accurate study of the ongoing processes.

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