Analysis of Uneven Distribution of Nodes Creating a Percolation Channel in Matrices with Translational Symmetry for Direct Current
In this study, the phenomenon of node percolation was tested using the Monte Carlo computer simulation method for square matrices with dimensions <i>L</i> = 55, 101 and 151. The number of samples for each matrix was 5 × 10<sup>6</sup>. The spatial distributions of the coordin...
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MDPI AG
2023-11-01
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| Series: | Energies |
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| Online Access: | https://www.mdpi.com/1996-1073/16/22/7647 |
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| author | Pawel Zukowski Pawel Okal Konrad Kierczynski Przemyslaw Rogalski Vitalii Bondariev |
| author_facet | Pawel Zukowski Pawel Okal Konrad Kierczynski Przemyslaw Rogalski Vitalii Bondariev |
| author_sort | Pawel Zukowski |
| collection | DOAJ |
| description | In this study, the phenomenon of node percolation was tested using the Monte Carlo computer simulation method for square matrices with dimensions <i>L</i> = 55, 101 and 151. The number of samples for each matrix was 5 × 10<sup>6</sup>. The spatial distributions of the coordinates of the nodes creating the percolation channel were determined, and maps of the density distribution of these nodes were created. It has been established that in matrices with finite dimensions, an edge phenomenon occurs, consisting of a decrease in the concentration of nodes creating a percolation channel as one approaches the edge of the matrix. As the matrix dimensions increase, the intensity of this phenomenon decreases. This expands the area in which values close to the maximum occur. The length distributions of the left and right clusters of non-conducting nodes were determined for the situation when the next randomly selected node connects them and thus reaches the percolation threshold. It was found that clusters whose dimensions are close to half of the matrix dimensions are most likely to occur. The research shows that both the values of the standard deviation of the percolation threshold and the intensity of the edge phenomenon are clearly related to the dimensions of the matrices and decrease as they increase. |
| first_indexed | 2024-03-09T16:51:33Z |
| format | Article |
| id | doaj.art-3655a36adff94d83b1b72554a9fd6231 |
| institution | Directory Open Access Journal |
| issn | 1996-1073 |
| language | English |
| last_indexed | 2024-03-09T16:51:33Z |
| publishDate | 2023-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Energies |
| spelling | doaj.art-3655a36adff94d83b1b72554a9fd62312023-11-24T14:40:39ZengMDPI AGEnergies1996-10732023-11-011622764710.3390/en16227647Analysis of Uneven Distribution of Nodes Creating a Percolation Channel in Matrices with Translational Symmetry for Direct CurrentPawel Zukowski0Pawel Okal1Konrad Kierczynski2Przemyslaw Rogalski3Vitalii Bondariev4Department of Economics, Vincent Pol University in Lublin, 2, Choiny Str., 20-816 Lublin, PolandDepartment of Electrical Devices and High Voltage Technology, Faculty of Electrical Engineering and Computer Science, Lublin University of Technology, 38A, Nadbystrzycka Str., 20-618 Lublin, PolandDepartment of Electrical Devices and High Voltage Technology, Faculty of Electrical Engineering and Computer Science, Lublin University of Technology, 38A, Nadbystrzycka Str., 20-618 Lublin, PolandDepartment of Electrical Devices and High Voltage Technology, Faculty of Electrical Engineering and Computer Science, Lublin University of Technology, 38A, Nadbystrzycka Str., 20-618 Lublin, PolandDepartment of Electrical Devices and High Voltage Technology, Faculty of Electrical Engineering and Computer Science, Lublin University of Technology, 38A, Nadbystrzycka Str., 20-618 Lublin, PolandIn this study, the phenomenon of node percolation was tested using the Monte Carlo computer simulation method for square matrices with dimensions <i>L</i> = 55, 101 and 151. The number of samples for each matrix was 5 × 10<sup>6</sup>. The spatial distributions of the coordinates of the nodes creating the percolation channel were determined, and maps of the density distribution of these nodes were created. It has been established that in matrices with finite dimensions, an edge phenomenon occurs, consisting of a decrease in the concentration of nodes creating a percolation channel as one approaches the edge of the matrix. As the matrix dimensions increase, the intensity of this phenomenon decreases. This expands the area in which values close to the maximum occur. The length distributions of the left and right clusters of non-conducting nodes were determined for the situation when the next randomly selected node connects them and thus reaches the percolation threshold. It was found that clusters whose dimensions are close to half of the matrix dimensions are most likely to occur. The research shows that both the values of the standard deviation of the percolation threshold and the intensity of the edge phenomenon are clearly related to the dimensions of the matrices and decrease as they increase.https://www.mdpi.com/1996-1073/16/22/7647metrological approachuncertainty of measurementpercolation phenomenonpercolation thresholdMonte Carlo methodcomputer simulation |
| spellingShingle | Pawel Zukowski Pawel Okal Konrad Kierczynski Przemyslaw Rogalski Vitalii Bondariev Analysis of Uneven Distribution of Nodes Creating a Percolation Channel in Matrices with Translational Symmetry for Direct Current Energies metrological approach uncertainty of measurement percolation phenomenon percolation threshold Monte Carlo method computer simulation |
| title | Analysis of Uneven Distribution of Nodes Creating a Percolation Channel in Matrices with Translational Symmetry for Direct Current |
| title_full | Analysis of Uneven Distribution of Nodes Creating a Percolation Channel in Matrices with Translational Symmetry for Direct Current |
| title_fullStr | Analysis of Uneven Distribution of Nodes Creating a Percolation Channel in Matrices with Translational Symmetry for Direct Current |
| title_full_unstemmed | Analysis of Uneven Distribution of Nodes Creating a Percolation Channel in Matrices with Translational Symmetry for Direct Current |
| title_short | Analysis of Uneven Distribution of Nodes Creating a Percolation Channel in Matrices with Translational Symmetry for Direct Current |
| title_sort | analysis of uneven distribution of nodes creating a percolation channel in matrices with translational symmetry for direct current |
| topic | metrological approach uncertainty of measurement percolation phenomenon percolation threshold Monte Carlo method computer simulation |
| url | https://www.mdpi.com/1996-1073/16/22/7647 |
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