Monte Carlo Simulation of Percolation Phenomena for Direct Current in Large Square Matrices
Artykuł w czasopiśmie
MNiSW
140
Lista 2023
| Status: | |
| Autorzy: | Żukowski Paweł, Okal Paweł, Kierczyński Konrad, Rogalski Przemysław, Bondariev Vitalii, Pogrebnjak Alexander D. |
| Dyscypliny: | |
| Aby zobaczyć szczegóły należy się zalogować. | |
| Rok wydania: | 2023 |
| Wersja dokumentu: | Drukowana | Elektroniczna |
| Język: | angielski |
| Numer czasopisma: | 24 |
| Wolumen/Tom: | 16 |
| Numer artykułu: | 8024 |
| Strony: | 1 - 14 |
| Web of Science® Times Cited: | 0 |
| Scopus® Cytowania: | 0 |
| Bazy: | Web of Science | Scopus |
| Efekt badań statutowych | NIE |
| Finansowanie: | The research was supported by the subsidy of the Ministry of Education and Science (Poland) for the Lublin University of Technology as funds allocated for scientific activities in the scientific discipline of Automation, Electronics, Electrical Engineering and Space Technologies—grants: FD-20/EE-2/701, FD-20/EE-2/702, FD-20/EE-2/705, FD-20/EE-2/707. |
| Materiał konferencyjny: | NIE |
| Publikacja OA: | TAK |
| Licencja: | |
| Sposób udostępnienia: | Witryna wydawcy |
| Wersja tekstu: | Ostateczna wersja opublikowana |
| Czas opublikowania: | W momencie opublikowania |
| Data opublikowania w OA: | 12 grudnia 2023 |
| Abstrakty: | angielski |
| In this study, an in-depth analysis of the percolation phenomenon for square matrices with dimensions from L = 50 to 600 for a sample number of 5 × 104 was performed using Monte Carlo computer simulations. The percolation threshold value was defined as the number of conductive nodes remaining in the matrix before drawing the node interrupting the last percolation channel, in connection with the overall count of nodes within the matrix. The distributions of percolation threshold values were found to be normal distributions. The dependencies of the expected value (mean) of the percolation threshold and the standard deviation of the dimensions of the matrix were determined. It was established that the standard deviation decreased with the increase in matrix dimensions, ranging from 0.0262253 for a matrix with L = 50 to 0.0044160 for L = 600, which is almost six-fold lower. The mean value of the percolation threshold was practically constant and amounted to approximately 0.5927. The analysis involved not only the spatial distributions of nodes interrupting the percolation channels but also the overall patterns of node interruption in the matrix. The distributions revealed an edge phenomenon within the matrices, characterized by the maximum concentration of nodes interrupting the final percolation channel occurring at the center of the matrix. As they approached the edge of the matrix, their concentration decreased. It was established that increasing the dimensions of the matrix slowed down the rate of decrease in the number of nodes towards the edge. In doing so, the area in which values close to the maximum occurred was expanded. Based on the approximation of the experimental results, formulas were determined describing the spatial distributions of the nodes interrupting the last percolation channel and the values of the standard deviation from the matrix dimensions. The relationships obtained showed that with increasing matrix dimensions, the edge phenomenon should gradually disapp |
