Analysis of Uneven Distribution of Nodes Creating a Percolation Channel in Matrices with Translational Symmetry for Direct Current

Pawel Zukowski, Pawel Okal, Konrad Kierczynski (), Przemyslaw Rogalski and Vitalii Bondariev
Additional contact information
Pawel Zukowski: Department of Economics, Vincent Pol University in Lublin, 2, Choiny Str., 20-816 Lublin, Poland
Pawel Okal: Department of Electrical Devices and High Voltage Technology, Faculty of Electrical Engineering and Computer Science, Lublin University of Technology, 38A, Nadbystrzycka Str., 20-618 Lublin, Poland
Konrad Kierczynski: Department of Electrical Devices and High Voltage Technology, Faculty of Electrical Engineering and Computer Science, Lublin University of Technology, 38A, Nadbystrzycka Str., 20-618 Lublin, Poland
Przemyslaw Rogalski: Department of Electrical Devices and High Voltage Technology, Faculty of Electrical Engineering and Computer Science, Lublin University of Technology, 38A, Nadbystrzycka Str., 20-618 Lublin, Poland
Vitalii Bondariev: Department of Electrical Devices and High Voltage Technology, Faculty of Electrical Engineering and Computer Science, Lublin University of Technology, 38A, Nadbystrzycka Str., 20-618 Lublin, Poland

Energies, 2023, vol. 16, issue 22, 1-14

Abstract: In this study, the phenomenon of node percolation was tested using the Monte Carlo computer simulation method for square matrices with dimensions L = 55, 101 and 151. The number of samples for each matrix was 5 × 10 6 . 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.

Keywords: metrological approach; uncertainty of measurement; percolation phenomenon; percolation threshold; Monte Carlo method; computer simulation (search for similar items in EconPapers)
JEL-codes: Q Q0 Q4 Q40 Q41 Q42 Q43 Q47 Q48 Q49 (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/1996-1073/16/22/7647/pdf (application/pdf)
https://www.mdpi.com/1996-1073/16/22/7647/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jeners:v:16:y:2023:i:22:p:7647-:d:1282849

Access Statistics for this article

Energies is currently edited by Ms. Agatha Cao

More articles in Energies from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().