Version 1
: Received: 16 September 2024 / Approved: 16 September 2024 / Online: 17 September 2024 (02:56:02 CEST)
How to cite:
Bondariev, V.; Okal, P.; Rogalski, P.; Pogrebnjak, A.; Zukowski, P. Research on the Influence of Matrix Shape on Percolation Threshold Values for Current Flow Conducted Using the Monte Carlo Simulation Method. Preprints2024, 2024091243. https://doi.org/10.20944/preprints202409.1243.v1
Bondariev, V.; Okal, P.; Rogalski, P.; Pogrebnjak, A.; Zukowski, P. Research on the Influence of Matrix Shape on Percolation Threshold Values for Current Flow Conducted Using the Monte Carlo Simulation Method. Preprints 2024, 2024091243. https://doi.org/10.20944/preprints202409.1243.v1
Bondariev, V.; Okal, P.; Rogalski, P.; Pogrebnjak, A.; Zukowski, P. Research on the Influence of Matrix Shape on Percolation Threshold Values for Current Flow Conducted Using the Monte Carlo Simulation Method. Preprints2024, 2024091243. https://doi.org/10.20944/preprints202409.1243.v1
APA Style
Bondariev, V., Okal, P., Rogalski, P., Pogrebnjak, A., & Zukowski, P. (2024). Research on the Influence of Matrix Shape on Percolation Threshold Values for Current Flow Conducted Using the Monte Carlo Simulation Method. Preprints. https://doi.org/10.20944/preprints202409.1243.v1
Chicago/Turabian Style
Bondariev, V., Alexander Pogrebnjak and Pawel Zukowski. 2024 "Research on the Influence of Matrix Shape on Percolation Threshold Values for Current Flow Conducted Using the Monte Carlo Simulation Method" Preprints. https://doi.org/10.20944/preprints202409.1243.v1
Abstract
In this study, in order to determine the effect of matrices shape on percolation threshold values, computer simulations were performed using the Monte Carlo method for a 200x200 square-shaped matrix and rectangular matrices containing the same number of nodes as the square matrix. Based on the simulations, the average values of percolation thresholds and standard deviations for current flow along and across the matrices were determined. It was determined that for a square-shaped matrix, the average values of percolation thresholds in both directions of current flow were the same. Extending the rectangular matrix while reducing its height causes the average value of the percolation threshold in the direction of current flow along the matrix to increase from 0.592740 to 0.759847, while in the transverse direction it decreases from 0.592664 to 0.403614. The values of the classical asymmetry coefficients of the probability distributions of percolation thresholds for both directions of current flow were determined. Histograms of the probability distributions of percolation threshold values for square-shaped matrix and rectangular matrices were made and compared with normal distributions. It was found that the occurrence of two percolation thresholds in rectangular layers should be considered when analyzing electrical conductivity measurements of nanocomposite thin films.
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
