IDEAS home Printed from https://ideas.repec.org/a/gam/jeners/v16y2023i22p7647-d1282849.html
   My bibliography  Save this article

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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Pawel Zukowski & Pawel Okal & Konrad Kierczynski & Przemyslaw Rogalski & Vitalii Bondariev, 2023. "Analysis of Uneven Distribution of Nodes Creating a Percolation Channel in Matrices with Translational Symmetry for Direct Current," Energies, MDPI, vol. 16(22), pages 1-14, November.
    • Handle: RePEc:gam:jeners:v:16:y:2023:i:22:p:7647-:d:1282849
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/1996-1073/16/22/7647/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/1996-1073/16/22/7647/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Wilkinson, Leland & Friendly, Michael, 2009. "The History of the Cluster Heat Map," The American Statistician, American Statistical Association, vol. 63(2), pages 179-184.
    2. Pawel Zukowski & Paweł Okal & Konrad Kierczynski & Przemyslaw Rogalski & Sebastian Borucki & Michał Kunicki & Tomasz N. Koltunowicz, 2023. "Investigations into the Influence of Matrix Dimensions and Number of Iterations on the Percolation Phenomenon for Direct Current," Energies, MDPI, vol. 16(20), pages 1-19, October.
    3. Li, Daqing & Zhang, Qiong & Zio, Enrico & Havlin, Shlomo & Kang, Rui, 2015. "Network reliability analysis based on percolation theory," Reliability Engineering and System Safety, Elsevier, vol. 142(C), pages 556-562.
    4. Cristopher Moore & M. E. J. Newman, 2000. "Epidemics and Percolation in Small-World Networks," Working Papers 00-01-002, Santa Fe Institute.
    5. Brouers, F. & Granovsky, A. & Sarychev, A. & Kalitsov, A., 1997. "The influence of boundary scattering on transport phenomena in ferromagnetic metal—dielectric nanocomposites," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 241(1), pages 284-288.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Pawel Zukowski & Paweł Okal & Konrad Kierczynski & Przemyslaw Rogalski & Sebastian Borucki & Michał Kunicki & Tomasz N. Koltunowicz, 2023. "Investigations into the Influence of Matrix Dimensions and Number of Iterations on the Percolation Phenomenon for Direct Current," Energies, MDPI, vol. 16(20), pages 1-19, October.
    2. Yang Shunkun & Zhang Jiaquan & Lu Dan, 2016. "Prediction of Cascading Failures in Spatial Networks," PLOS ONE, Public Library of Science, vol. 11(4), pages 1-11, April.
    3. Ganjeh-Ghazvini, Mostafa & Masihi, Mohsen & Ghaedi, Mojtaba, 2014. "Random walk–percolation-based modeling of two-phase flow in porous media: Breakthrough time and net to gross ratio estimation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 406(C), pages 214-221.
    4. Pan, Ya-Nan & Lou, Jing-Jing & Han, Xiao-Pu, 2014. "Outbreak patterns of the novel avian influenza (H7N9)," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 401(C), pages 265-270.
    5. Accominotti, Olivier & Lucena-Piquero, Delio & Ugolini, Stefano, 2023. "Intermediaries’ substitutability and financial network resilience: A hyperstructure approach," Journal of Economic Dynamics and Control, Elsevier, vol. 153(C).
    6. Monfared, M.A.S. & Rezazadeh, Masoumeh & Alipour, Zohreh, 2022. "Road networks reliability estimations and optimizations: A Bi-directional bottom-up, top-down approach," Reliability Engineering and System Safety, Elsevier, vol. 222(C).
    7. Di Maio, Francesco & Pettorossi, Chiara & Zio, Enrico, 2023. "Entropy-driven Monte Carlo simulation method for approximating the survival signature of complex infrastructures," Reliability Engineering and System Safety, Elsevier, vol. 231(C).
    8. Greg Morrison & L Mahadevan, 2012. "Discovering Communities through Friendship," PLOS ONE, Public Library of Science, vol. 7(7), pages 1-9, July.
    9. Floortje Alkemade & Carolina Castaldi, 2005. "Strategies for the Diffusion of Innovations on Social Networks," Computational Economics, Springer;Society for Computational Economics, vol. 25(1), pages 3-23, February.
    10. Qin, Yang & Zhong, Xiaoxiong & Jiang, Hao & Ye, Yibin, 2015. "An environment aware epidemic spreading model and immune strategy in complex networks," Applied Mathematics and Computation, Elsevier, vol. 261(C), pages 206-215.
    11. Velarde, Carlos & Robledo, Alberto, 2021. "Statistical mechanical model for growth and spread of contagions under gauged population confinement," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 573(C).
    12. I. Vieira & R. Cheng & P. Harper & V. Senna, 2010. "Small world network models of the dynamics of HIV infection," Annals of Operations Research, Springer, vol. 178(1), pages 173-200, July.
    13. Zhang, Jianhua & Wang, Ziqi & Wang, Shuliang & Shao, Wenchao & Zhao, Xun & Liu, Weizhi, 2021. "Vulnerability assessments of weighted urban rail transit networks with integrated coupled map lattices," Reliability Engineering and System Safety, Elsevier, vol. 214(C).
    14. Sáenz-Royo, Carlos & Lozano-Rojo, Álvaro, 2023. "Authoritarianism versus participation in innovation decisions," Technovation, Elsevier, vol. 124(C).
    15. Limiao, Zhang & Daqing, Li & Pengju, Qin & Bowen, Fu & Yinan, Jiang & Zio, Enrico & Rui, Kang, 2016. "Reliability analysis of interdependent lattices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 452(C), pages 120-125.
    16. Chu, Xiaolei & Wang, Ziqi, 2025. "Maximum entropy-based modeling of community-level hazard responses for civil infrastructures," Reliability Engineering and System Safety, Elsevier, vol. 254(PA).
    17. Vilches, T.N. & Esteva, L. & Ferreira, C.P., 2019. "Disease persistence and serotype coexistence: An expected feature of human mobility," Applied Mathematics and Computation, Elsevier, vol. 355(C), pages 161-172.
    18. Yin, Rongrong & Li, Linhui & Wang, Yumeng & Hao, Zhenyang & Zhang, Le, 2025. "Robustness of networks with dependence clusters against hybrid cascading failure induced by fluctuating load," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 660(C).
    19. Tomovski, Igor & Kocarev, Ljupčo, 2015. "Network topology inference from infection statistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 436(C), pages 272-285.
    20. Li, Xun & Cao, Lang, 2016. "Diffusion processes of fragmentary information on scale-free networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 450(C), pages 624-634.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jeners:v:16:y:2023:i:22:p:7647-:d:1282849. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.