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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Autor*in:	Pawel Zukowski [verfasserIn] Pawel Okal [verfasserIn] Konrad Kierczynski [verfasserIn] Przemyslaw Rogalski [verfasserIn] Vitalii Bondariev [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2023

Schlagwörter:	metrological approach uncertainty of measurement percolation phenomenon percolation threshold Monte Carlo method computer simulation

Übergeordnetes Werk:	In: Energies - MDPI AG, 2008, 16(2023), 22, p 7647
Übergeordnetes Werk:	volume:16 ; year:2023 ; number:22, p 7647

Links:	Link aufrufen Link aufrufen Link aufrufen Journal toc

DOI / URN:	10.3390/en16227647

Katalog-ID:	DOAJ101249985

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allfields	10.3390/en16227647 doi (DE-627)DOAJ101249985 (DE-599)DOAJ3655a36adff94d83b1b72554a9fd6231 DE-627 ger DE-627 rakwb eng Pawel Zukowski verfasserin aut Analysis of Uneven Distribution of Nodes Creating a Percolation Channel in Matrices with Translational Symmetry for Direct Current 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier 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. metrological approach uncertainty of measurement percolation phenomenon percolation threshold Monte Carlo method computer simulation Technology T Pawel Okal verfasserin aut Konrad Kierczynski verfasserin aut Przemyslaw Rogalski verfasserin aut Vitalii Bondariev verfasserin aut In Energies MDPI AG, 2008 16(2023), 22, p 7647 (DE-627)572083742 (DE-600)2437446-5 19961073 nnns volume:16 year:2023 number:22, p 7647 https://doi.org/10.3390/en16227647 kostenfrei https://doaj.org/article/3655a36adff94d83b1b72554a9fd6231 kostenfrei https://www.mdpi.com/1996-1073/16/22/7647 kostenfrei https://doaj.org/toc/1996-1073 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2055 GBV_ILN_2108 GBV_ILN_2111 GBV_ILN_2119 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 16 2023 22, p 7647
spelling	10.3390/en16227647 doi (DE-627)DOAJ101249985 (DE-599)DOAJ3655a36adff94d83b1b72554a9fd6231 DE-627 ger DE-627 rakwb eng Pawel Zukowski verfasserin aut Analysis of Uneven Distribution of Nodes Creating a Percolation Channel in Matrices with Translational Symmetry for Direct Current 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier 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. metrological approach uncertainty of measurement percolation phenomenon percolation threshold Monte Carlo method computer simulation Technology T Pawel Okal verfasserin aut Konrad Kierczynski verfasserin aut Przemyslaw Rogalski verfasserin aut Vitalii Bondariev verfasserin aut In Energies MDPI AG, 2008 16(2023), 22, p 7647 (DE-627)572083742 (DE-600)2437446-5 19961073 nnns volume:16 year:2023 number:22, p 7647 https://doi.org/10.3390/en16227647 kostenfrei https://doaj.org/article/3655a36adff94d83b1b72554a9fd6231 kostenfrei https://www.mdpi.com/1996-1073/16/22/7647 kostenfrei https://doaj.org/toc/1996-1073 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2055 GBV_ILN_2108 GBV_ILN_2111 GBV_ILN_2119 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 16 2023 22, p 7647
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allfieldsGer	10.3390/en16227647 doi (DE-627)DOAJ101249985 (DE-599)DOAJ3655a36adff94d83b1b72554a9fd6231 DE-627 ger DE-627 rakwb eng Pawel Zukowski verfasserin aut Analysis of Uneven Distribution of Nodes Creating a Percolation Channel in Matrices with Translational Symmetry for Direct Current 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier 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. metrological approach uncertainty of measurement percolation phenomenon percolation threshold Monte Carlo method computer simulation Technology T Pawel Okal verfasserin aut Konrad Kierczynski verfasserin aut Przemyslaw Rogalski verfasserin aut Vitalii Bondariev verfasserin aut In Energies MDPI AG, 2008 16(2023), 22, p 7647 (DE-627)572083742 (DE-600)2437446-5 19961073 nnns volume:16 year:2023 number:22, p 7647 https://doi.org/10.3390/en16227647 kostenfrei https://doaj.org/article/3655a36adff94d83b1b72554a9fd6231 kostenfrei https://www.mdpi.com/1996-1073/16/22/7647 kostenfrei https://doaj.org/toc/1996-1073 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2055 GBV_ILN_2108 GBV_ILN_2111 GBV_ILN_2119 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 16 2023 22, p 7647
allfieldsSound	10.3390/en16227647 doi (DE-627)DOAJ101249985 (DE-599)DOAJ3655a36adff94d83b1b72554a9fd6231 DE-627 ger DE-627 rakwb eng Pawel Zukowski verfasserin aut Analysis of Uneven Distribution of Nodes Creating a Percolation Channel in Matrices with Translational Symmetry for Direct Current 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier 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. metrological approach uncertainty of measurement percolation phenomenon percolation threshold Monte Carlo method computer simulation Technology T Pawel Okal verfasserin aut Konrad Kierczynski verfasserin aut Przemyslaw Rogalski verfasserin aut Vitalii Bondariev verfasserin aut In Energies MDPI AG, 2008 16(2023), 22, p 7647 (DE-627)572083742 (DE-600)2437446-5 19961073 nnns volume:16 year:2023 number:22, p 7647 https://doi.org/10.3390/en16227647 kostenfrei https://doaj.org/article/3655a36adff94d83b1b72554a9fd6231 kostenfrei https://www.mdpi.com/1996-1073/16/22/7647 kostenfrei https://doaj.org/toc/1996-1073 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2055 GBV_ILN_2108 GBV_ILN_2111 GBV_ILN_2119 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 16 2023 22, p 7647
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author	Pawel Zukowski
spellingShingle	Pawel Zukowski misc metrological approach misc uncertainty of measurement misc percolation phenomenon misc percolation threshold misc Monte Carlo method misc computer simulation misc Technology misc T Analysis of Uneven Distribution of Nodes Creating a Percolation Channel in Matrices with Translational Symmetry for Direct Current
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topic_title	Analysis of Uneven Distribution of Nodes Creating a Percolation Channel in Matrices with Translational Symmetry for Direct Current metrological approach uncertainty of measurement percolation phenomenon percolation threshold Monte Carlo method computer simulation
topic	misc metrological approach misc uncertainty of measurement misc percolation phenomenon misc percolation threshold misc Monte Carlo method misc computer simulation misc Technology misc T
topic_unstemmed	misc metrological approach misc uncertainty of measurement misc percolation phenomenon misc percolation threshold misc Monte Carlo method misc computer simulation misc Technology misc T
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title	Analysis of Uneven Distribution of Nodes Creating a Percolation Channel in Matrices with Translational Symmetry for Direct Current
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title_full	Analysis of Uneven Distribution of Nodes Creating a Percolation Channel in Matrices with Translational Symmetry for Direct Current
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title_sort	analysis of uneven distribution of nodes creating a percolation channel in matrices with translational symmetry for direct current
title_auth	Analysis of Uneven Distribution of Nodes Creating a Percolation Channel in Matrices with Translational Symmetry for Direct Current
abstract	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.
abstractGer	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.
abstract_unstemmed	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.
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title_short	Analysis of Uneven Distribution of Nodes Creating a Percolation Channel in Matrices with Translational Symmetry for Direct Current
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