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<p>The percolation theory is applied widely to the study of heat transfer and other kinetic processes in systems with disordered structures. This paper develops a phenomenological approach that combines the percolation theory methods and multifractal analysis to model a percolation cluster in 3D infinite medium with multifractal properties. The developed model gives unambiguous numerical values for topology-critical indices and a critical conductivity index. The model reveals new relations between critical indices and defines the threshold conditions that separate the qualitatively-different modes of system behavior in the correlation length scales. The system order parameter has a relation with the golden ratio and this indicates a universal nature of the found relationships.</p>

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Phenomenological approach to finding the critical indices for 3D percolation in multifractal media

  • 期刊论文

  • 发表日期：

    2025年11月1日

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  • B. P. Kolesnikov

摘要

The percolation theory is applied widely to the study of heat transfer and other kinetic processes in systems with disordered structures. This paper develops a phenomenological approach that combines the percolation theory methods and multifractal analysis to model a percolation cluster in 3D infinite medium with multifractal properties. The developed model gives unambiguous numerical values for topology-critical indices and a critical conductivity index. The model reveals new relations between critical indices and defines the threshold conditions that separate the qualitatively-different modes of system behavior in the correlation length scales. The system order parameter has a relation with the golden ratio and this indicates a universal nature of the found relationships.