Percolation threshold of the permeable disks on the projective plane

International Workshop on Physical and Chemical Processes in Atomic Systems

Borman, V.D.^1 ; Grekhov, A.M.^1 ; Tronin, I.V.^1 ; Tronin, V.N.^1

National Research Nuclear University MEPhI, Moscow Engineering Physics Institute, Kashirskoe highway 31, Moscow

115409, Russia^1

关键词: Continuum percolation;    Klein bottles;    Percolation thresholds;    Projective planes;    Two-dimensional problem;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/751/1/012036/pdf
DOI  :  10.1088/1742-6596/751/1/012036

来源: IOP

【 摘 要 】

The percolation threshold and wrapping probability for the two-dimensional problem of continuum percolation on the projecive plane have been calculated by the Monte Carlo method with the Newman-Ziff algorithm for completely permeable disks. It has been shown that the percolation threshold of disks on the projective plane coincides with the percolation threshold of disks on the surfaces of a torus and Klein bottle, indicating that this threshold is topologically invariant.