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Circles of equal radii randomly placed on a plane: some rigorous results, asymptotic behavior, and application to transparent electrodes

Akhunzhanov, R K ; Tarasevich, Y Y ; Vodolazskaya, I V

Journal of statistical mechanics, 2020-03, Vol.2020 (3), p.33202 [Periódico revisado por pares]

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Título:
Circles of equal radii randomly placed on a plane: some rigorous results, asymptotic behavior, and application to transparent electrodes
Autor: Akhunzhanov, R K ; Tarasevich, Y Y ; Vodolazskaya, I V
É parte de: Journal of statistical mechanics, 2020-03, Vol.2020 (3), p.33202
Notas: JSTAT_016P_0819
Descrição: We consider N circles of equal radii, r, having their centers randomly placed within a square domain of size with periodic boundary conditions (). When two or more circles intersect each other, each circle is divided by the intersection points into several arcs. We found the exact length distribution of the arcs. In the limiting case of dense systems and large size of the domain ( in such a way that the number of circle per unit area, n = N/L2, is constant), the arc distribution approaches the probability density function (PDF) , where is the central angle subtended by the arc. This PDF is then used to estimate the sheet resistance of transparent electrodes based on conductive rings randomly placed onto a transparent insulating film.
Editor: IOP Publishing and SISSA
Idioma: Inglês

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