Effective electrical conductivity of random resistor networks generated using a Poisson--Voronoi tessellation
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866913164736593920 |
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| author | Tarasevich, Yuri Yu. Vodolazskaya, Irina V. Eserkepov, Andrei V. |
| author_facet | Tarasevich, Yuri Yu. Vodolazskaya, Irina V. Eserkepov, Andrei V. |
| contents | We studied the effective electrical conductivity of dense random resistor networks (RRNs) produced using a Voronoi tessellation when its seeds are generated by means of a homogeneous Poisson point process in the two-dimensional Euclidean space. Such RRNs are isotropic and in average homogeneous, however, local fluctuations of the number of edges per unit area are inevitably. These RRNs may mimic, e.g., crack-template-based transparent conductive films. The RRNs were treated within a mean-field approach (MFA). We found an analytical dependency of the effective electrical conductivity on the number of conductive edges (resistors) per unit area, $n_\text{E}$. The effective electrical conductivity is proportional to $\sqrt{n_\text{E}}$ when $n_\text{E} \gg 1$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2310_03405 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Effective electrical conductivity of random resistor networks generated using a Poisson--Voronoi tessellation Tarasevich, Yuri Yu. Vodolazskaya, Irina V. Eserkepov, Andrei V. Disordered Systems and Neural Networks Statistical Mechanics We studied the effective electrical conductivity of dense random resistor networks (RRNs) produced using a Voronoi tessellation when its seeds are generated by means of a homogeneous Poisson point process in the two-dimensional Euclidean space. Such RRNs are isotropic and in average homogeneous, however, local fluctuations of the number of edges per unit area are inevitably. These RRNs may mimic, e.g., crack-template-based transparent conductive films. The RRNs were treated within a mean-field approach (MFA). We found an analytical dependency of the effective electrical conductivity on the number of conductive edges (resistors) per unit area, $n_\text{E}$. The effective electrical conductivity is proportional to $\sqrt{n_\text{E}}$ when $n_\text{E} \gg 1$. |
| title | Effective electrical conductivity of random resistor networks generated using a Poisson--Voronoi tessellation |
| topic | Disordered Systems and Neural Networks Statistical Mechanics |
| url | https://arxiv.org/abs/2310.03405 |