Effective resistances of two dimensional resistor networks
| Autor: | Himadri Barman, Rajat Chandra Mishra |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Physics
Hexagonal crystal system Network on 05 social sciences Mathematical analysis Lattice (group) 050301 education General Physics and Astronomy Classical Physics (physics.class-ph) FOS: Physical sciences Physics - Classical Physics 01 natural sciences law.invention law Simple (abstract algebra) Consistency (statistics) 0103 physical sciences Resistor 010306 general physics 0503 education Network analysis |
| DOI: | 10.48550/arxiv.2007.10796 |
| Popis: | We investigate the behavior of two dimensional resistor networks, with finite sizes and different kinds (rectangular, hexagonal, and triangular) of lattice geometry. We construct the network by having a network-element repeat itself $L_x$ times in $x$-direction and $L_y$ times in the $y$-direction. We study the relationship between the effective resistance ($R_\mathrm{eff}$) of the network on dimensions $L_x$ and $L_y$. The behavior is simple and intuitive for a network with rectangular geometry, however, it becomes non-trivial for other geometries which are solved numerically. We find that $R_\mathrm{eff}$ depends on the ratio $L_x/L_y$ in all the three studied networks. We also check the consistency of our numerical results experimentally for small network sizes. Comment: 27 figures |
| Databáze: | OpenAIRE |
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