| Autor: |
Anjos, Petrus H. R. dos, Oliveira, Fernando A., Azevedo, David L. |
| Rok vydání: |
2024 |
| Předmět: |
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| Zdroj: |
Eur. Phys. J. B 97, 121 (2024) |
| Druh dokumentu: |
Working Paper |
| DOI: |
10.1140/epjb/s10051-024-00750-z |
| Popis: |
We propose two new kinds of infinite resistor networks based on the Fibonacci sequence: a serial association of resistor sets connected in parallel (type 1) or a parallel association of resistor sets connected in series (type 2). We show that the sequence of the network's equivalent resistance converges uniformly in the parameter $\alpha=\frac{r_2}{r_1} \in [0,+\infty)$, where $r_1$ and $r_2$ are the first and second resistors in the network. We also show that these networks exhibit self-similarity and scale invariance, which mimics a self-similar fractal. We also provide some generalizations, including resistor networks based on high-order Fibonacci sequences and other recursive combinatorial sequences. |
| Databáze: |
arXiv |
| Externí odkaz: |
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