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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2409.00229 |
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| _version_ | 1866914931823083520 |
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| author | Anjos, Petrus H. R. dos Oliveira, Fernando A. Azevedo, David L. |
| author_facet | Anjos, Petrus H. R. dos Oliveira, Fernando A. Azevedo, David L. |
| contents | 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 $α=\frac{r_2}{r_1} \in [0,+\infty)$, 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_00229 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Fractality in resistive circuits: The Fibonacci resistor networks Anjos, Petrus H. R. dos Oliveira, Fernando A. Azevedo, David L. Statistical Mechanics 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 $α=\frac{r_2}{r_1} \in [0,+\infty)$, 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. |
| title | Fractality in resistive circuits: The Fibonacci resistor networks |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2409.00229 |