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arXiv · 1605.03890

Power dissipation in fractal AC circuits

Joe P. Chen·Luke G. Rogers·Loren Anderson·Ulysses Andrews·Antoni Brzoska·Aubrey Coffey·Hannah Davis·Lee Fisher·Madeline Hansalik·Stephew Loew·Alexander Teplyaev
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Abstract

We extend Feynman's analysis of an infinite ladder circuit to fractal circuits, providing examples in which fractal circuits constructed with purely imaginary impedances can have characteristic impedances with positive real part. Using (weak) self-similarity of our fractal structures, we provide algorithms for studying the equilibrium distribution of energy on these circuits. This extends the analysis of self-similar resistance networks introduced by Fukushima, Kigami, Kusuoka, and more recently studied by Strichartz et al.

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Joe P. Chen, Luke G. Rogers, Loren Anderson, Ulysses Andrews, Antoni Brzoska, Aubrey Coffey, Hannah Davis, Lee Fisher, Madeline Hansalik, Stephew Loew, Alexander Teplyaev. 2017-02-12. Power dissipation in fractal AC circuits. https://doi.org/10.1088/1751-8121%2Faa7a66

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