English

Power dissipation in fractal AC circuits

Mathematical Physics 2017-07-17 v2 math.MP

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.

Keywords

Cite

@article{arxiv.1605.03890,
  title  = {Power dissipation in fractal AC circuits},
  author = {Joe P. Chen and Luke G. Rogers and Loren Anderson and Ulysses Andrews and Antoni Brzoska and Aubrey Coffey and Hannah Davis and Lee Fisher and Madeline Hansalik and Stephew Loew and Alexander Teplyaev},
  journal= {arXiv preprint arXiv:1605.03890},
  year   = {2017}
}

Comments

v2: 16 pages, 8 figures. See also the recent preprint arXiv:1701.08039

R2 v1 2026-06-22T13:59:33.419Z