2016/05/31 by Joe P. Chen, Joe P Chen, Luke G. Rogers +11 · 12 citations
Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Dissipation #Distribution (mathematics) #Electrical impedance #Electronic circuit #Energy (signal processing) #Fractal #Graph theory and applications #Power (physics) #Theoretical and Computational Physics #Topology (electrical circuits) #math-ph #math.MP #msc:28A80 #msc:78A02 #msc:94C05
paper · pdf · doi:10.1088/1751-8121/aa7a66
published in Journal of Physics A Mathematical and Theoretical 50(32), 325205 (Institute of Physics) · v2: 16 pages, 8 figures. See also the recent preprint arXiv:1701.08039
openalex created_date 2016/06/24 · arxiv created 2017/02/12 · openalex publication_date 2017/06/20 · arxiv updated 2017/07/17 · openalex updated_date 2026/08/05
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 .