Power dissipation in fractal AC circuits. (14th July 2017)

• Record Type: Journal Article
• Authors: Chen, Joe P; Rogers, Luke G; Anderson, Loren; Andrews, Ulysses; Brzoska, Antoni; Coffey, Aubrey; Davis, Hannah; Fisher, Lee; Hansalik, Madeline; Loew, Stephen; Teplyaev, Alexander
• Is Part Of: Journal of physics. Volume 50:Number 32(2017)
• Publication Date: 2017-07-14
• Subjects: AC circuit -- complex impedances -- harmonic functions -- analysis on fractals; Mathematical physics -- Periodicals; Statistical physics -- Periodicals; Quantum theory -- Periodicals; Matter -- Properties -- Periodicals; 530.105
• DOI: 10.1088/1751-8121/aa7a66
• Languages: English
• ISSNs: 1751-8113

Abstract

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 .