Topological Calculus: between Algebraic Topology and Electromagnetic fields

##article.authors##

  • Walter Arrighetti
  • Giorgio Gerosa

##semicolon##

https://doi.org/10.1685/

##article.abstract##

The Topological Calculus, based on Algebraic Topology, is introduced as a discrete Field Theory. Diagonalization of simplicial complex adjacency matrices allows to extract information about domain topology and Helmholtz equation eigenfunctions. Electromagnetic analysis of IFS fractals for Sierpinski gasket/carpet is then carried out: self-similar topology deeply influences the type of e.m. fields, as well as its finite TEM modes (as many as the domain's Euler characteristic; represented by harmonic fields) and self-similar distribution of resonating frequencies. This proves that even in such discrete model many features of guided waves depend on the topology rather than metrics. [DOI: 10.1685 / CSC06013] About DOI

##submission.downloads##

##submissions.published##

2007-10-01

##issue.issue##

##issue.vol## 1 (2006)

##section.section##

Articles

##submission.license##

Authors who submit to this journal agree to the following terms: a) Authors retain copyright over their work, while allowing the SIMAI to place this accepted work under a Creative Commons Attribution License (CC license), which allows others to freely access, use, and share the work, with an acknowledgement of the work's authorship. b) Authors are able to waive the terms of the CC license and enter into separate, additional contractual arrangements for the non-exclusive distribution and subsequent publication of this work (e.g., publish a revised version in a journal, post it to an institutional repository or publish it in a book). with an acknowledgement of its initial publication on “Communications to SIMAI Congress”. c) In addition, authors are encouraged to post and share their work online (e.g., in institutional repositories or on their website).