Abstract
It is known that electrical networks with resistors are related to the Laplace operator and random walk on weighted graphs. In this paper we consider more general electrical networks with coils, capacitors, and resistors. We give two mathematical models of such networks: complex-weighted graphs and graphs with weights from the ordered field of rational functions. The notion of effective impedance in both approaches is defined.
| Original language | English |
|---|---|
| Pages (from-to) | 723-741 |
| Number of pages | 19 |
| Journal | Operators and Matrices |
| Volume | 14 |
| Issue number | 3 |
| DOIs | |
| Publication status | Published - 2020 |
Keywords
- weighted graphs
- electrical networks
- Laplace operator
- ordered field of rational functions
- Ordered field of rational functions
- Weighted graphs
- Electrical network
ASJC Scopus subject areas
- Analysis
- Algebra and Number Theory
Fields of Expertise
- Information, Communication & Computing