The effective impedances of infinite ladder networks and Dirichlet problem on graphs
Abstract
We calculate effective impedances of infinite $LC$ and $CL$ ladder networks as limits of effective impedances of finite network approximations, using a new method, which involves precise mathematical concepts. These concepts are related to the classical differential operators on weighted graphs. As an auxiliary result, we solve a discrete boundary value Dirichlet problem on a finite ladder network.
 Publication:

arXiv eprints
 Pub Date:
 April 2020
 arXiv:
 arXiv:2004.09284
 Bibcode:
 2020arXiv200409284M
 Keywords:

 Mathematics  Combinatorics;
 Mathematical Physics;
 05C22;
 34B45;
 39A12;
 94C05;
 78A25
 EPrint:
 18 pages, 10 figures