## Seminario

Data evento:

Wednesday, 18 January, 2017 - 14:00

Alexander Teplyaev

University of Connecticut

Aula 1B1

title: Average power dissipation in AC fractal networks abstract: Energy forms on graphs and on fractals can be interpreted in terms of electric linear networks by assuming that current flows between nodes (vertices) connected by resistors (edges). A resistor is called a dissipative element because there is a loss of energy when an alternating current runs through it. To the contrary, no loss is caused when the current flows through a non-dissipative element such an inductor or a capacitor. In the 60s Feynman described an infinite passive AC linear network (the infinite ladder), whose nodes were connected by inductors and capacitors, that would lead to actual power dissipation at some frequencies. Based on this idea, we study the concept of power dissipation on graphs and fractals associated to passive linear networks with non-dissipative components. We present in detail the so-called Sierpinski ladder fractal network and construct the power dissipation measure associated with continuous potentials in this network and prove it to be continuous as well as singular with respect to an appropriate Hausdorff measure defined on the fractal dust related to the network. The talk will be based on recent results of Patricia Alonso-Ruiz, and earlier preprints arXiv:1507.05682 arXiv:1605.03890