Localization on Snowflake Domains

Abstract

The geometric features of the square and triadic Koch snowflake drums are compared using a position entropy defined on the grid points of the discretizations (pre-fractals) of the two domains. Weighted graphs using the geometric quantities are created and random walks on the two pre-fractals are performed. The aim is to understand if the existence of narrow channels in the domain may cause the `localization' of eigenfunctions.

arXiv comment37 pages, 22 figures