Localization on Snowflake Domains

Details Localization on Snowflake Domains Localization on Snowflake Domains

2006-09-28

arxiv.org/abs/math/0609798v1

Mathematics

Numerical Analysis

37 pages, 22 figures

Scientific paper

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.

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