Einstein relation on fractal objects

Uta Renata Freiberg

doi:10.3934/dcdsb.2012.17.509

Article Contents

2012, Volume 17, Issue 2: 509-525. Doi: 10.3934/dcdsb.2012.17.509

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Einstein relation on fractal objects

Uta Renata Freiberg^1,

1.
Universität Siegen, Département für Mathematik, Walter–Flex–Straße 3, D–57068 Siegen

Received: August 2010

Revised: July 2011

Published: March 2012

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Abstract

Many physical phenomena proceed in or on irregular objects which are often modeled by fractal sets. Using the model case of the Sierpinski gasket, the notions of Hausdorff, spectral and walk dimension are introduced in a survey style. These characteristic numbers of the fractal are essential for the Einstein relation, expressing the interaction of geometric, analytic and stochastic aspects of a set.

Keywords:

Mathematics Subject Classification: Primary: 28A80; Secondary: 31C25, 34B45, 35P20, 60J45.

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