Modelling transport in disordered media via diffusion on fractals

Ben Hambly and Owen Dafydd Jones

Abstract: When viewed at an appropriate scale, a disordered medium can behave as if it is strictly less than three dimensional. As fractals typically have non-integer dimensions, they are natural models for disordered media, and diffusion on fractals can be used to model transport in disordered media. In particular, such diffusion processes can be used to obtain bounds on the fundamental solution to the heat equation on a fractal. In this paper we review the work in this area and describe how bounds on branching processes lead to bounds on heat kernels.

Acknowledgement: This worked was funded by the Australian Research Council.

The authors:

• Ben Hambly, Department of Mathematics and Statistics, The University of Edinburgh. bmh@maths.ed.ac.uk
• Owen Jones, Discipline of Mathematics, The University of Queensland. Owen.Jones@maths.anu.edu.au

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Last modified: 28th April 1997