Research and Teaching Activities

University of Alberta

Fractals

adeeb@ualberta.ca

 

Fractal Stiffness

Most of our attempts to model nature start with that the assumption of continuous fields. However, another modeling attempt is to assume that the rough fragmented nature of our surrounding is the final result of a recursive function whose input is nothing but the output of the previous step.

http://en.wikipedia.org/wiki/Fractal

 

In order to deal with the concept of fractals in the realm of structure mechanics, the stiffness matrix of a fractal-like structure has been investigated. Check the following references:

 Epstein, M. and Adeeb, S.M. (2008). The stiffness of self-similar fractals. International Journal of Solids and Structures, Accepted for Publication.

 Adeeb, S.M. and Epstein, M. (2008). Fractal Elements. Journal of Mechanics of Materials and Structures, Submitted for Publication.

 Epstein, M. and Adeeb, S.M. (2008). Fractal Structural Elements. The Tenth Pan American Congress of Applied Mechanics (PACAM X), January 7-11, Cancun, Mexico.

 

 

Fractal Analysis of Bone

The Fractal Dimension of an object can be a measure of the space filling characteristic of a curve. By studying the edges of an object, the fractal dimension can be a measure of how complex the connectivity of such object is. We are currently working on trying to evaluate whether the fractal dimension is a good measure of the development of bone disease. In other words, can the fractal dimension of bone indicate bone loss?

This project is being conducted by Anthony NG.

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