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A Note on Stereology

The best place to start is Wikipedia: http://en.wikipedia.org/wiki/Stereology.

Most active research in stereology is done in medical and biological community.

In engineering, in USA, Prof. Rhines and Prof. de Hoff, both of the University of Florida at Gainesville did a lot of pioneering work. The stereological researchers active in engineering in USA are mostly limited to the "progenies" of the Florida school. These include (and I quote off-hand): Prof. Arun Gokhale of GeogiaTech and Prof. Burton Patterson of the University of Alabama at Birmingham (who was my guide at my first attempt at PhD). 

One neat thing about stereological models in diffusion-related phenomena (such as, for instance, theories of sintering in powder metallurgical components) is that the stereological models are, as a rule, far closer to actual physical reality as compared to the mean field theories, because the former have been *local* in nature. In contrast, the mean-field models are more traditional, more popular---and more approximate, because they are less amenable to a direct description in terms of actual diffusive fluxes of the actually diffusing species (atoms).

Since stress concentration is a highly local phenomenon (think St. Venant's principle or the local crack deflection near an inclusion), it would be desirable to have a purely local model for stress analysis, so as to better model the local stress variations at and due to, say, partially debonded interfaces in composites.

To the best of my knowledge, none has put forth something like a truly local model of stress analysis. It will be a wonderful and practically useful innovation to have it.

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