George Frantziskonis, Professor, University of Arizona
In late 1980s and early 1990s, there were many scientific papers published about so-called surface instabilities in rocks, since surface spalling in deep mines often results in death of miners and extensive physical damage. Even though the problem was theoretically and experimentally well understood, solutions of the instability problems were very difficult to obtain. A colleague of mine had obtained specific solutions, and at a conference he showed me the relevant derivations that were done by hand and filled up a whole notebook. Soon after that I found general solutions, using Mathematica, and my colleague’s solution was a very special case. At a conference I showed him the solutions, and he asked if his solutions were correct, given the extend of the hand derivations. He was so relieved to learn there was no mistake in his derivations.
These are some relevant papers where Mathematica appears either in the acknowledgments or in the citations: “Heterogeneity and Implicated Surface Effects: Statistical, Fractal Formulation and Relevant Analytical Solution” and
“On the Possibly Multifractal Properties of Dissipated Energy in Brittle Materials.” After that, practically every paper I have published includes results obtained by Mathematica in one way or another.
Lately I have become an advanced amateur photographer, so I use Mathematica to project photos on various types of 3D surfaces, and have also made attempts to create 3D structure from 2D photos using Mathematica.