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When a microstructure is analyzed, then all the local currents/stresses/strains are available, since the full problem has been solved for every pixel. This information can be used to generate pictures or maps of what a quantity looks like throughout a microstructure. This is useful qualitative information. The same information can be used to generate histograms, or distribution functions, of a quantity of interest, which is a more rigorous way of looking at the same data. A histogram can give information on current or stress distributions and moments of these distributions. The basic kind of graph has area or volume fraction as the ordinate, and current or stress as the abscissa. A point with coordinates (g,p) means that a fraction p of the system has property g.
It should be noted that system averages of current or stress, that define the effective conductivity or elastic moduli, are generally quite reliable and accurate, as has been seen in the examples in Section 5. However, the actual pixel-by-pixel values of current or stress can be somewhat off, due mostly to discretization errors and digital boundaries. At a boundary which should be curved, locally one cannot have anything but flat pixel boundaries. This can throw off some of the values near the boundary.