Next: References
Up: Making and analyzing
Previous: Examples of histograms
If a phase percolates in a given direction in a microstructure, that means that the phase is continuous from one side of the microstructure to the other in that direction. This is important topological information and affects greatly the ability of the phase to affect the overall properties [9,10,24,42]. There are two auxiliary programs included with the finite element and finite difference programs, BURN2D.F and BURN3D.F, for computing phase percolation in 2-D and 3-D using the burning algorithm [42]. Given a phase label, these programs check for continuity of this phase in each of the principal directions.
The burning algorithm in principle "lights" a fire at one end of the microstructure, in the chosen phase, and lets the fire burn in that phase until there are no more pixels of that phase left unburned, at least ones that the fire can get to via nearest-neighbor connections. The other side of the microstructure is then checked to see if the fire reached there or not. If it did, then the chosen phase must be connected from one side to the other. If it did not, then the phase does not percolate.
The microstructure is read into the programs. As these are simple programs, the comments contained in the programs should suffice to describe their operation. These programs can be used to analyze an original microstructure. They can also be used to analyze a current or stress map, in the following way. Suppose we would like to know if the high currents in a current map are limited to a few hot spots, or are continuous across the microstructure. One could create an image where all pixels with currents above a certain value are given a phase label of one, and all other pixels a phase label of two. Then the burning programs could be used to see if the high current phase percolated or not.
The listing for BURN3D.F is given in Sec. 9.3.7. BURN2D.F is similar to the 3-D version.