The Effect of Different Geometries on Percolation in Two Dimensions

A. Morgan, J. Wedell, A. Feinerman
2013 The Journal of Undergraduate Research at the University of Illinois at Chicago  
Using the model simulation developed by Weddell and Feinerman, this study found results for the percolation threshold as a function of aspect ratio for rectangle shaped holes and then compared these results to Weddell et. al.'s elliptical ones.1 We developed a slightly different experimental set-up than Weddell, proving that this method for collecting percolation data is repeatable and valid. The percolation threshold for both shapes has been found to exhibit a similar trend - as aspect ratio
more » ... creases, percolation threshold increases. At small aspect ratios, when both shapes are almost indistinguishable lines, the percolation threshold results are very similar. For larger aspect ratios, the differences in percolation threshold are much greater. More shapes need to be considered, but these results imply that there exists a point at which the aspect ratio of a shape does influence the percolation threshold.
doi:10.5210/jur.v6i1.7517 fatcat:qcybhqttzfayja7zzu5nqvdhva