Abstract
Percolation is the study of random networks and their nature of connectivity. An exponential relationship between the percolation threshold and the aspect ratio of a shape is observed within this paper. Matlab simulations and a novel experimental method are utilized to determine the percolation threshold across a conductive sheet as triangles of variable aspect ratios are cut with a Universal Laser System X2-600 100 Watt CO2 laser. Resistance is measured as a voltage of 100mV is applied across the conductive sheet of aluminum coated Mylar film. This data is then analyzed to yield the percolation threshold relating to a triangle with a specified aspect ratio. We establish an equilateral triangle to have an aspect ratio of one.
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More From: The Journal of Undergraduate Research at the University of Illinois at Chicago
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