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Universal Conductivity Curve For A Plane Containing Random Holes., E. J. Garboczi, M. F. Thorpe, M. S. Devries, Anthony Roy Day
Universal Conductivity Curve For A Plane Containing Random Holes., E. J. Garboczi, M. F. Thorpe, M. S. Devries, Anthony Roy Day
Anthony Roy Day
This paper examines the general percolation problem of cutting randomly centered insulating holes in a two-dimensional conducting sheet, and explores how the electrical conductivity sigma decreases with the remaining area fraction. This problem has been studied in the past for circular, square, and needlelike holes, using both computer simulations and analog experiments. In this paper, we extend these studies by examining cases where the insulating hole is of arbitrary shape, using digital-image-based numerical techniques in conjunction with the Y- [nabla] algorithm. We find that, within computational uncertainty, the scaled percolation threshold, xc=nc=5.9±0.4, is a universal quantity for all the cases …