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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 …
Spectral Dimensionality Of Random Superconducting Networks, Anthony Roy Day, W. Xia, M. F. Thorpe
Spectral Dimensionality Of Random Superconducting Networks, Anthony Roy Day, W. Xia, M. F. Thorpe
Anthony Roy Day
We compute the spectral dimensionality d-tilde of random superconducting-normal networks by directly examining the low-frequency density of states at the percolation threshold. We find that d-tilde=4.1±0.2 and 5.8±0.3 in two and three dimensions, respectively, which confirms the scaling relation d-tilde=2d/(2-s/ nu ), where s is the superconducting exponent and nu the correlation-length exponent for percolation. We also consider the one-dimensional problem where scaling arguments predict, and our numerical simulations confirm, that d-tilde=0. A simple argument provides an expression for the density of states of the localized high-frequency modes in this special case. We comment on the connection between our calculations …
Splay Rigidity In The Diluted Central Force Elastic Network, Anthony Roy Day, A.-M. S. Tremblay, R. R. Tremblay
Splay Rigidity In The Diluted Central Force Elastic Network, Anthony Roy Day, A.-M. S. Tremblay, R. R. Tremblay
Anthony Roy Day
A Comment on the Letter by Wang and Harris, Phys. Rev. Lett. 55, 2459 (1985).