One-time step spread modification in simple cubic lattice site percolation

Date

4-2009

Degree

Bachelor of Science in Applied Physics

College

College of Arts and Sciences (CAS)

Adviser/Committee Chair

Allan L. Alinea

Abstract

The effect of one-time step spread modification on the total time of percolation in a simple cubic lattice (3D) for varying probability of occupancy p was determined. Twenty-six modifications, Corresponding to the perturbation of percolation to all nearest neighboring sites, were introduced. The resulting deviations from the unmodified approach were investigated. Simulation results suggested that the one-time step modification tends to alter the total time of percolation with respect to the regular approach. These deviations in the total time was found to be significant at (i) p > pc for South East (1,-1,0), (ii) p pc for North East (1,1,0), and (iii) p= p= and p 1 for East (1,0,0) modification, where pc is the critical probability of occupancy. The effect of one-time step modification on the total time of percolation is dependent on the symmetry of the modification with respect to the lattice. For large lattice sizes (100x100.100), this trend of time deviation with respect to the probability of occupancy is similar for modifications that are symmetric with respect to the vertical axis of the lattice. No significant relationship was observed between the time deviation due to modification and its point of introduction in the lattice. It was also found that the increase in lattice dimensionality, from a square (2D) to a simple cubic (3D) lattice, does not affect the total time of percolation with respect to the one-time step modification. PACS: 64.60.ah (Percolation), 02.50.Ey (Stochastic processes), 02.60.Cb (Numerical simulation)

Language

English

Location

UPLB Main Library Special Collections Section (USCS)

Call Number

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Document Type

Thesis

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