Date of Award

Fall 1982

Degree Type

Thesis - Restricted

Degree Name

Master of Science (MS)

Department

Physics

First Advisor

Karioris, Frank G.

Second Advisor

Mendelson, Kenneth S.

Third Advisor

Burch, Thaddeus J.

Abstract

This thesis is a research project under Prof. Frank G. Karioris and Dr. Kenneth S. Mendelson to investigate and to determine the effect of lattice size and of anisotropy on the values obtained for percolation threshold and the critical exponents. Measurements of the electrical resistance along the two principal directions of the network are made for a sequence of fractions of filled sites for each of six sizes of the array . The resistance network acts as an analog computer which instantly solves the N2 simultaneous equations each time the state of any site or groups of sites is changed. The solution is read directly on a digital ohmmeter. Xerox Sigma 9 computer was used in the generation of random numbers and in the analysis, reduction and interpretation of experimental data. There are two rather unique aspects in this study: (1) measurements of conductivities have been made throughout the range in which any conduction occurs on at least 17 samples of a finite sized array, and (2) six different array sizes have been studied. We are not aware of any other studies in the literature in which parameters have been studied over such a range. In many instances data reported here is displayed on three decades of log-log paper whereas most reports in the literature cover approximately one decade. Error bars are used frequently to illustrate the large variance which is observed in conductivity data near the threshold. I~ all instance the values of parameters generated in this study agree very well with values reported in the literature.

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