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Percolation theory enters in various areas of research including critical phenomena and phase transitions. Bond-site percolation is a generalization of pure percolation motivated by the fact that bond-site is close to many physical realities. This work relies on a numerical study of percolation in lattices. A lattice is a regular pattern of sites also known as nodes or vertices connected by bonds also known as links or edges. Sites may be occupied or unoccupied, where the concentration ps is the fraction of occupied sites. The quantity pb is the fraction of open bonds. A cluster is a set of occupied sites connected by opened bonds. The bond-site percolation problem is formulated as follows: we consider an infinite lattice whose sites and bonds are at random or correlated and either allowed or forbidden with probabilities ps and pb that any site and any bond are occupied and open respectively. If those probabilities are small, there appears a sprinkling of isolated clusters each consisting of occupied sites connected by open bonds surrounded by numerous unoccupied sites. As the probabilities increase, reaching critical values above which there is an infinitely large cluster, then percolation is taking place. This means that one can cross the entire lattice by going successively from one occupied site connected by a opened bond to a neighbouring occupied site. The sudden onset of a spanning cluster happens at particular values of ps and pb, called the critical concentrations. Quantities related to cluster configuration (mean cluster and correlation length) and individual cluster structure (size and gyration radius of clusters ) are determined and compared for different models. In our studies, the Monte Carlo approach is applied while some authors used series expansion and renormalization group methods. The contribution of this work is the application of models in which the probability of opening a bond depends on the occupancy of sites. Compared with models in which probabilities of opening bonds are uncorrelated with the occupancy of sites, in the suppressed bond-site percolation, the higher site occupancy is needed to reach percolation. The approach of suppressed bond-site percolation is extended by considering direction of percolation along bonds (directed suppressed bond-site percolation). Fundamental results for models of suppressed bond-site percolation and directed suppressed bond-site percolation are the numerical determination of phase boundary between the percolating and non-percolating regions. Also, it appears that the spanning cluster around critical concentration is independent on models. This is an intrinsic property of a system. / Thesis (Ph.D.)-University of KwaZulu-Natal, Pietermaritzburg, 2007.

A large MULANA based analysis package, written in FORTRAN, for computing the cross section for proton - nucleus collisions at 400 GeV/c momentum from data taken in experiment E609 at FNAL, was implemented on a Z-386, 16 MHz microcomputer workstation featuring an 80 Mbyte hard drive, and a three Gbyte 8-mm Exebyte tape drive, based in the Ball State High Energy Physics Laboratory, in a feasibility study of conducting such analysis on a workstation as a viable alternative and/or adjunct to the Ball State University VAX system. One of 40 large 1600 bpi 9-track data tapes from Experiment 609 provided the data file for the computation. The analysis package was first run on the VAX system. Special problems solved in connection with using the software package included converting the large data file to a suitable form for use at the workstation, transporting that file from the VAX to the workstation, modifying the VAX FORTRAN software package for implementation in the OS/2 workstation operating system environment, and graphical exposition of the results. With the results of conducting the analysis on the VAX system serving as a benchmark, it was determined first that the quantitative analysis results were identical, second, that computing times were similar, and third that the workstation provided unique conveniences. Overall, the results showed that the workstation is a reasonable alternative to using the VAX for High Energy Physics analysis work but also suggest the attractiveness of using similar but faster workstations in the near future. / Department of Physics and Astronomy

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