This section summarizes the contents of the remainder chapters of this dissertation, which includes an additional five chapters, two appendices, and a bibliography.
In chapter II we derive equations for Monte Carlo eigenvalue calculation methods. It is important to understand the basic Monte Carlo eigenvalue algorithms before one studies Monte Carlo eigenvalue perturbation methods. Both the source iteration technique and the fission matrix approach are described in this chapter. All the statistical quantities associated with Monte Carlo eigenvalue calculation are also presented. Numerical results are shown for both the source iteration and the fission matrix methods. We also investigate two variations of the fission matrix algorithm, the cycle fission matrix algorithm and the cumulative fission matrix algorithm.
Chapter III explains in detail the correlated sampling technique. We show that subtracting two independent Monte Carlo simulations to evaluate perturbation effects is problematical for realistic problems. Next, the mathematical basis behind the correlated sampling technique is established. We also introduce the idea of performing the Monte Carlo simulation in an artificial reference system which is different from both the unperturbed and perturbed systems. We show that combining the correlated sampling and source iteration techniques to calculate perturbation effects fails, whereas combining the correlated sampling and fission matrix techniques can successfully evaluate perturbation effects in eigenvalue. Numerical results are shown to support all the theories developed in this chapter.
Chapter IV explains how the ideas of the fission matrix method, correlated sampling, and the artificial reference system generated in the last two chapters can be combined to develop a multiple perturbation Monte Carlo method. This method allows the calculation of multiple perturbations of the eigenvalue of the Boltzmann transport equation from a single Monte Carlo simulation, and results in significant savings in overall computational effort. The extension of this method to the multigroup case is also explained. Numerical examples are provided to show the accuracy and efficiency of this multiple perturbation method.
Chapter V deals with the implementation of particle transport Monte Carlo algorithms on parallel computers. We explain the basic concepts behind Monte Carlo parallel algorithms used to simulate particle transport. Quantities such as speedup, efficiency, parallel and serial fractions, and communication times are defined specifically for Monte Carlo parallel algorithms. Results of implementing a photon transport algorithm on the KSR-1 and BBN Butterfly computers, and three Monte Carlo eigenvalue algorithms (source iteration, fission matrix and correlated sampling) on the IBM-SP2 are shown.
Chapter VI contains the conclusions of this research and recommendations for future work. We explain what has been achieved in this dissertation research. We summarize the different theories that lead to the development of the numerical technique for multiple eigenvalue perturbation calculations. Areas that need more study and could lead to further research topics are also addressed.
In appendix A we perform a computational parametric study on the choice of the artificial reference system different from both the unperturbed and perturbed systems. In this dissertation work, the cross sections of the artificial reference system were chosen as the average of the cross sections for the unperturbed and of all perturbed systems. This parametric study of appendix A is based only on computational experiments. We believe that this study requires more theoretical investigation, which we leave as one of the future extensions of this research.
In appendix B we perform accuracy test for the TWODANT code. We vary the mesh
size and the quadrature sets for a given problem to determine the accuracy of
TWODANT eigenvalue results. These results are used in determining the number
of significant figures necessary in TWODANT calculated 
Ks against which
the Monte Carlo results are compared.