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A semianalytical technique to study the charged-particle transport in one-dimensional finite media is developed. For this purpose, the transport equation is written in the form of coupled integral equations, separating the spatial and energy-angle transmissions. Legendre polynomial representation for the source, flux, and scattering kernel are used to solve the equations. For evaluation of the spatial transmission, discrete ordinate representation in space, energy, and direction cosine is used for the particle and source flux. The integral equations are then solved by the fast iteration technique. The computer code CHASFIT, written on the basis of the above formulation, is described. The fast convergence of the iteration process which is characteristic of charged-particle transport is demonstrated. Convergence studies are carried out with a number of mesh points and polynomial approximations. The method is applied to study the depth-dose distributions due to 140-, 200-, 300-, 400-, 600-, and 740-MeV protons incident normally on a 30-cm-thick tissue slab. The values of the quality factor at the surface and at 5 cm depth, as well as the total average quality factor, are calculated. The results thus obtained are compared with those predicted by the Monte Carlo method. This method can also be applied to multienergy, multiregion systems with arbitrary degree of anisotropy.

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A mathematical model has been developed for prediction of off axis ratio (OAR), using Wood - Saxon term used to represent nuclear potential. This method has been satisfactorily applied for predicting OAR in case of 60Co γ-rays and high energy X-rays. Investigations are considered upto a depth of 25 cm in the case of 4MV LINAC for which measurements were carried out in our laboratory using indigenously developed Radiation Field Analyzer. For 60Co γ-rays as well as 6 and 18MV LINAC beams we could get off-axis profiles only upto 20 cm. The shift δ between measured and predicted OAR is within ±2 mm except for 20 cm depth near the falling edge of the penumbra, where it is 2.80 mm. Software has been developed in Visual Basic 6 on Windows platform to plot Isodose curves, which is based on the mathematical modeling of OAR and central axis percentage depth dose.

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In this paper, we design and implement a variety of parallel algorithms for both sweep spin selection and random spin selection. We analyze our parallel algorithms on LogP, a portable and general parallel machine model. We then obtain rigorous theoretical runtime results on LogP for all the parallel algorithms. Moreover, a guiding equation is derived for choosing data layouts (blocked vs. stripped) for sweep spin selection. In regard to random spin selection, we are able to develop parallel algorithms with efficient communication schemes. We introduce two novel schemes, namely the FML scheme and the α-scheme. We analyze randomness of our schemes using statistical methods and provide comparisons between the different schemes.

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