In recent years, there has been much improvement in radiation therapy delivery systems used in the treatment of cancer; however, in order to fully exploit this enhancement, the computational methodology associated with radiation therapy must improve as well. It is important to accurately determine where the radiation is depositing its energy within the patient. The treatment should allow for the maximal dose at the tumor site, while minimal radiation dose to the surrounding health tissue and structures. In the Computational Reactor and Medical Physics Group here at Georgia Tech, a heterogeneous coarse-mesh transport method (COMET) has been developed for neutron transport to analyze whole-core criticality. COMET decomposes a large, heterogeneous global problem into a set of small fixed source local problems. Response functions, or rather detailed solutions, are obtained for each unique local problem. These response functions are all precomputed and stored in a library. The solution to the global solution is then bound by a linear superposition of the local problems. In this project, COMET is applied for the first time to the transport of photons in human tissues. The parameter of interest in this case is the amount of energy (dose) deposition in tissue. To determine the strengths and weaknesses of the current system, it is important to construct benchmark problems for comparison. This project will encompass a number of benchmarks. The first will involve modeling a simple two-dimensional water phantom. A second benchmark problem involves the use of a heterogeneous phantom composed of different tissues. A third benchmark problem will involve transport through slabs of aluminum, water, and lung tissue. A last, more clinically relevant benchmark problem will involve using the data from a CT scan. For each of these cases the results from COMET will be compared to the computational results obtained from EGSnrc, a Monte Carlo particle transport code. In this study, it was found that generally the results using COMET were comparable with those obtained from the Monte Carlo solutions of EGSnrc. The COMET results were also typically found thousands of times faster than the reference solution.

A pulse height tally response expansion (PHRE) method is developed for detectors. By expanding the incident flux at the detector window/surface, a set of response functions is constructed via Monte Carlo estimators for pulse height tallies. B-spline functions are selected to perform the expansion of the response functions as well as for the expansion of the incident flux in photon energy. The method is verified for several incident flux spectra on a CsI(Na) detector. Results are compared to the solutions generated using direct Monte Carlo calculations. It is found that the method is several orders faster than MCNP5 while maintaining paralleled accuracy.

Thesis (Ph.D.). / Written for the Dept. of Physics. Title from title page of PDF (viewed 2009/06/08). Includes bibliographical references.

published_or_final_version / Physics / Doctoral / Doctor of Philosophy

published_or_final_version / abstract / Dentistry / Doctoral / Doctor of Philosophy

published_or_final_version / abstract / Physics / Master / Master of Philosophy

published_or_final_version / abstract / Physics / Doctoral / Doctor of Philosophy

The primary purpose of this study is to model the water vapor flow produced by a comet impact on the Moon using the Direct Simulation Monte Carlo (DSMC) method. Toward that end, our DSMC solver was modified in order to model the cometary water from the time of impact until it is either destroyed due to escape or photodestruction processes or captured inside one of the lunar polar cold traps. In order to model the complex flow induced by a comet impact, a 3D spherical parallel version of the DSMC method was implemented. The DSMC solver was also modified to take as input the solution from the SOVA hydrocode for the impact event at a fixed interface. An unsteady multi-domain approach and a collision limiting scheme were also added to the previous implementation in order to follow the water from the continuum regions near the point of impact to the much later rarefied atmospheric flow around the Moon. The present implementation was tested on a simple unsteady hemispherical expansion flow into a vacuum. For these simulations, the data at the interface were provided by a 1D analytical model instead of the SOVA solution. Good results were obtained downstream of the interface for density, temperature and radial velocity. Freezing of the vibrational modes was also observed in the transitional regime as the flow became collisionless. The 45° oblique impact of a 1 km radius ice sphere at 30 km/s was simulated up to several months after impact. Most of the water crosses the interface under 5 s moving mostly directly downstream of the interface. Most of the water escapes the gravity well of the Moon within the first few hours after impact. For such a comet impact, only ~3% of the comet mass remains on the Moon after impact. As the Moon rotates, the molecules begin to migrate until they are destroyed or captured in a cold trap. Of the 3% of the water remaining on the Moon after impact, only a small fraction, ~0.14% of the comet mass, actually reaches the cold traps; nearly all of the rest is photo-destroyed. Based on the surface area of the cold traps used in the present simulations, ~1 mm of ice would have accumulated in the polar cold traps after such an impact. Estimates for the total mass of water accumulated in the polar cold traps over one billion years are consistent with recent observations. / text

In chapter one, we explain briefly the continuum limit, scaling, and high temperature expansion of critical phenomena, Monte Carlo algorithms and fitting. In chapter two, different continuum limits of the Ising model in dimensions (D) 2, 3 and 4 are investigated numerically. The data indicate that triviality occurs for D = 4 and fails for D < 4 in each limit. In chapter three, a relation between the critical exponents of the leading and confluent scaling terms is derived using the finite size scaling argument. We also determine the new scaling variable of the 4D Ising model based on a new Monte Carlo simulation data. In chapter four, a Monte Carlo study of two dimensional diluted Ising systems is reported. It is shown that regular dilution does not affect critical exponents, while a random one does, with critical exponents varying continuously with impurity concentration. The importance of fluctuations in producing such effects is emphasized. In chapter five, a different point of view regarding the critical exponent of the specific heat of the 3D Ising model is presented. Based on the analysis of high temperature expansion, finite size scaling and Monte Carlo data in the symmetric phase of the 3D Ising model, it is shown that logarithmic scaling behavior of specific heat is more consistent than power scaling behavior.

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