Some Approximations to the Radiative Transfer Equation and Their Applications

To my parents, Laiping Sheng and Chengai Shi, who offered me unconditional love and support all the way since the beginning of my studies. This brief dedication is not enough room to express my gratitude that they are my parents. ii ACKNOWLEDGEMENTS I would like to thank several people for their help making this thesis possible. First and foremost, my greatest thankfulness goes to my advisor, Professor Weimin Han, for his wise guidance, constant encouragement, and support throughout my time as a graduate researcher. His excellent mentorship will continue to shape my career long after I leave Iowa. I want to personally thank Joe Eichholz for his help on the Matlab and C code used to generate the numerical examples presented in this thesis and valuable discussion on programming techniques. for their time reviewing my work. They have positively influenced me in one way or another throughout my graduate studies. Finally, I would like to thank my family for their endless encouragement. Their support has truly been a driving factor in my life.