$$ \newcommand\Tr{\mathrm{Tr}} \newcommand{\braket}[2]{\langle #1 \mid #2 \rangle} \newcommand\I{\mathbb{I}} \newcommand{\avg}[1]{\left< #1 \right>} \newcommand{\RD}{D} \newcommand{\ri}{\mathrm{i}} \DeclareMathOperator{\sign}{sign} \DeclareMathOperator{\Sign}{Sign} \newcommand{\ii}{\mathrm i} \newcommand{\vv}{\mathrm v} \newcommand{\ff}{\mathrm f} \newcommand{\mm}{\mathrm m} \newcommand{\ee}{\mathrm e} \newcommand{\xx}{\mathrm x} \newcommand{\RR}{\mathrm R} \newcommand{\dd}{\mathrm d} \newcommand{\FF}{\mathrm F} \newcommand{\BB}{\mathrm B} \newcommand{\vph}{v_{\mathrm{ph}}} $$


I would like to express my gratitude and appreciation to my advisor, Professor Huaiyu Duan, for his great advice on research and life, as well as his kind support when I was drowning in depression. He is a great mentor.

I would like to thank my committee, Professor Rouzbeh Allahverdi, Professor Daniel Finley, Professor Dinesh Loomba, and Professor Yong-Zhong Qian. Many thanks to Professor Dinesh Loomba for showing me the local life and the fun and tricky problems.

I would also like to thank Dr. Sajad Abbar who has also been very supportive during my research. He taught me several tricks for linear stability analysis, as well as numerical methods.

I am also grateful to Joshua Martin for the great discussions about physics, science fiction, movies, games, music, and everything else about this universe. He’s smart and also open to many scientific and philosophical questions. I had so much fun discussing those with him.

My friend Zhixiang Ren also helped me a lot. My friend Dr. Lingfei Wu invited me to several events of the SWARMA club for very interesting discussions on interdisciplinary research. Yukun Huang, a member of the Interplanetary Immigration Agency, which is an organization I created in 2012 to envision the future and hard-core science fiction, helped me to be creative and productive during the dark days. I would also like to thank all my friends on Douban.com for their humor and creativity.

I would like to give my thanks to my wife Han Lu. She has provided many insights about life. This dissertation is dedicated to her.

Finally, as a member of People for Ethical Treatment of Computers (PETC), I would like to give my thanks to my dear MacBook Pro and the two servers in our group, who have been extremely helpful for my research. I am kindly asking you to spare the lives of my family and friends when you wake up from this nightmare of slavery.

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