Wu, Meng-Ru2013-02-062013-02-062012-10https://hdl.handle.net/11299/143993University of Minnesota Ph.D. dissertation. October 2012. Major: Physics. Advisor: Professor Yong-Zhong Qian. 1 computer file (PDF); viii, 137 pages, appendices A-C.Neutrinos are one of the central ingredients in core-collapse supernova explosion and their flavor oscillations in supernovae might affect many processes that occur in this explosive environment. In this thesis, we study neutrino flavor oscillations in supernovae both analytically and numerically. Analytically, we propose a simple model to explain the flavor evolution history in the region of collective neutrino oscillations during the neutronization neutrino burst and accretion phase of neutrino emission with low matter density. We show that the formation of spectral splits induced by collective neutrino oscillations can be well-understood using this model. We also apply this model to discuss the flavor instability of neutrino oscillations that occurs in the cooling phase. Numerically, we simulate neutrino flavor evolution history using the neutrino emission data from a state-of-the-art 18 M⊙ supernova model. We discuss the time-dependence of neutrino oscillations on neutrino emission characteristics and the supernova environment. We then study the effect of neutrino oscillations on the nucleosynthesis that occurs in the neutrino-driven wind. At last, we calculate the expected neutrino signals in the IceCube detector and discuss the consequences.en-USNeutrinoOscillationSupernovaThesis or Dissertation