This work is devoted to calculating the first passage probabilities of one-dimensional diffusion processes. For a one-dimensional diffusion process, we construct a sequence of Markov chains so that their absorption pr...This work is devoted to calculating the first passage probabilities of one-dimensional diffusion processes. For a one-dimensional diffusion process, we construct a sequence of Markov chains so that their absorption probabilities approximate the first passage probability of the given diffusion process. This method is especially useful when dealing with time-dependent boundaries.展开更多
It is known that in supernova explosions, there might be a reverse shock wave in addition to the forward shock wave during the explosion phase, when the mass of supernova is in a certain range. In this paper, we propo...It is known that in supernova explosions, there might be a reverse shock wave in addition to the forward shock wave during the explosion phase, when the mass of supernova is in a certain range. In this paper, we propose to add the reverse shock wave to the previous supernova model, in which only the forward shock wave was included, and thus obtain a new model. By analyzing the resonance condition as well as the density jump in the new model and using the Landau-Zener method, an expression for the crossing probability in high density matter （PH） is given. We proceed to study how PH varies with time and with neutrino energy when both the reverse shock wave and the forward shock wave are considered. From comparison with the previous results, where only the effects of the forward shock wave were considered, it is clear that the reverse shock wave brings significant changes to PH.展开更多
基金This work was supported in part by the National Natural Science Foundation of Ghina （Grant Nos. 11301030, 11431014）, the 985-Project, and the Beijing Higher Education Young Elite Teacher Project.
文摘This work is devoted to calculating the first passage probabilities of one-dimensional diffusion processes. For a one-dimensional diffusion process, we construct a sequence of Markov chains so that their absorption probabilities approximate the first passage probability of the given diffusion process. This method is especially useful when dealing with time-dependent boundaries.
基金Supported by National Natural Science Foundation of China(11605150)Natural Science Foundation of Shandong Province(ZR2016AQ02)
文摘It is known that in supernova explosions, there might be a reverse shock wave in addition to the forward shock wave during the explosion phase, when the mass of supernova is in a certain range. In this paper, we propose to add the reverse shock wave to the previous supernova model, in which only the forward shock wave was included, and thus obtain a new model. By analyzing the resonance condition as well as the density jump in the new model and using the Landau-Zener method, an expression for the crossing probability in high density matter （PH） is given. We proceed to study how PH varies with time and with neutrino energy when both the reverse shock wave and the forward shock wave are considered. From comparison with the previous results, where only the effects of the forward shock wave were considered, it is clear that the reverse shock wave brings significant changes to PH.
