0  0.2  0.4  0.6  0.8 1 sin 2 2 13 =10 -2 normal hierarchy 0  0.2  0.4  0.6  0.8 1 sin 2 2 13 =10 -4 0  0.2  0.4  0.6  0.8 1  10  20  30  40  50  60 sin 2 2 13 =10 -5 0  0.2  0.4  0.6  0.8 1 sin 2 2 13 =10 -3 0  0.2  0.4  0.6  0.8 1 sin 2 2 13 =10 -3 0  0.2  0.4  0.6  0.8 1 sin 2 2 13 =10 -4 0  0.2  0.4  0.6  0.8 1 sin 2 2 13 =10 -2 inverted hierarchy 0  0.2  0.4  0.6  0.8 1  10  20  30  40  50  60 sin 2 2 13 =10 -5 FIG. 2: Calculated results of the survival probabil ities, P ( E$_{ν}$ ) and ¯ P ( E$_{ν}$ ), in every 1 second. Left panels are the survival probabilities of ν$_{e}$ , P ( E$_{ν}$ ), in normal hierarchy, and right panels are the survival probabilities of ¯ ν$_{e}$ , ¯ P ( E$_{ν}$ ), in inverted hierarchy. Red, green, blue, purple, sky blue and orange lines are t = 0, 1, 2, 3, 4 and 5 sec after co re bounce. The value of sin $^{2}$2 θ$_{13}$ is 10 − $^{2}$, 10 − $^{3}$, 10 − 4 and 10 − 5 from top to bottom. 2 8