is interesting to note that such fast variability is less pronounced in our 3D model (red lines in the bottom panel). This is qualitatively consistent with @lund12 who analyzed the neutrino signals from 2D and 3D models, in which an approximate neutrino transport was solved [@annop10] as in @scheck06.

![Top panel shows time evolution of neutrino luminosities and mean energies of electron ($\nu_e$), anti-electron ($\bar{\nu}_e$), or heavy-lepton ($\nu_X$) neutrinos for models 3D-H-2 (green line) and 3D-H-3 (red line), respectively. Bottom panel is the same as the top panel but for the comparison between 2D and 3D (for models 3D-H-1 and 2D-H-1). These quantities are estimated at 500 km.[]{data-label="fig3"}](f3.eps "fig:"){width=".8\linewidth"} ![Top panel shows time evolution of neutrino luminosities and mean energies of electron ($\nu_e$), anti-electron ($\bar{\nu}_e$), or heavy-lepton ($\nu_X$) neutrinos for models 3D-H-2 (green line) and 3D-H-3 (red line), respectively. Bottom panel is the same as the top panel but for the comparison between 2D and 3D (for models 3D-H-1 and 2D-H-1). These quantities are estimated at 500 km.[]{data-label="fig3"}](lumi2D3D.eps "fig:"){width=".8\linewidth"}

Figure \[pns\] shows evolution of the average PNS radius for the 1D (blue line), 2D (green line), and 3D models (red line), respectively, that are defined by a fiducial density of 