7, average behaviors are plotted, which were obtained by taking the mass-average as a function of $T_{\rm max}$.

Figures 6 and 7 show that the distribution of ($T_{\rm max}$, $\rho_{\rm max}$) is similar for all the models at $T_{{\rm max}, 9} \gsim 3$ (corresponding to $\rho_{\rm max} 
\sim \rho_{\rm DDT}$). This reflects the fact that the local properties of the deflagration flame are basically independent from the geometry. Interestingly, despite the different prescription of the deflagration flame propagation and different expansion time scale (see e.g., Travaglio et al. 2004a), we note a similarity with the outcome of the W7 in this respect.

At $T_{{\rm max}, 9} \lsim 3$, the models differ. Note that the behavior of W7 in this temperature regime shown in Figures 6 and 7 is not real; the deflagration is turned off at $T_{{\rm max}, 9} \sim 2$, where the flame is already near the surface in the W7 model. Our deflagration model extends to lower $T_{\rm max}$ and $\rho_{\rm max}$. In the two delayed detonation models, this temperature range corresponds to the detonation phase, and thus the behavior is expected to deviate from the deflagration models, and indeed it does. The two detonation models show a 