What can DUNE and JUNO detectors tell us about flavor transitions of galactic supernova neutrinos?

We present a method to verify MSW effect during the propagation of SN neutrinos from the SN core to the Earth. The non-MSW scenario to be distinguished from the MSW one is the incoherent flavor transition probability for neutrino propagation in the vacuum.  Our approach involves studying time evolution of neutrino event rates in liquid Argon and liquid scintillation detectors. The former (latter) detector is sensitive to $ u_e$ ($ar{ u}_e$) flux which is a linear combination of $ u_e$ ($ar{ u}_e$) and $ u_{mu, au}$ ($ar{ u}_{mu, au}$) fluxes from the source with the weighting of each component dictated by the flavor transition mechanism. Using currently available simulations for SN neutrino emissions, the time evolution of $ u_e{ m Ar}$ and $ar{ u}_e$ IBD event rates and the corresponding cumulative event fractions are calculated up to $t=100~{ m ms}$ in DUNE and JUNO detectors, respectively.  It is shown that the area under the cumulative time distribution curve from $t=0$ to $t=100~{ m ms}$ in each detector and their ratio can be used to discriminate different flavor transition scenarios of SN neutrinos.