Magnetized, cold, dense molecular cloud cores provide the birth environment for stars and disks. In this contribution, I will summarize the outcome of numerical simulations that probe the gravitational collapse process involving the transition of an isolated low-mass pre-stellar core to a protostar with a surrounding disk. In our hybrid scheme, we treat the gas as a fluid and dust as Lagrangian particles. We use the PLUTO code to perform two-dimensional radiation (magneto-)hydrodynamic simulations to understand the role of various micro- and macrophysical processes during the early embedded stages. These include the effects of self-gravity, radiation transport, an accurate gas equation of state (to model the influence of molecular hydrogen dissociation), and ohmic resistivity. We trace the spatial and temporal evolution of up to 100 micron-sized dust grains. Our results highlight the effects of gas and dust dynamics in the formation phases. We find regions of dust concentration and an enhancement in the local dust-to-gas mass ratio within the first hydrostatic core and protostellar disk. This study can help constrain the impact of gas and dust interaction on disk substructure formation and initial conditions for planet formation.
[Poster PDF File]