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Signposts of early planet formation are ubiquitous in substructured young discs. Dense, hot and high-pressure regions formed during gravitational collapse process, integral to star formation, facilitate dynamical mixing of dust within the protostellar disc. This provides an incentive to constrain the role of gas-dust interaction and resolve zones of dust concentration during star-disc formation. We explore if thermal and dynamical conditions developed during disc formation can generate gas flows that efficiently mix and transport well-coupled gas and dust components. We simulated the collapse of dusty molecular cloud cores with the hydrodynamics code PLUTO augmented with radiation transport and self-gravity. We used a 2D axisymmetric geometry and follow the azimuthal component of velocity. Dust was treated as Lagrangian particles that are subject to drag from the gas, whose motion is computed on a Eulerian grid. We considered 1, 10 and 100 micron-sized neutral spherical dust. Importantly, the equation of state accurately includes molecular hydrogen dissociation. We focus on molecular cloud core masses of 1 and 3 Msun and explore effects of initial rotation rates and cloud core sizes. Our study underlines mechanisms for early transport of dust from inner hot disc regions via the occurrence of meridional flows and outflow. The vortical flow fosters dynamical mixing and retention of dust while thermal pressure driven outflow replenishes dust in the outer disc. Young dynamical precursors to planet-forming discs exhibit regions with complex hydrodynamical gas features and high-temperature structures. These can play a crucial role in concentrating dust for subsequent growth into protoplanets. Dust transport, especially, from sub-au scales surrounding the protostar to outer relatively cooler parts, offers an efficient pathway for thermal reprocessing during pre-stellar core collapse. Abridged
Bhandare et al. (Sun,) studied this question.