  Dense core collisions, previously regarded as minor in star formation, are
proposed to play a significant role in structure formation around protostellar
envelopes and binary formation. Using archival data of nearby star-forming
regions, we determine the frequencies of core collisions. Our calculations
reveal that a typical core is likely to undergo multiple interactions with
other cores throughout its lifetime. To further investigate the core collision
process, we employ adaptive mesh refinement hydrodynamic simulations with sink
particles. Our simulations demonstrate that following the formation of a
protostar within a gravitationally-unstable core, the merging core's accreting
gas gives rise to a rotationally-supported circumstellar disk. Meanwhile, the
region compressed by the shock between the cores develops into asymmetric arms
that connect with the disk. Gas along these arms tends to migrate inward,
ultimately falling toward the protostar. One of the arms, a remnant of the
shock-compressed region, dominates over the second core gas, potentially
exhibiting a distinct chemical composition. This is consistent with recent
findings of large-scale streamers around protostars. Additionally, we found
that collisions with velocities of $\sim$ 1.5 km s$^{-1}$ result in the
formation of a binary system, as evidenced by the emergence of a sink particle
within the dense section of the shocked layer. Overall, dense core collisions
are highlighted as a critical process in creating $10^3$ au-scale streamers
around protostellar systems and binary stars.
