The neutrino-driven wind from proto-neutron stars has long been considered a possible site for interesting nucleosynthesis of heavy elements, via either an r-process, in which heavy elements are made via rapid neutron captures onto seed nuclei, or a $\nu$p-process, in which heavy elements are forged by neutrino-assisted proton captures onto seed nuclei. Many recent studies have indicated that a fiducial wind heated only by neutrino interactions does not attain a high enough entropy or a sufficiently fast expansion to allow these processes to build the heaviest elements found in nature, despite promising results in the early literature. However, a secondary heating source in the wind could strongly enhance heavy nucleosynthesis by disrupting seed nucleus formation, and allowing extended nucleon captures to build heavier elements. A promising physical source of such secondary heating is gravito-acoustic waves, launched by vigorous convection in the proto-neutron star, which form shocks and deposit energy into the wind. In this thesis, we derive a numerical model for examining the effects of such propagating waves on both the dynamics and the nucleosynthetic processes active in the wind. We explore, via parameter studies, the effects of these wave on both neutron- and proton-rich winds, and how potential r- and $\nu$p-processes are affected. Finally, we compute the integrated nucleosynthesis from a realistic proto-neutron star evolution to examine the effects of propagating waves on the different stages of nucleosynthesis a time-dependent wind undergoes, and to predict the full nucleosynthetic yield of realistic winds. We find that gravito-acoustic waves propagating through the wind have a substantial impact on both r- and $\nu$p-processing, via heating due to shock formation as well as the momentum flux carried by the waves. The combination of these effects also reduces the asymptotic electron fraction of the wind by up to 20\%. We even find that, for winds in which the wave luminosity is $\gtrsim 1\%$ of the wave luminosity, a third-peak, albeit suppressed, r-process attains despite proton-rich conditions in the wind. Though a full r-process is not realized in the realistic, time-integrated wind from a simulated proto-neutron star, this is likely due to the low-mass ($\sim 1.35\,\Msun$) neutron star formed. If a heavier (e.g., $1.6\,\Msun$) proto-neutron star forms with a similar neutrino spectrum and convective properties, our results suggest that a full r-process can proceed.
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