We investigate trends in the yields of ux{44}{Ti} and ux{56}{Ni}
as material with a specified initial electron fraction both cools
and rarefies along exponential, power-law, and post-processing
thermodynamic trajectories. We use the exponential and power-law
expansion profiles to identify 6 distinct regions in the peak
temperature-density plane and extensively probe the sensitivity of
the isotopic yields to the input nuclear physics. The 6 regions
are largely driven by different phase transitions within the
quasi-statistical equilbrium cluster as the material undergoes
freeze-out. Most Si-group and Fe-group isotopes are affected by
the transitions, with the exception of a small group centralized
around 56Ni. Reactions that affect all yields globally are the
3-alpha, p(e-,nu_e)n and n(e+, nubar_e)p, while 44Ti is mainly
affected by 44Ti(a,p)47V, 40Ca(a,g)44Ti and 45V(p,g)46Cr. Trends
due to electron fraction variations may be largely explained in
terms of an empirical rule for the major nuclear flows where the
most abundant isotopes at any given time in the thermodynamic
evolution are generally the ones whose individual proton to nucleon
ratio is within a small range from the current value of the electron
fraction in combination with a minimization of the Helmholtz free
energy. We compare the yields of 44Ti and 56Ni produced from
post-processing the thermodynamic trajectories from three different
core-collapse models -- a Cas A progenitor, a double shock hypernova
progenitor, and a rotating 2D explosion -- with the yields from the
exponential and power-law trajectories. The peak temperatures and
densities achieved in these core-collapse models span several of
the 6 regions we identify, resulting in different trends in the
44Ti and 56Ni yields for different mass elements. The 44Ti and
56Ni mass fraction profiles from the exponential and power-law
profiles generally explain the tendencies of the post-processed
yields, depending on which regions are traversed by the model. We
find integrated yields of 44Ti and 56Ni from the exponential and
power-law trajectories are generally within a factor 2 or less of
the post-process yields. Our analysis suggests that not all 44Ti
need be produced in an alpha-rich freeze-out in core-collapse events,
and that that reaction rate equilibria in combination with timescale
effects for the expansion profile may account for the paucity of
44Ti observed in supernovae remnants.
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