  Using 3D Vorono\text{\"i} analysis, we explore the local dynamics of small,
settling, inertial particles in isotropic turbulence using Direct Numerical
Simulations (DNS). We independently vary the Taylor Reynolds number $R_\lambda
\in[90,398]$, Froude number $Fr\equiv a_\eta/g\in[0.052,\infty]$ (where
$a_\eta$ is the Kolmogorov acceleration, and $g$ is the acceleration due to
gravity), and Kolmogorov scale Stokes number
$St\equiv\tau_p/\tau_\eta\in[0,3]$. In agreement with previous results using
global measures of particle clustering, such as the Radial Distribution
Function (RDF), we find that for small Vorono\text{\"i} volumes (corresponding
to the most clustered particles), the behavior is strongly dependent upon $St$
and $Fr$, but only weakly dependent upon $R_\lambda$, unless $St>1$. However,
larger Vorono\text{\"i} volumes (void regions) exhibit a much stronger
dependence on $R_\lambda$, even when $St\leq 1$, and we show that this, rather
than the behavior at small volumes, is the cause of the sensitivity of the
standard deviation of the Vorono\text{\"i} volumes that has been previously
reported. We also show that the largest contribution to the particle settling
velocities is associated with increasingly larger Vorono\text{\"i} volumes as
the settling parameter $Sv\equiv St/Fr$ is increased. Our local analysis of the
acceleration statistics of settling inertial particles shows that clustered
particles experience a net acceleration in the direction of gravity, while
particles in void regions experience the opposite. The particle acceleration
variance, however, is a convex function of the Vorono\text{\"i} volumes, with
or without gravity, which seems to indicate a non-trivial relationship between
the Vorono\text{\"i} volumes and the sizes of the turbulent flow scales.
Results for the variance of the fluid acceleration at the inertial particle
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