  The binary Voronoi mixture is a fluid model whose interactions are local and
many-body. Here we perform molecular-dynamics (MD) simulations of an equimolar
mixture that is weakly polydisperse and additive. For the first time we study
the structural relaxation of this mixture in the supercooled-liquid regime.
From the simulations we determine the time- and temperature-dependent
scattering functions for a large range of wave vectors, as well as the
mean-square displacements of both particle species. We perform a detailed
analysis of the dynamics by comparing the MD results with the
first-principles-based idealized mode-coupling theory (MCT). To this end, we
employ two approaches: fits to the asymptotic predictions of the theory, and
fit-parameter-free binary MCT calculations based on static-structure-factor
input from the simulations. We find that many-body interactions of the Voronoi
mixture do not lead to strong qualitative differences relative to similar
analyses carried out for simple liquids with pair-wise interactions. For
instance, the fits give an exponent parameter $\lambda \approx 0.746$
comparable to typical values found for simple liquids, the wavevector
dependence of the Kohlrausch relaxation time is in good agreement with
literature results for polydisperse hard spheres, and the MCT calculations
based on static input overestimate the critical temperature, albeit only by a
factor of about 1.2. This overestimation appears to be weak relative to other
well-studied supercooled-liquid models such as the binary Kob--Andersen
Lennard-Jones mixture. Overall, the agreement between MCT and simulation
suggests that it is possible to predict several microscopic dynamic properties
with qualitative, and in some cases near-quantitative, accuracy based solely on
static two-point structural correlations, even though the system itself is
inherently governed by many-body interactions.
