  In heavy-ion collisions, the harmonic flow $V_n$ of final-state particles are
driven by the eccentricity vector ${\mathcal{E}}_n$ that describe the shape of
the initial fireball projected in the transverse plane. It is realized recently
that the structure and shape of the fireball, and consequently the
${\mathcal{E}}_n$, fluctuate in pseudorapidity $\eta$ in a single event,
${\mathcal{E}}_n(\eta)$. This leads to eccentricity decorrelation between
different $\eta$, driving the longitudinal flow decorrelations observed in the
experiments. Using a Glauber model with a paramerterized longitudinal
structure, we have estimated the eccentricity decorrelations and related them
to the measured flow decorrelation coefficients for elliptic flow $n=2$ and
triangular flow $n=3$. We investigated the dependence of eccentricity
decorrelations on the choice of collision system in terms of the size,
asymmetry and deformation of the nuclei. We found that these nuclear geometry
effects lead to significant and characteristic patterns on the eccentricity
decorrelations, which describe the measured ratios of the flow decorrelations
between Xe+Xe and Pb+Pb collisions. These patterns can be searched for using
existing experimental data at RHIC and the LHC, and if confirmed, they will
provide a mean to improve our understanding of the initial state of the
heavy-ion collisions.
