  We investigate the fast $\beta$- and Johari-Goldstein (JG) $\beta$-relaxation
processes, along with the elastic scattering response of glass-forming (GF)
liquids and the Boson peak, in a simulated Al-Sm GF material exhibiting a
fragile-strong (FS) transition. These dynamical processes are universal in
'ordinary' GF fluids and collectively describe their 'fast dynamics', and we
find these relaxation processes also arise in a GF liquid exhibiting a
fragile-strong transition. String-like particle motion, having both an
irreversible and reversible nature ('stringlets') component, occurs in the
fast-dynamics regime, corresponding to a ps timescale. String-like collective
motion associated with localized unstable modes facilitate irreversible and
intermittent particle 'jumping' events at long times associated with the JG
$\beta$-relaxation process, while stringlets associated with localized stable
modes and corresponding perfectly reversible atomic motion give rise to the
Boson peak. To further clarify the origin of the Boson peak, we calculate the
density of states for both the stringlet particles and the 'normal' particles
and find that the stringlet particles give rise to a Boson peak while the
normal atoms do not. The growth of stringlets upon heating ultimately also
leads to the 'softening' of these excitations, and the Boson peak frequency and
shear modulus drop in concert with this softening. The growth of string-like
collective motion upon heating in the fast-dynamics regime is further shown to
be responsible for the growth in the intensity of the fast relaxation process.
Relaxation in cooled liquids clearly involves a hierarchy of relaxation
processes acting on rather different time and spatial scales.
