  Using extensive non-equilibrium molecular dynamics simulations, we
investigate a glassforming binary Lennard-Jones mixture under shear. Both
supercooled liquids and glasses are considered. Our focus is on the
characterization of inhomogeneous flow patterns such as shear bands that appear
as a transient response to the external shear. For the supercooled liquids, we
analyze the crossover from Newtonian to non-Newtonian behavior with increasing
shear rate $\dot{\gamma}$. Above a critical shear rate $\dot{\gamma}_c$ where a
non-Newtonian response sets in, the transient dynamics are associated with the
occurrence of short-lived vertical shear bands, i.e. bands of high mobility
that form perpendicular to the flow direction. In the glass states, long-lived
horizontal shear bands, i.e. bands of high mobility parallel to the flow
direction, are observed in addition to vertical ones. The systems with shear
bands are characterized in terms of mobility maps, stress-strain relations,
mean-squared displacements, and (local) potential energies. The initial
formation of a horizontal shear band provides an efficient stress release,
corresponds to a local minimum of the potential energy, and is followed by a
slow broadening of the band towards the homogeneously flowing fluid in the
steady-state. Whether a horizontal or a vertical shear band forms cannot be
predicted from the initial undeformed sample. Furthermore, we show that with
increasing system size the probability for the occurrence of horizontal shear
bands increases.
