  Using extensive molecular dynamics simulations of an equilibrium,
glass-forming Lennard-Jones mixture, we characterize in detail the local atomic
motions. We show that spatial correlations exist among particles undergoing
extremely large (``mobile'') or extremely small (``immobile'') displacements
over a suitably chosen time interval. The immobile particles form the cores of
relatively compact clusters, while the mobile particles move cooperatively and
form quasi-one-dimensional, string-like clusters. The strength and length scale
of the correlations between mobile particles are found to grow strongly with
decreasing temperature, and the mean cluster size appears to diverge at the
mode-coupling critical temperature. We show that these correlations in the
particle displacements are related to equilibrium fluctuations in the local
potential energy and local composition.

Soft Condensed Matter