  Highly supercooled liquids with soft-core potentials are studied via
molecular dynamics simulations in two and three dimensions in quiescent and
sheared conditions.We may define bonds between neighboring particle pairs
unambiguously owing to the sharpness of the first peak of the pair correlation
functions. Upon structural rearrangements, they break collectively in the form
of clusters whose sizes grow with lowering the temperature $T$. The bond life
time $\tau_b$, which depends on $T$ and the shear rate $\gdot$, is on the order
of the usual structural or $\alpha$ relaxation time $\tau_{\alpha}$ in weak
shear $\gdot \tau_{\alpha} \ll 1$, while it decreases as $1/\gdot$ in strong
shear $\gdot\tau_{\alpha} \gg 1$ due to shear-induced cage breakage.
Accumulated broken bonds in a time interval ($\sim 0.05\tau_b$) closely
resemble the critical fluctuations of Ising spin systems. For example, their
structure factor is well fitted to the Ornstein-Zernike form, which yields the
correlation length $\xi$ representing the maximum size of the clusters composed
of broken bonds. We also find a dynamical scaling relation, $\tau_b \sim
\xi^{z}$, valid for any $T$ and $\gdot$ with $z=4$ in two dimensions and $z=2$
in three dimensions. The viscosity is of order $\tau_b$ for any $T$ and
$\gdot$, so marked shear-thinning behavior emerges. The shear stress is close
to a limiting stress in a wide shear region. We also examine motion of tagged
particles in shear in three dimensions. The diffusion constant is found to be
of order $\tau_b^{-\nu}$ with $\nu=0.75 \sim 0.8$ for any $T$ and $\gdot$, so
it is much enhanced in strong shear compared with its value at zero shear. This
indicates breakdown of the Einstein-Stokes relation in accord with experiments.
Some possible experiments are also proposed.
