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 τ_b, which depends on T and the shear

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... , is on the order of the usual structural or α relaxation time τ_α in weak shear τ_α≪ 1, while it decreases as 1/ in strong shear τ_α≫ 1 due to shear-induced cage breakage. Accumulated broken bonds in a time interval (∼ 0.05τ_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 ξ representing the maximum size of the clusters composed of broken bonds. We also find a dynamical scaling relation, τ_b ∼ξ^z, valid for any T and with z=4 in two dimensions and z=2 in three dimensions. The viscosity is of order τ_b for any T and , 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 τ_b^-ν with ν=0.75 ∼ 0.8 for any T and , 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.