Softness Correlations Across Length Scales

In disordered systems, it is believed that mechanical failure begins with localized particle rearrangements. Recently, a machine learning method has been introduced to identify how likely a particle is to rearrange given its local structural environment, quantified by \textit{softness}. We calculate the softness of particles in simulations of atomic Lennard-Jones mixtures, molecular Lennard-Jones oligomers, colloidal systems and granular systems. In each case, we find that the length scale characterizing spatial correlations of softness is approximately a particle diameter. These results provide a rationale for why localized rearrangements---whose size is presumably set by the scale of softness correlations---might occur in disordered systems across many length scales.