  Recent progress on studies of the nanoscale mechanical responses in
disordered systems has highlighted a strong degree of heterogeneity in the
elastic moduli. In this contribution, using computer simulations, we study the
elastic heterogeneities in athermal amorphous solids, composed of isotropic,
static, sphere packings, near the jamming transition. We employ techniques,
based on linear response methods, that are amenable to experimentation. We find
that the local elastic moduli are randomly distributed in space and are
described by Gaussian probability distributions, thereby lacking any
significant spatial correlations, that persists all the way down to the
transition point. However, the shear modulus fluctuations grow as the jamming
threshold is approached, which is characterized by a new power-law scaling.
Through this diverging behavior we are able to identify a characteristic length
scale, associated with shear modulus heterogeneities, that distinguishes
between bulk and local elastic responses.
