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Recent progress on studies of the nanoscale mechanical responses indisordered systems has highlighted a strong degree of heterogeneity in theelastic moduli. In this contribution, using computer simulations, we study theelastic 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 findthat the local elastic moduli are randomly distributed in space and aredescribed by Gaussian probability distributions, thereby lacking anysignificant spatial correlations, that persists all the way down to thetransition point. However, the shear modulus fluctuations grow as the jammingthreshold is approached, which is characterized by a new power-law scaling.Through this diverging behavior we are able to identify a characteristic lengthscale, associated with shear modulus heterogeneities, that distinguishesbetween bulk and local elastic responses.

Spatial Distributions of Local Elastic Moduli Near the Jamming Transition