  Shear modulus of frictionless granular materials near the jamming transition
under oscillatory shear is numerically investigated. It is found that the shear
modulus $G$ satisfies a scaling law to interpolate between $G \sim (\phi -
\phi_J)^{1/2}$ and $G \sim \gamma_0^{-1/2}(\phi-\phi_J)$ for a linear spring
model of the elastic interaction between contacting grains, where $\phi$,
$\phi_J$, and $\gamma_0$ are, respectively, the volume fraction of grains, the
fraction at the jamming point, and the amplitude of the oscillatory shear. The
linear relation between the shear modulus and $\phi - \phi_J$ can be understood
by slip avalanches.
