  In marginally jammed solids confined by walls, we calculate the particle and
ensemble averaged value of an order parameter, $\left<\Psi(r)\right>$, as a
function of the distance to the wall, $r$. Being a microscopic indicator of
structural disorder and particle mobility in solids, $\Psi$ is by definition
the response of the mean square particle displacement to the increase of
temperature in the harmonic approximation and can be directly calculated from
the normal modes of vibration of the zero-temperature solids. We find that, in
confined jammed solids, $\left<\Psi(r)\right>$ curves at different pressures
can collapse onto the same master curve following a scaling function,
indicating the criticality of the jamming transition. The scaling collapse
suggests a diverging length scale and marginal instability at the jamming
transition, which should be accessible to sophisticatedly designed experiments.
Moreover, $\left<\Psi(r)\right>$ is found to be significantly suppressed when
approaching the wall and anisotropic in directions perpendicular and parallel
to the wall. This finding can be applied to understand the $r$-dependence and
anisotropy of the structural relaxation in confined supercooled liquids,
providing another example of understanding or predicting behaviors of
supercooled liquids from the perspective of the zero-temperature amorphous
solids.
