  Deep inelastic scattering of $\mathcal{R}$-currents and the scattering of a
small dipole on finite length hot $\mathcal{N}=4$ SYM matter are discussed. In
each case we find the scale when scattering becomes strong is determined by a
saturation momentum $Q^2_s \sim LT^3/x$ where $L$ is the length of the matter.
For $\mathcal{R}$-currents we analyze the operator product expansion. For
infinite length matter the series generated by the OPE is not Borel summable
but we are able to determine the exponential part of the tunneling amplitude
determining $F_2$ when $\frac{Q^2}{Q^2_s}\gg 1$ from the position of the
singularity closest to the origin on the real axis of the Borel plane. In
finite length matter the OPE series is not convergent but it is Borel summable.
When a small dipole, and the string connecting the ends of the dipole, pass
through hot matter there is an induced motion of the string in the $5^{th}$
dimension. When $T^4 L \cosh \eta$, with the $\eta$ the rapidity of the string,
is large enough the string would normally break into several parts after
leaving the medium, however, this cannot happen in the classical approximation
in which we work.
