  (Abridged) We study the interaction of relativistic jets from AGNs with the
ISM in their host galaxy, using a series of Adaptive Mesh Refinement
simulations of the evolution of the interaction between the cocoon produced by
the jet with a dense cloud, placed very near the cocoon's path. We vary only
the jet's input power between P_{jet} = 10^{41}-10^{47} {\rm erg/sec}. The
density Probability Distribution Function (PDF) within the cocoon can be
described in terms of two distinct components, which are also spatially
distinct: a low- and a high-density component. The PDF of the post-shocked
region is well approximated by a modified lognormal distribution, for all
values of $P_{jet}$. During the active phase, when the jet is fed by the AGN,
the cloud is subject both to compression and stripping, which tend to increase
its density and diminish its total mass. When the jet is switched off (i.e.
during the passive phase) the shocked cloud cools further and tends to become
more filamentary, under the action of a back-flow which develops within the
cocoon. We study the evolution of the star formation rate within the cloud,
assuming that is determined by a Schmidt-Kennicutt law, and we analyze the
different physical factors which have an impact on the star formation rate. We
show that, although the star formation rate can occasionally increase, on time
scales of the order of $10^{5}-10^{6}$ yrs, star formation will be inhibited
and the cloud fragments. The cooling time of the environment within which the
cloud is embedded is however very long: thus, star formation from the
fragmented cloud remains strongly inhibited.
