  We revisit the problem of secular resonance sweeping during the dissipation
of a protoplanetary disk and its possible role in exciting the orbits of
primordial asteroids, in the light of recent models of solar system evolution.
We develop an integrator that incorporates the gravitational effect of a
uniformly (or not) depleting, axisymmetric disk with arbitrary surface density
profile; its performance is verified by analytical calculations. The secular
response of fictitious asteroids, under perturbations from Jupiter, Saturn and
a decaying disk, is thoroughly studied. Note that the existence of a symmetry
plane induced by the disk, lifts the inherent degeneracy of the two-planet
system, such that the '$s_5$' nodal frequency can also play a major role. We
examine different resonant configurations for the planets (2:1, 3:2, 5:3), disk
models and depletion scenarios. For every case we compute the corresponding
time paths of secular resonances, which show when and where resonance crossing
occurs. The excitation of asteroids, particularly in inclination, is studied in
the various models and compared to analytical estimates. We find that
inclination excitation in excess of $\sim 10^{\circ}$ is possible in the
asteroid belt, but the nearly uniform spread of $\Delta i\sim 20^{\circ}$
observed calls for the combined action of secular resonance sweeping with other
mechanisms (e.g. scattering by Mars-sized embryos) that would be operating
during terrestrial planet formation. Our results are also applicable to
extrasolar planetary systems.
