  This paper explores the intermediate-time dynamics of newly formed solar
systems with a focus on possible mechanisms for planetary migration. We
consider two limiting corners of the available parameter space -- crowded
systems containing N=10 giant planets in the outer solar system, and solar
systems with N=2 planets that are tidally interacting with a circumstellar
disk. For a given set of initial conditions, dynamical relaxation leads to a
well-defined distribution of possible solar systems. For each class of initial
conditions, we perform large numbers of N-body simulations to obtain a
statistical description of the possible outcomes. For N=10 planet systems, we
consider several different planetary mass distributions; we also perform
secondary sets of simulations to explore chaotic behavior and longer term
dynamical evolution. For systems with 10 planets initially populating the
radial range 5 - 30 AU, these scattering processes naturally produce planetary
orbits with $a\sim1$ AU and the full range of possible eccentricity, but
shorter period orbits are difficult to achieve. To account for the observed
eccentric giant planets, we also explore a mechanism that combines dynamical
scattering and tidal interactions with a circumstellar disk. This combined
model naturally produces the observed range of semi-major axis and
eccentricity. We discuss the relative merits of the different migration
mechanisms for producing the observed eccentric giant planets.
