  The torques exerted by a locally isothermal disk on an embedded planet lead
to rapid inward migration. Recent work has shown that modeling the
thermodynamics without the assumption of local isothermality reveals regions
where the net torque on an embedded planet is positive, leading to outward
migration of the planet. When a region with negative torque lies directly
exterior to this, planets in the inner region migrate outwards and planets in
the outer region migrate inwards, converging where the torque is zero. We
incorporate the torques from an evolving non-isothermal disk into an N-body
simulation to examine the behavior of planets or planetary embryos interacting
in the convergence zone. We find that mutual interactions do not eject objects
from the convergence zone. Small numbers of objects in a laminar disk settle
into near resonant orbits that remain stable over the 10 Myr periods that we
examine. However, either or both increasing the number of planets or including
a correlated, stochastic force to represent turbulence drives orbit crossings
and mergers in the convergence zone. These processes can build gas giant cores
with masses of order ten Earth masses from sub-Earth mass embryos in 2-3 Myr.
