  We give a full nonlinear numerical treatment of time-dependent 5d braneworld
geometry, which is determined self-consistently by potentials for the scalar
field in the bulk and at two orbifold branes, supplemented by boundary
conditions at the branes. We describe the BraneCode, an algorithm which we
designed to solve the dynamical equations numerically. We applied the BraneCode
to braneworld models and found several novel phenomena of the brane dynamics.
Starting with static warped geometry with de Sitter branes, we found
numerically that this configuration is often unstable due to a tachyonic mass
of the radion during inflation. If the model admits other static configurations
with lower values of de Sitter curvature, this effect causes a violent
re-structuring towards them, flattening the branes, which appears as a lowering
of the 4d effective cosmological constant. Braneworld dynamics can often lead
to brane collisions. We found that in the presence of the bulk scalar field,
the 5d geometry between colliding branes approaches a universal, homogeneous,
anisotropic strong gravity Kasner-like asymptotic, irrespective of the
bulk/brane potentials. The Kasner indices of the brane directions are equal to
each other but different from that of the extra dimension.
