  We consider the TASEP on Z with two blocks of particles having different jump
rates. We study the large time behavior of particles' positions. It depends
both on the jump rates and the region we focus on, and we determine the
complete process diagram. In particular, we discover a new transition process
in the region where the influence of the random and deterministic parts of the
initial condition interact. Slow particles may create a shock, where the
particle density is discontinuous and the distribution of a particle's position
is asymptotically singular. We determine the diffusion coefficient of the shock
without using second class particles. We also analyze the case where particles
are effectively blocked by a wall moving with speed equal to their intrinsic
jump rate.
