  The asymmetric exclusion process is an idealised stochastic model of
transport, whose exact solution has given important insight into a general
theory of nonequilibrium statistical physics. In this work, we consider a
totally asymmetric exclusion process with multiple species of particles on a
one-dimensional lattice in contact with reservoirs. We derive the exact
nonequilibrium phase diagram for the system in the long time limit. We find two
new phenomena in certain regions of the phase diagram: when the density of a
species becomes zero throughout the system, and dynamical localisation when the
density of a species is nonzero only within an interval far from the
boundaries. We give a complete explanation of the macroscopic features of the
phase diagram using what we call nested fat shocks.
