  Using a recently developed continuum theory of dislocation dynamics, we
derive three new predictions about plasticity and grain boundary formation in
crystals. (1) There will be a residual stress jump across grain boundaries and
plasticity-induced cell walls, which self-consistently acts to form the
boundary by attracting neighboring dislocations; we derive the asymptotic
late-time dynamics of the grain-boundary formation process. (2) At grain
boundaries formed at high temperatures, there will be a cusp in the elastic
energy density. (3) In early stages of plasticity, when only one type of
dislocation is active (single-slip stage I plasticity), cell walls will not
form; instead we predict the formation of jump singularities in the dislocation
density.
