### Non-crystallographic motion of dislocations as a fine mixture of
rectlinear paths

Paolo Cermelli

Universitá

Dipartimento di Matematica

We discuss the convergence of an approximation scheme for the
solution, near an attractor, of a discontinuous dynamical system
arising in the theory of dislocations in crystalline solids. It is
well known that dislocations can only move along a finite number of
crystallographic directions: in two dimensions, the resulting
trajectories are piecewise rectilinear paths. However, in special
situations such as near an attractor, dislocations are forced to move
along curved paths: we characterize this class of motions as fine
mixtures of crystallographic motions, using the notion of generalized
curves due to L. C. Young, and explicitly compute the parametrized
measure associated to a sequence of polygonals. The result is then
used to motivate a simple numerical scheme, and show that it is
physically consistent.