  Malleability of metals is an example of how dynamics of defects like
dislocations induced by external stresses alters material properties and
enables technological applications. However, these defects move merely to
comply with the mechanical forces applied on macroscopic scales whereas the
molecular and atomic building blocks behave like rigid particles. Here we
demonstrate how motions of crystallites and defects between them can arise
within the soft matter medium in an oscillating electric field applied to a
chiral liquid crystal with polycrystalline quasi-hexagonal arrangements of
self-assembled topological solitons called "torons". Periodic oscillations of
electric field applied perpendicular to the plane of hexagonal lattices prompt
repetitive shear-like deformations of the solitons, which synchronize the
electrically-powered self-shearing directions. The temporal evolution of
deformations upon turning voltage on and off is not invariant upon reversal of
time, prompting lateral translations of the crystallites of torons within
quasi-hexagonal periodically deformed lattices. We probe how these motions
depend on voltage and frequency of oscillating field applied in an experimental
geometry resembling that of liquid crystal displays. We study the
inter-relations between synchronized deformations of the soft solitonic
particles and their arrays and the ensuing dynamics and giant number
fluctuations mediated by motions of crystallites, 5-7 defects pairs and grain
boundaries in the orderly organizations of solitons. We discuss how our
findings may lead to technological and fundamental science applications of
dynamic self-assemblies of topologically protected but highly deformable
particle-like solitons.
