Uniform states in slightly defective crystals
A slightly defective crystal is a material whose response to deformation depends on a density, three linearly independent lattice or director vectors, the gradient of the density, and the curl of the lattice vectors at each point (the body has fields of these quantities defined on it). Uniform states of slightly defective crystals are states where the density is constant, the six inner products of the lattice vectors are constant, the gradient of the density is zero, and the nine inner products of the lattice vectors with their curls are constant over the whole body. The solution of these 15 equations is shown to be a field of rotation operators, and a uniform state is a configuration where the lattice vectors are rotated by varying amounts about a single fixed axis.
three linearly independent lattice or director vectors
six inner products of the lattice vectors are constant
nine inner products of the lattice vectors with their curls are constant
scientific article; zbMATH DE number 4174431