The almost periodic rigidity of crystallographic bar-joint frameworks
  A crystallographic bar-joint framework C is shown to be almost periodically infinitesimally rigid if and only if it is strictly periodically infinitesimally rigid and the rigid unit mode (RUM) spectrum is a singleton. Moreover the almost periodic infinitesimal flexes of C are characterised in terms of a matrix-valued function on the d-torus determined by a full rank translation symmetry group and an associated motif of joints and bars. 
G. Badri, D. Kitson and S. C. Power
math.MG math-ph math.MP