Connectivity in waves and vibrations: One-to-six, one-to-all, all-to-all and random connections
This paper develops a theory of propagation based on connectivity templates. Connectivity describes how the elastic connections distribute. A visual counterpart is the structure of the stiffness matrix. D'Alembert equation refers to classical elasticity based on closest neighbors connectivity and is characterized by propagation of waves, which can be classified as one-to-six, since each particle of the scheme is connected only with two other particles for each direction. However, very different connectivity schemes can be introduced, e.g.