The band gap for elastic waves propagating in a cubical lattice of spherical scatterers is observed through a series of numerical simulations. Along the direction of the incident wave, scatterer arrangements are viewed as comprising layers of scatterers, within which scatterers form a square grid. Starting from one layer and by increasing the number of layers, near-field forward and backward wave propagation spectra are computed as the number of layers increases. In the computations, scatterer polymerization methodology is used. This methodology is based on an analytically exact solution to a general three-dimensional multiple scattering problem obtained by the authors. It can be used to reduce an assemblage of actual scatterers to a lesser number of abstract scatterers. These simulations also demonstrate that the computational system has the capability to simulate multiple scattering of elastic waves in three-dimensional space.

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