Abstract The issue of how to find the best acoustical fit to a set of anisotropic elastic constants is addressed. The optimal moduli are determined which minimize the orientation averaged squared-norm of the difference in the acoustical tensors. The optimal moduli are derived explicitly and turn out to be identical to those obtained by minimizing the Euclidean distance function, or equivalently...

The paper draws on the similarities between the well-known process of whiskerization of microfibres and the recent idea of bristled nanowires. The new method for evaluation of the effective elastic properties of such materials is suggested based on the model of four-component composition. This model assumes the transverse isotropy of continuum and predicts five elastic moduli and density as ind...

The issue of how to define and determine an optimal acoustical fit to a set of anisotropic elastic constants is addressed. The optimal moduli are defined as those which minimize the mean-squared difference in the acoustical tensors between the given moduli and all possible moduli of a chosen higher material symmetry. The solution is shown to be identical to minimizing a Euclidean distance funct...

A new general tight-binding total energy (TBTE) method is presented that accurately predicts energy diierences caused by small perturbations such as those occurring in the evaluation of elastic constants and phonon spectra as well as energy diierences from large changes in structure such as structural energy diierences, equations of state, and defect energies. Unlike other quantitative TBTE mod...