First-principles study of phonon linewidths in noble metals

Phonon lifetimes in Cu, Ag, and Au at low and high temperatures were calculated along high symmetry directions using density functional theory combined with second-order perturbation theory. Both harmonic and third-order anharmonic force constants were computed using a supercell small displacement method, and the two-phonon densities of states were calculated for all three-phonon processes consistent with the kinematics of energy and momentum conservation. A nonrigorous Grüneisen model with no q-dependence of the anharmonic coupling constants offers a simple separation of the potential and the kinematics, and proved semiquantitative for Cu, Ag, and Au. A rule is reported for finding the most anharmonic phonon mode in fcc metals

Anharmonicity-induced phonon broadening in aluminum at high temperatures

Thermal phonon broadening in aluminum was studied by theoretical and experimental methods. Using second-order perturbation theory, phonon linewidths from the third-order anharmonicity were calculated from first-principles density-functional theory (DFT) with the supercell finite-displacement method. The importance of all three-phonon processes were assessed and individual phonon broadenings are presented. The good agreement between calculations and prior measurements of phonon linewidths at 300 K and new measurements of the phonon density of states to 750 K indicates that the third-order phonon-phonon interactions calculated from DFT can account for the lifetime broadenings of phonons in aluminum to at least 80% of its melting temperature

Flexible Clustering with a Sparse Mixture of Generalized Hyperbolic Distributions

Robust clustering of high-dimensional data is an important topic because, in many practical situations, real data sets are heavy-tailed and/or asymmetric. Moreover, traditional model-based clustering often fails for high dimensional data due to the number of free covariance parameters. A parametrization of the component scale matrices for the mixture of generalized hyperbolic distributions is proposed by including a penalty term in the likelihood constraining the parameters resulting in a flexible model for high dimensional data and a meaningful interpretation. An analytically feasible EM algorithm is developed by placing a gamma-Lasso penalty constraining the concentration matrix. The proposed methodology is investigated through simulation studies and two real data sets