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Overview of Drude-Lorentz type models and their applications

Abstract This paper presents an overview of mathematical models for a better understanding of mechanical processes, as well as dynamics, at the nanoscale. After a short introduction related to semi-empirical and ab initio formulations, molecular dynamics simulations, atomic-scale finite element method, multiscale computational methods, the paper focuses on the Drude-Lorentz type models for the study of dynamics, considering the results of a recently appeared generalization of them for the nanoscale domain. The theoretical framework is illustrated and some examples are considered.