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Overview of Drude-Lorentz type models and their applications

100%

Di Sia P.

Nanoscale Systems: Mathematical Modeling, Theory and Applications

2014

tom 3

nr 1

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.

Subdifferential inclusions and quasi-static hemivariational inequalities for frictional viscoelastic contact problems

100%

Migórski S.

Open Mathematics

2012

tom 10

nr 6

1953-1968

We survey recent results on the mathematical modeling of nonconvex and nonsmooth contact problems arising in mechanics and engineering. The approach to such problems is based on the notions of an operator subdifferential inclusion and a hemivariational inequality, and focuses on three aspects. First we report on results on the existence and uniqueness of solutions to subdifferential inclusions. Then we discuss two classes of quasi-static hemivariational ineqaulities, and finally, we present ideas leading to inequality problems with multivalued and nonmonotone boundary conditions encountered in mechanics.

Ograniczanie wyników

1 Nanoscale Systems: Mathematical Modeling, Theory and Applications

1 Open Mathematics

1 Di Sia P.

1 Migórski S.

1 2014

1 2012

Wyniki wyszukiwania

Overview of Drude-Lorentz type models and their applications

Subdifferential inclusions and quasi-static hemivariational inequalities for frictional viscoelastic contact problems