Aifantis, E.C. (2019) Fractional Generalizations of Gradient Mechanics. In: Tarasov, V.E., Ed., Handbook of Fractional Calculus with Applications, Volume 4, De Gruyter, Berlin, 241-262.
https://doi.org/10.1515/9783110571707-010

has been cited by the following article:

• TITLE: From Gradient Elasticity to Gradient Interatomic Potentials: The Case-Study of Gradient London Potential

  AUTHORS: Kostas Parisis, Fei Shuang, Bo Wang, Pu Hu, Andreas Giannakoudakis, Avraam Konstantinidis

  KEYWORDS: Gradient Elasticity, London’s Potential, Gradient Interatomic Potentials

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.8 No.9, September 15, 2020

  ABSTRACT: Motivated by the special theory of gradient elasticity (GradEla), a proposal is advanced for extending it to construct gradient models for interatomic potentials, commonly used in atomistic simulations. Our focus is on London’s quantum mechanical potential which is an analytical expression valid until a certain characteristic distance where “attractive” molecular interactions change character and become “repulsive” and cannot be described by the classical form of London’s potential. It turns out that the suggested internal length gradient (ILG) generalization of London’s potential generates both an “attractive” and a “repulsive” branch, and by adjusting the corresponding gradient parameters, the behavior of the empirical Lennard-Jones potentials is theoretically captured.