On the equivalence of the two foundational formulations for atomistic flux in inhomogeneous transport processes. (20th March 2019)

• Record Type: Journal Article
• Authors: Diaz, Adrian; Davydov, Denis; Chen, Youping
• Is Part Of: Proceedings. Volume 475:Number 2223(2019)
• Publication Date: 2019-03-20
• Subjects: statistical mechanics formalism -- local stress and heat flux -- Irving–Kirkwood procedure -- atomistic flux -- transient transport fluxes -- Dirac delta distribution; Physical sciences -- Periodicals; Engineering -- Periodicals; Mathematics -- Periodicals; 500
• DOI: 10.1098/rspa.2018.0688
• Languages: English
• ISSNs: 1364-5021

Abstract

Abstract : Although there are numerous formulae for atomic-level fluxes, they are expressed either in terms of a singlet density, resulting from Irving and Kirkwood's statistical mechanics formulation of hydrodynamical equations, or a pair density, proposed in kinetic theories of transport processes. Flux formulae using singlet density have been further developed and widely implemented in molecular dynamics (MD) simulations by either replacing the Dirac delta with a volumetric averaging function or performing a surface average of the flux operators. Pair density-based flux formulae have also been further developed by using spatial-averaging kernels; these formulae, however, have rarely been implemented or used in modern MD. In this work, distributional calculus is used to reformulate the fluxes in momentum and energy transport processes. The formulation results demonstrate that these two types of existing flux formulae are mathematically equivalent when expressed with the Dirac delta. The lasting confusion regarding these two different types of flux formulae from two different formalisms is thus resolved.