On the equivalence of the two foundational formulations for atomistic flux in inhomogeneous transport processes
Diaz A, Davydov D, Chen Y (2019)
Publication Type: Journal article
Publication year: 2019
Journal
Proceedings of the Royal Society A-Mathematical Physical and Engineering Sciences
Royal Society, The
Book Volume: 475
Article Number: 20180688
Journal Issue: 2223
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.
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APA:
Diaz, A., Davydov, D., & Chen, Y. (2019). On the equivalence of the two foundational formulations for atomistic flux in inhomogeneous transport processes. Proceedings of the Royal Society A-Mathematical Physical and Engineering Sciences, 475(2223). https://dx.doi.org/10.1098/rspa.2018.0688
MLA:
Diaz, Adrian, Denis Davydov, and Youping Chen. "On the equivalence of the two foundational formulations for atomistic flux in inhomogeneous transport processes." Proceedings of the Royal Society A-Mathematical Physical and Engineering Sciences 475.2223 (2019).
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