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Title: Physical foundation and consistent formulation of atomic-level fluxes in transport processes

Abstract

Irving and Kirkwood derived the transport equations from the principles of classical statistical mechanics using the Dirac delta to define local densities. Thereby, formulas for fluxes were obtained in terms of molecular variables. The Irving and Kirkwood formalism has inspired numerous formulations. Many of the later developments, however, considered it more rigorous to replace the Dirac delta with a continuous volume-weighted averaging function and subsequently defined fluxes as a volume density. Although these volume-averaged flux formulas have dominated the literature for decades and are widely implemented in popular molecular dynamics (MD) software, they are a departure from the well-established physical concept of fluxes. We review the historical developments that led to the unified physical concept of fluxes for transport phenomena. We then use MD simulations to show that these popular flux formulas conserve neither momentum nor energy, nor do they produce fluxes that are consistent with their physical definitions. We also use two different approaches to derive fluxes for general many-body potentials. The results of the formulation show that atomistic formulas for fluxes can be fully consistent with the physical definitions of fluxes and conservation laws.

Authors:
 [1];  [1]
  1. Univ. of Florida, Gainesville, FL (United States). Dept. of Mechanical and Aerospace Engineering
Publication Date:
Research Org.:
Univ. of Florida, Gainesville, FL (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)
OSTI Identifier:
1481908
Alternate Identifier(s):
OSTI ID: 1481938
Grant/Contract Number:  
SC0006539
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review E
Additional Journal Information:
Journal Volume: 98; Journal Issue: 5; Journal ID: ISSN 2470-0045
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
74 ATOMIC AND MOLECULAR PHYSICS; nonequilibrium statistical mechanics

Citation Formats

Chen, Youping, and Diaz, Adrian. Physical foundation and consistent formulation of atomic-level fluxes in transport processes. United States: N. p., 2018. Web. doi:10.1103/PhysRevE.98.052113.
Chen, Youping, & Diaz, Adrian. Physical foundation and consistent formulation of atomic-level fluxes in transport processes. United States. doi:10.1103/PhysRevE.98.052113.
Chen, Youping, and Diaz, Adrian. Tue . "Physical foundation and consistent formulation of atomic-level fluxes in transport processes". United States. doi:10.1103/PhysRevE.98.052113. https://www.osti.gov/servlets/purl/1481908.
@article{osti_1481908,
title = {Physical foundation and consistent formulation of atomic-level fluxes in transport processes},
author = {Chen, Youping and Diaz, Adrian},
abstractNote = {Irving and Kirkwood derived the transport equations from the principles of classical statistical mechanics using the Dirac delta to define local densities. Thereby, formulas for fluxes were obtained in terms of molecular variables. The Irving and Kirkwood formalism has inspired numerous formulations. Many of the later developments, however, considered it more rigorous to replace the Dirac delta with a continuous volume-weighted averaging function and subsequently defined fluxes as a volume density. Although these volume-averaged flux formulas have dominated the literature for decades and are widely implemented in popular molecular dynamics (MD) software, they are a departure from the well-established physical concept of fluxes. We review the historical developments that led to the unified physical concept of fluxes for transport phenomena. We then use MD simulations to show that these popular flux formulas conserve neither momentum nor energy, nor do they produce fluxes that are consistent with their physical definitions. We also use two different approaches to derive fluxes for general many-body potentials. The results of the formulation show that atomistic formulas for fluxes can be fully consistent with the physical definitions of fluxes and conservation laws.},
doi = {10.1103/PhysRevE.98.052113},
journal = {Physical Review E},
number = 5,
volume = 98,
place = {United States},
year = {2018},
month = {11}
}

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