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Title: Unifying temperature definition in atomistic and field representations of conservation laws
In this work, a field representation of the conservation law of linear momentum is derived from the atomistic, using the theory of distributions as the mathematical tool, and expressed in terms of temperature field by defining temperature as a derived quantity as that in molecular kinetic theory and atomistic simulations. The formulation leads to a unified atomistic and continuum description of temperature and a new linear momentum equation that, supplemented by an interatomic potential, completely governs thermal and mechanical processes across scales from the atomic to the continuum. The conservation equation can be used to solve atomistic trajectories for systems at finite temperatures, as well as the evolution of field quantities in space and time, with atomic or multiscale resolution. Four sets of numerical examples are presented to demonstrate the efficacy of the formulation in capturing the effect of temperature and thermal fluctuations, including phonon density of states, thermally activated dislocation motion, dislocation formation during epitaxial processes, and attenuation of longitudinal acoustic waves as a result of their interaction with thermal phonons.  more » « less
Award ID(s):
2054607
PAR ID:
10528829
Author(s) / Creator(s):
Publisher / Repository:
The Royal Society
Date Published:
Journal Name:
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume:
480
Issue:
2283
ISSN:
1364-5021
Page Range / eLocation ID:
20230606
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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