Unifying temperature definition in atomistic and field representations of conservation laws

IF 2.9 3区 综合性期刊 Q1 MULTIDISCIPLINARY SCIENCES Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences Pub Date : 2024-02-07 DOI:10.1098/rspa.2023.0606
Youping Chen
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Abstract

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.
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统一守恒定律原子表征和场表征中的温度定义
在这项工作中,利用分布理论作为数学工具,从原子论推导出了线性动量守恒定律的场表示法,并通过将温度定义为分子动理论和原子模拟中的导出量来表示温度场。通过这种表述方法,可以对温度进行统一的原子和连续描述,并建立一个新的线性动量方程,辅以原子间势能,可以完全控制从原子到连续尺度的热过程和机械过程。该守恒方程可用于求解有限温度下系统的原子轨迹,以及具有原子或多尺度分辨率的场量在空间和时间上的演化。本文介绍了四组数值示例,展示了该公式在捕捉温度和热波动影响方面的功效,包括声子态密度、热激活的位错运动、外延过程中的位错形成,以及纵向声波与热声子相互作用产生的衰减。
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来源期刊
CiteScore
6.40
自引率
5.70%
发文量
227
审稿时长
3.0 months
期刊介绍: Proceedings A has an illustrious history of publishing pioneering and influential research articles across the entire range of the physical and mathematical sciences. These have included Maxwell"s electromagnetic theory, the Braggs" first account of X-ray crystallography, Dirac"s relativistic theory of the electron, and Watson and Crick"s detailed description of the structure of DNA.
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