Coarse-Graining of Atomistic Models to the Continuum Scale with Applications to Elastodynamics and Diffusive Processes
Nonequilibrium phenomena are ubiquitous in nature as well as industrial applications. However, their modeling and simulation faces a strong compromise between physical fidelity and computational efficiency, with atomistic simulations and continuum descriptions lying towards the two ends of this spectrum. In this dissertation, we will first revisit several continuum modeling strategies for the formulation of nonequilibrium evolution equations, and show by means of an example, inconsistencies that can arise between the various formalisms. This example will serve as a motivation for developing coarse-graining strategies that can directly link atomistic and continuum models in the context of reversible and irreversible evolutions. With regard to reversible phenomena, we will present an upscaling scheme that provides a new angle to the classical thermodynamic description of the elastodynamics of solids at finite temperature as the spatio-temporal continuum limit of atomistic Hamiltonian dynamics. This scheme identifies suitable macroscopic (slow) variables and provides its effective equations of motion via elimination of the fast degrees of freedom in the limit of infinite time/space scale separation. In addition, it provides highly intuitive mathematical explanations to various well-known thermodynamic relations. For purely irreversible processes, a novel coarse-graining strategy is proposed that numerically delivers the entire continuum evolution equation (and not just parameters therein) from particle fluctuations via an infinite-dimensional fluctuation-dissipation relation. The methodology is exemplified for a diffusion process with known analytical solution, where an excellent agreement is obtained for the density evolution. The text in this dissertation, particularly Sections 3, 4 and parts of the introduction, closely follows the papers by the authors Li & Reina (2019), Li et al. (2019).
Li, Xiaoguai, "Coarse-Graining of Atomistic Models to the Continuum Scale with Applications to Elastodynamics and Diffusive Processes" (2019). Dissertations available from ProQuest. AAI22588557.