Constitutive models in nanoscience and engineering often poorly represent the physics due to significant deviations in model form from their macroscale counterparts. In Part 1 of this study, this problem was explored by considering a continuum scale heat conduction constitutive law inferred directly from molecular dynamics (MD) simulations. In contrast, this work uses Bayesian inference based on the MD data to construct a Gaussian process emulator of the heat flux as a function of temperature and temperature gradient. No assumption of Fourier-like behavior is made, requiring alternative approaches to assess the well-posedness and accuracy of the emulator. Validation is provided by comparing continuum scale predictions using the emulator model against a larger all-MD simulation representing the true solution. The results show that a Gaussian process emulator of the heat conduction constitutive law produces an empirically unbiased prediction of the continuum scale temperature field for a variety of time scales, which was not observed when Fourier’s law is assumed to hold. Finally, uncertainty is propagated in the continuum model and quantified in the temperature field so the impact of errors in the model on continuum quantities can be determined.
Advances in technology for electrochemical energy storage require increased understanding of electrolyte/electrode interfaces, including the electric double layer structure, and processes involved in charging of the interface, and the incorporation of this understanding into quantitative models. Simplified models such as Helmholtz's electric double-layer (EDL) concept don't account for the molecular nature of ion distributions, solvents, and electrode surfaces and therefore cannot be used in predictive, high-fidelity simulations for device design. This report presents theoretical results from models that explicitly include the molecular nature of the electrical double layer and predict critical electrochemical quantities such as interfacial capacitance. It also describes development of experimental tools for probing molecular properties of electrochemical interfaces through optical spectroscopy. These optical experimental methods are designed to test our new theoretical models that provide descriptions of the electric double layer in unprecedented detail.