In many scientific fields, empirical models are employed to facilitate computational simulations of engineering systems. For example, in fluid mechanics, empirical Reynolds stress closures enable computationally-efficient Reynolds Averaged Navier Stokes simulations. Likewise, in solid mechanics, constitutive relations between the stress and strain in a material are required in deformation analysis. Traditional methods for developing and tuning empirical models usually combine physical intuition with simple regression techniques on limited data sets. The rise of high performance computing has led to a growing availability of high fidelity simulation data. These data open up the possibility of using machine learning algorithms, such as random forests or neural networks, to develop more accurate and general empirical models. A key question when using data-driven algorithms to develop these empirical models is how domain knowledge should be incorporated into the machine learning process. This paper will specifically address physical systems that possess symmetry or invariance properties. Two different methods for teaching a machine learning model an invariance property are compared. In the first method, a basis of invariant inputs is constructed, and the machine learning model is trained upon this basis, thereby embedding the invariance into the model. In the second method, the algorithm is trained on multiple transformations of the raw input data until the model learns invariance to that transformation. Results are discussed for two case studies: one in turbulence modeling and one in crystal elasticity. It is shown that in both cases embedding the invariance property into the input features yields higher performance at significantly reduced computational training costs.
Given the unique optical properties of LiF, it is often used as an observation window in high-temperature and -pressure experiments; hence, estimates of its transmission properties are necessary to interpret observations. Since direct measurements of the thermal conductivity of LiF at the appropriate conditions are difficult, we resort to molecular simulation methods. Using an empirical potential validated against ab initio phonon density of states, we estimate the thermal conductivity of LiF at high temperatures (1000-4000 K) and pressures (100-400 GPa) with the Green-Kubo method. We also compare these estimates to those derived directly from ab initio data. To ascertain the correct phase of LiF at these extreme conditions, we calculate the (relative) phase stability of the B1 and B2 structures using a quasiharmonic ab initio model of the free energy. We also estimate the thermal conductivity of LiF in an uniaxial loading state that emulates initial stages of compression in high-stress ramp loading experiments and show the degree of anisotropy induced in the conductivity due to deformation.
Accurate simulation of the plastic deformation of ductile metals is important to the design of structures and components to performance and failure criteria. Many techniques exist that address the length scales relevant to deformation processes, including dislocation dynamics (DD), which models the interaction and evolution of discrete dislocation line segments, and crystal plasticity (CP), which incorporates the crystalline nature and restricted motion of dislocations into a higher scale continuous field framework. While these two methods are conceptually related, there have been only nominal efforts focused at the global material response that use DD-generated information to enhance the fidelity of CP models. To ascertain to what degree the predictions of CP are consistent with those of DD, we compare their global and microstructural response in a number of deformation modes. After using nominally homogeneous compression and shear deformation dislocation dynamics simulations to calibrate crystal plasticity ow rule parameters, we compare not only the system-level stress-strain response of prismatic wires in torsion but also the resulting geometrically necessary dislocation density fields. To establish a connection between explicit description of dislocations and the continuum assumed with crystal plasticity simulations we ascertain the minimum length-scale at which meaningful dislocation density fields appear. Furthermore, our results show that, for the case of torsion, that the two material models can produce comparable spatial dislocation density distributions.
In this report we explore the sensitivities of the insulation resistance between two loops of wire embedded in insulating materials with a simple, approximate model. We discuss limita- tions of the model and ideas for improvements.
TlBr is promising for g- and x- radiation detection, but suffers from rapid performance degradation under the operating external electric fields. To enable molecular dynamics (MD) studies of this degradation, we have developed a Stillinger-Weber type of TlBr interatomic potential. During this process, we have also addressed two problems of wider interests. First, the conventional Stillinger-Weber potential format is only applicable for tetrahedral structures (e.g., diamond-cubic, zinc-blende, or wurtzite). Here we have modified the analytical functions of the Stillinger-Weber potential so that it can now be used for other crystal structures. Second, past modifications of interatomic potentials cannot always be applied by a broad community because any new analytical functions of the potential would require corresponding changes in the molecular dynamics codes. Here we have developed a polymorphic potential model that simultaneously incorporates Stillinger-Weber, Tersoff, embedded-atom method, and any variations (i.e., modified functions) of these potentials. As a result, we have implemented this polymorphic model in MD code LAMMPS, and demonstrated that our TlBr potential enables stable MD simulations under external electric fields.
We present a Green-Kubo method to spatially resolve transport coefficients in compositionally heterogeneous mixtures. We develop the underlying theory based on well-known results from mixture theory, Irving-Kirkwood field estimation, and linear response theory. Then, using standard molecular dynamics techniques, we apply the methodology to representative systems. With a homogeneous salt water system, where the expectation of the distribution of conductivity is clear, we demonstrate the sensitivities of the method to system size, and other physical and algorithmic parameters. Then we present a simple model of an electrochemical double layer where we explore the resolution limit of the method. In this system, we observe significant anisotropy in the wall-normal vs. transverse ionic conductances, as well as near wall effects. Finally, we discuss extensions and applications to more realistic systems such as batteries where detailed understanding of the transport properties in the vicinity of the electrodes is of technological importance.