We compare the molecular dynamics Green-Kubo and direct methods for calculating thermal conductivity κ, using as a test case crystalline silicon at temperatures T in the range 500-1000 K (classical regime). We pay careful attention to the convergence with respect to simulation size and duration and to the procedures used to fit the simulation data. We show that in the Green-Kubo method the heat current autocorrelation function is characterized by three decay processes, of which the slowest lasts several tens of picoseconds so that convergence requires several tens of nanoseconds of data. Using the Stillinger-Weber potential we find excellent agreement between the two methods. We also use the direct method to calculate κ(T) for the Tersoff potential and find that the magnitude and the temperature-dependence are different for the two potentials and that neither potential agrees with experimental data. We argue that this implies that using the Stillinger-Weber or Tersoff potentials to predict trends in kappa as some system parameter is varied may yield results which are specific to the potential but not intrinsic to Si.
The molecular dynamics non-equilibrium direct method is a well-established way of predicting thermal conductivity , but in good thermal conductors such as crystalline semi-conductors it can yield unacceptably large statistical uncertainties in the extrapolation to a bulk system, . We show how to extract more information from the simulation data in order to reliably calculate tight confidence intervals for . We prove that the measurement error in for a single simulation of size L i and duration D i is proportional to D i L 3 i −1/2 , so that using very large simulations reduces the error more efficiently than using very long durations, as we confirm explicitly with molecular dynamics data. By considering the error propagation we derive an algorithm to determine the optimal set of L i D i which minimizes the probable measurement error in for given total computational effort. Overall, these improvements reduce by an order of magnitude the computational effort required to calculate with a given statistical uncertainty.
In subtractive manufacturing, process monitoring systems are used to observe the manufacturing process, to predict maintenance actions and to suggest process optimizations. One challenge, however, is that the observable signals are influenced not only by the degradation of the cutting tool, but also by deviations in machinability among material batches. Thus it is necessary to first predict the respective material batch before making maintenance decisions. In this study, an approach is shown for batch-aware tool condition monitoring using feature extraction and unsupervised learning to analyze high-frequency control data in order to detect clusters of materials with different machinability, and subsequently optimize the respective manufacturing process. This approach is validated using cutting experiments and implemented as an edge framework.
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