The software package ESPEI has been developed for efficient evaluation of thermodynamic model parameters within the CALPHAD method. ESPEI uses a linear fitting strategy to parameterize Gibbs energy functions of single phases based on their thermochemical data and refine the model parameters using phase equilibrium data through Bayesian optimization within a Markov Chain Monte Carlo machine learning approach. In this paper, the methodologies employed in ESPEI are discussed in detail and demonstrated for the Cu-Mg system down to 0 K using unary descriptions based on segmented regression. The model parameter uncertainties are quantified and propagated to the Gibbs energy functions. a − J J J , where J is the chemical potential of the target hyperplane calculated in step 1.
This paper discusses methods of interpreting the backscattering signals received from a weakly scattering atmosphere. It is established that the interpretation of these signals can be made more accurate by using an efficient averaging procedure on a section of the probe path and a linear approximation of the transmittance.
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