Events
Place: 4th Sino-German Symposium, Ruhr-Universität Bochum, Bochum, Germany
Irina Roslyakova
Holger Dette, Mathematik III, Ruhr-Universität Bochum, Bochum, Germany
Traditionally in applied thermo-physics the temperature dependence of the heat capacity is described by high-order polynomials [1], with adjustable parameters fitted to experimental data. This approach led to fitting coefficients that lack any physical meaning and it is not valid below 298.15K. To overcome this difficulty, in this work we propose more physical approach that requires the modeling of several contributions (e.g. electronic, vibrational, etc.). Since these contributions appear in different temperature ranges [1, 2], the segmented regression methodology [3, 4] was applied for developing of mathematical model for heat capacity of materials. Several segmented regression functions were considered, analyzed and validated by using several statistical tests [5]. Corresponding confidence intervals have been calculated using the bootstrap method [3]. Moreover we investigated the consistency of underlying fitting results, by calculating other physical properties of interest, such as the enthalpy, that can be derived directly from the heat capacity of the studied material. Finally, based on the results, we constructed Gibbs energy function of studied material for the temperature range from 1K up to melting point and compared it with traditional SGTE description. Additionally to this practical issue, the asymptotic theory [3, 6] for the proposed model has being developing. The results of this study are several theorems on consistency and asymptotic normality of nonlinear least square estimator in case of independent not identically distributed random errors.
References:
[1] B. Sundman, H. Lukas, S. Fries (2007). Computational Thermodynamics: The Calphad Method.
[2] G. Grimvall (1986). Thermophysical properties of materials.
[3] G. A. F. Seber, C. J. Wild (1989). Nonlinear Regression.
[4] Chui G. (2002). Bent-Cable Regression for Assessing Abruptness of Change. PhD-Thesis
[5] NIST Engineering Statistic Handbook.
[6] J. Shao (1988). Asymptotic theory in heteroskedastic nonlinear models. Technical report #88-2.
