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Some aspects of mathematical statistics as applied to nonisothermal kinetics

Part III. Unified approach to the analysis of kinetic functions

Journal of Thermal Analysis and Calorimetry
Authors: S. Vyazovkin and A. Lesnikovich
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Some aspects of mathematical statistics as applied to nonisothermal kinetics V

Comparison of the amount of information obtained in traditional and nontraditional approaches

Journal of Thermal Analysis and Calorimetry
Authors: S. V. Vyazovkin and A. I. Lesnikovich

The paper gives a quantitative comparison of two methodological approaches to the solution of the inverse kinetic problem: the traditional approach and the nontraditional approach suggested by the authors. It is shown that the amount of information (in the sense of Shannon) obtained within the scope of the nontraditional approach is always greater than that obtained with the use of the traditional approach.

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This review deals with the choice of a method of solving the inverse kinetic problem (IKP) which would provide the most definite description of the process under conditions of ambiguity. Two fundamentally different methodologies are possible for the IKP solution: one is based on the principle of unambiguous description (discrimination), while the other relies upon the complementarity principle (generalized descriptions). Specific IKP solution methods have been classified, the methodological differences being taken into account. In the first part of this review, general and special limitations in discrimination of formal models have been analysed.

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Some aspects of mathematical statistics as applied to non-isothermal kinetics

Part II. Sensitivity of the kinetic parameter calculation method to the form of the kinetic function

Journal of Thermal Analysis and Calorimetry
Authors: S. V. Vyazovkin and A. I. Lesnikovich

As a numerical characteristic of the sensitivity of the kinetic parameter calculation method to the form of the kinetic function in non-isothermal kinetics, the value of the curvature of the line plotting residual dispersionvs. formal reaction order at the minimum point is suggested. The efficiency of this characteristic is exemplified.

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