Parameter computation and optimization for phase transitions of the first kind in chemically active materials

Abstract

Numerous features, bifurcations and catastrophes (“jumps”) arise in problems of optimization, control and decision making. They can be detected by calculation extreme values of the respective functions. The selection of optimum control parameters for a number of technological processes is closely related to detection of initial and final moments of phase transitions of the first kind. This problem is based on the analysis of behavior of thermodynamic potentials and of their derivatives. Mathematical descriptions of phase transitions of the first kinds within the framework of phenomenological thermodynamics using the symplectic geometry formalism have indicated that in general they are accompanied by a weak disruption, or “jump” of the first derivative of the thermodynamic potential with respect to extensive parameter. Changes in physical condition of the studied materials are accompanied by changes of electric impedances and temperatures. A method has been suggested for detection of phase transition moments in order to achieve optimum composition of materials and optimum control of their strengthening and hardening processes. A special case of such materials are samples of freshly-mixed concrete. They form the experimental basis for the researches. Statistical analysis has demonstrated high correlation between the moments of kinetic phase transition of the first kind and the concentration surface-active substances in chemically active materials.