Binary relations between magnitudes of different dimensions used in material science optimization problems. Pseudo-state equation of Soft Magnetic Composities

TL;DR

This paper introduces a pseudo-state equation for soft magnetic composites, enabling improved optimization of their manufacturing parameters by leveraging binary relations between magnitudes of different dimensions under scaling laws.

Contribution

It develops a mathematical framework for using binary relations of different dimensional magnitudes in optimization, leading to a new pseudo-state equation for soft magnetic composites.

Findings

Derived a formal pseudo-state equation for SMC.

Validated the use of binary relations in scaling-based optimization.

Enhanced algorithms for optimizing technological parameters.

Abstract

Suplementary algoritm for optimizing technological parameters of soft magnetic compozities has been derived on the base of topological structure of the power loss characteristics. In optimization processes of magnitudes obeying scaling it happen binary relations of magnitudes having different dimensions. From mathematical point of view in general case such a procedure is not permissible. However, in a case of the system obeying the scaling law it is so. It has been shown that in such systems binary relations of magnitudes of different dimensions is correct and has mathematical meaning which is important for practical use of scaling in optimization processes. Derived here structure of the set of all power loss characteristics in soft magnetic composite enables us to derive a formal pseudo-state equation of SMC. This equation constitutes a realation of the hardening temperature, the compaction pressure and a parameter characterizing the power loss characteristic. Finally, the pseudo-state equation improves the algoritm for designing the best values of technological parameters.