Binary relations between magnitudes of different dimensions used in   material science optimization problems. Pseudo-state equation of Soft   Magnetic Composities
  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. 
Krzysztof Zdzis{\l}aw Sokalski, Bartosz Jankowski and Barbara   \'Slusarek
cond-mat.mtrl-sci