Binary Relations between Magnitudes of Different Dimensions Used in Material Science Optimization Problems Pseudo-State Equation of Soft Magnetic Composites

作     者：Krzysztof Z.Sokalski Bartosz Jankowski Barbara Slusarek 

作者机构：Institute of Computer SciencesCzestochowa University of TechnologyCzestochowaPoland Tele and Radio Research InstituteWarszawaPoland 

出 版 物：《Materials Sciences and Applications》 (材料科学与应用期刊（英文）)

年 卷 期：2014年第5卷第14期

页      面：1040-1047页

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：supported by National Center of Science within the framework of research project Grant N N507 249940 

主　　题：Soft Magnetic Composites Scaling Binary Relations Pseudo-State Equation 

摘      要：New algorithm for optimizing technological parameters of soft magnetic composites has been derived on the base of topological structure of the power loss characteristics. In optimization magnitudes obeying scaling, it happens that one has to consider binary relations between the 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, the binary relations of magnitudes of different dimensions is correct and has mathematical meaning which is important for practical use of scaling in optimization processes. The derived structure of the set of all power loss characteristics in soft magnetic composite enables us to derive a formal pseudo-state equation of Soft Magnetic Composites. This equation constitutes a relation of the hardening temperature, the compaction pressure and a parameter characterizing the power loss characteristic. Finally, the pseudo-state equation improves the algorithm for designing the best values of technological parameters.