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

Abstract

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.

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Sokalski, K. , Jankowski, B. and Ślusarek, B. (2014) Binary Relations between Magnitudes of Different Dimensions Used in Material Science Optimization Problems Pseudo-State Equation of Soft Magnetic Composites. Materials Sciences and Applications, 5, 1040-1047. doi: 10.4236/msa.2014.514107.

Conflicts of Interest

The authors declare no conflicts of interest.

 [1] Slusarek, B., Jankowski, B., Sokalski, K. and Szczyglowski, J. (2013) Characteristics of Power Loss in Soft Magnetic Composites a Key for Designing the Best Values of Technological Parameters. Journal of Alloys and Compounds, 581, 699-704. http://dx.doi.org/10.1016/j.jallcom.2013.07.084 [2] Sokalski, K., Szczyglowski, J., Najgebauer, M. and Wilczynski, W. (2007) Losses Scaling in Soft Magnetic Materials. COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, 26, 640-649. http://dx.doi.org/10.1108/03321640710751118 [3] Sokalski, K. and Szczyglowski, J. (2009) Formula for Energy Loss in Soft Magnetic Materials and Scaling. Acta Physica Polonica A, 115, 920-924. [4] Sokalski, K., Szczyglowski, J. and Wilczynski, W. (2013) Scaling Conception of Power Loss’ Separationin Soft Magnetic Materials. International Journal of Condensed Matter, Advanced Materials, and Superconductivity Research (NOVA), 12, Nr. 4. [5] Bertotti, G. (1984) A General Statistical Approach to the Problem of Eddy Current Losses. Journal of Magnetism and Magnetic Materials, 41, 253. http://dx.doi.org/10.1016/0304-8853(84)90192-6 [6] Bertotti, G. (1988) General Properties of Power Losses in Soft Ferromagnetic Materials. IEEE Transactions on Magnetics, 24, 621. http://dx.doi.org/10.1109/20.43994 [7] Ree, F.H. and Hoover, W.G. (1964) Fifth and Sixth Virial Coefficients for Hard Spheres and Hard Disks. The Journal of Chemical Physics, 40, 939. http://dx.doi.org/10.1063/1.1725286 [8] Egenhofer, M. (1989) A Formal Definition of Binary Topological Relationships. In: Litwin, W. and Schek, H.J., Eds., Proceedings of the 3rd International Conference on Foundations of Data Organization and Algorithms (FODO), Paris, France, Lecture Notes in Computer Science, 367, (Springer-Verlag, New York, 1989) 457-472. [9] Nedas, K.A., Egenhofer, M.J. and Wilmsen, D. (2007) Definitions of Line-Line Relations. International Journal of Geographical Information Science, 21, 21-48.