A best-fit model of power losses in cold rolled-motor lamination steel operating in a wide range of frequency and magnetization

A procedure is described for identifying a mathematical model of core losses in ferromagnetic steel based on a minimal amount of experimental data. The new model has a hysteresis loss multiplicative coefficient variable only with frequency, a hysteresis loss power coefficient variable both with frequency and induction and a combined coefficient for eddy-current and excess losses that is, within a set frequency range, variable only with induction. Validation was successfully performed on a large number of different samples of nongrain oriented fully and semiprocessed steel alloys. Over a wide range of frequencies between 20 Hz and 2.1 kHz and inductions from 0.05 up to 2 T, the errors of the proposed model are substantially lower than those of a conventional model with fixed value coefficients

Shy and Fixed-Distance Couplings of Brownian Motions on Manifolds

In this paper we introduce three Markovian couplings of Brownian motions on smooth Riemannian manifolds without boundary which sit at the crossroad of two concepts. The first concept is the one of shy coupling put forward in \cite{Burdzy-Benjamini} and the second concept is the lower bound on the Ricci curvature and the connection with couplings made in \cite{ReSt}. The first construction is the shy coupling, the second one is a fixed-distance coupling and the third is a coupling in which the distance between the processes is a deterministic exponential function of time. The result proved here is that an arbitrary Riemannian manifold satisfying some technical conditions supports shy couplings. If in addition, the Ricci curvature is non-negative, there exist fixed-distance couplings. Furthermore, if the Ricci curvature is bounded below by a positive constant, then there exists a coupling of Brownian motions for which the distance between the processes is a decreasing exponential function of time. The constructions use the intrinsic geometry, and relies on an extension of the notion of frames which plays an important role for even dimensional manifolds. In fact, we provide a wider class of couplings in which the distance function is deterministic in Theorem \ref{t:100} and Corollary~\ref{Cor:9}. As an application of the fixed-distance coupling we derive a maximum principle for the gradient of harmonic functions on manifolds with non-negative Ricci curvature. As far as we are aware of, these constructions are new, though the existence of shy couplings on manifolds is suggested by Kendall in \cite{Kendall}.Comment: This version is a refinement expansion and simplification of the previous versio