Stochastic model of hysteresis

The methods of the probability theory have been used in order to build up a new model of hysteresis. It turns out that the reversal points of the control parameter (e. g., the magnetic field) are Markov points which determine the stochastic evolution of the process. It has been shown that the branches of the hysteresis loop are converging to fixed limit curves when the number of cyclic back-and-forth variations of the control parameter between two consecutive reversal points is large enough. This convergence to limit curves gives a clear explanation of the accommodation process. The accommodated minor loops show the return-point memory property but this property is obviously absent in the case of non-accommodated minor loops which are not congruent and generally not closed. In contrast to the traditional Preisach model the reversal point susceptibilities are non-zero finite values. The stochastic model can provide a good approximation of the Raylaigh quadratic law when the external parameter varies between two sufficiently small values.Comment: 13 pages, 14 figure

Hysteresis losses along open transformations

It is shown that the analytical theory of hysteresis, which determines the value of J at the end of an arbitrary path of H if the magnetization curve and the saturation loop are known, can be extended to compute the energy losses due to hysteresis along an arbitrary transformation, open or closed, in the (J, H) plane. The theoretical data have been computed for a soft iron specimen and for an Alnico type material. The latter have been compared with experimental data taken by Bates and Simpson on a similar material. The quantitative agreement between theoretical and experimental curves is quite satisfactory.Si la courbe d'aimantation et le cycle à saturation sont connus, on démontre que la théorie analytique de l'hystérésis, qui détermine la valeur de J à la fin d'un parcours arbitraire de H, peut être étendue au calcul des pertes causées par l'hystérésis au cours d'une transformation arbitraire, ouverte ou fermée, dans le plan (J, H). Les données théoriques ont été calculées pour un échantillon de fer doux et pour un matériau du type Alnico. Ces dernières ont été comparées avec les données expérimentales de Bates et Simpson obtenues pour un matériau analogue. L'accord quantitatif entre les courbes expérimentale et théorique est satisfaisant