On the product Preisach model of hysteresis

The product model is an output-dependent modification of the traditional Preisach model in order to remove its non-real congruency property. The differential susceptibility is proposed to be a product of a magnetization-dependent factor and an expression containing two terms: one for the reversible process and the other an integral of a Preisach type distribution for the irreversible part. Thus the magnetization is an indirect function, in which the saturation is a natural property of the hysteresis model, and the reversible and irreversible parts of the magnetization are added up indirectly. The envelope function is related to the paramagnetic process and in the specific case of uni-axial anisotropy it is a hyperbolic tangent function. The measurement of the anhysteretic curve may provide the direct link to the evaluation methods of experimental data applied for traditional Preisach modeling. reserved.