A phenomenological mathematical model of hysteresis

This paper starts with the description of a purely mathematical model of th e saturation curve and the hysteresis loop based on the fundamental similar ities between the Langevin function the specified T(x) function and the sig moid shape. The T(x) function which is composed of tangent hyperbolic and l inear functions with its free parameters can describe the regular anhystere tic magnetisation curve. Developed from this function the model describes n ot only the regular hysteresis loop but also the biased and other minor loo ps like the ones produced by the interrupted and reversed magnetisation pro cess and the open "loops" created by a piecewise monotonic magnetising fiel d input of diminishing amplitude. The remanent magnetism as the function of the interrupted field co-ordinates is predicted by the model in this mathe matical form for the first time. The model presented here is based on the p rinciple that all processes follow the shape of the T(x) function describin g the shape of the major hysteresis loop of the ferromagnetic specimen unde r investigation. The model is also applicable to hysteretic processes in ot her fields.