approximated better. In the limit as approaches infinity, we obtain the continuous Preisach model. Preisach plane One of the easiest ways to look at the Preisach model is using a geometric interpretation. Consider a plane of coordinates . On this plane, each point is mapped to a specific relay hysteron . Each relay can be plotted on this so-called Preisach plane with its values. Depending on their distribution on the Preisach plane, the relay hysterons can represent hysteresis with good accuracy. We consider only the half-plane as any other case does not have a physical equivalent in nature. Next, we take a specific point on the half plane and build a right triangle by drawing two lines parallel to the axes, both from the point to the line . We now present the Preisach density function, denoted . This function describes the amount of relay hysterons of each distinct values of . As a default we say that outside the right triangle . A modified formulation of the classical Preisach model has been presented, allowing analytical expression of the Everett function. This makes the model considerably faster and especially adequate for inclusion in electromagnetic field computation or electric circuit analysis codes. Vector Preisach model The vector Preisach model is constructed as the linear superposition of scalar models. For considering the uniaxial anisotropy of the material, Everett functions are expanded by Fourier coefficients. In this case, the measured and simulated curves are in a very good agreement. Another approach uses different relay hysteron, closed surfaces defined on the 3D input space. In general spherical hysteron is used for vector hysteresis in 3D, and circular hysteron is used for vector hysteresis in 2D. Computer implementation of Preisach model The Preisach model has been implemented in Python and Matlab. Applications The Preisach model has been applied to model hysteresis in a wide variety of fields, including to study irreversible changes in soil hydraulic conductivity as a result of saline and sodic conditions, the modeling of soil water retention and the effect of stress and strains on soil and rock structures. See also Jiles–Atherton model Stoner–Wohlfarth model References External links University College, Cork Hysteresis Tutorial Budapest University of Technology and Economics, Hungary Matlab implementation of the Preisach model developed by Zs. Szabó. Python implementation of Preisach Model. Matlab implementation of Preisach Model. Magnetic hysteresis Hysteresis