Magnetic vector hysteresis model with dry friction-like pinning

On optimal control of a sweeping process coupled with an ordinary differential equation

“…Differential inclusion (1) can be understood as a special form of the maximal dissipation principle in evolution systems with convex constraints. Models of this type play a central role in modeling nonequilibrium processes with rate-independent memory in mechanics of elastoplastic and thermoelastoplastic materials as well as in ferromagnetism, piezoelectricity or phase transitions, see [1], [6], [20] or [39]. Furthermore, differential inclusion (1) is a special case of a sweeping process which was introduced (in its basic form) in [29] and then gradually generalized in a number of papers, e. g. [15] or [25].…”

“…For applications to game theory and Nash equilibria see [7], [26] or [36]. If the aforementioned conditions are not fulfilled, inclusion (1) can be reformulated as a mixture of a differential variational inequality and a differential algebraic equation [3]. For these reformulations see again [31].…”

“…The authors considered only a fixed set Z and made use of the rate-independence of the solution map y → z defined by (1). We utilize some of their results and demonstrate the usefulness of this model by means of a simple example from the area of queuing theory.…”

A Remark on the Local Lipschitz Continuity of Vector Hysteresis Operators

“…[1], [2], [4], [5], [10], [12], [15], [16]) (1.1)      u(t) −ẋ(t), x(t) − w 0 ∀w ∈ Z, x(t) ∈ Z ∀t ∈ [0, T ],…”

Comparison of macroscopic descriptions of magnetization curves

“…[47][48][49]. Figure 4 depicts a saturating hysteresis loop and some first order reversal curves (FORCs) simulated with the GRUCAD model.…”