Mathematical Models of Hysteresis

Abstract

Thus, before discussing the proposed research in detail, it is worthwhile to describe and summarize the main results achieved in the course of the research work under the above contract.The ongoing research has largely been forcused on the development of mathematical models 6f hysteretic nonlinearities with "nonlocal memories". The distinct feature of these nonlinearities is that their current states depend on past histories of input variations. It turns out that memories of hysteretic nonlinearities are quite selective. Indeed, experimentsshow that only some past input extrema (not the entire input variations) leave their marks upon future states of hysteretic nonlinearities. Thus special mathematical tools are need in order to describe nonlocal selective memories of hysteretic nonlinearities. The origin of such tools can be traced back to the landmark paper of Preisach.Our research has been primarily concerned with Preisach-type models of hysteresis.All these models have a common generic feature; they are constructed as superpositions of simplest hysteretic noiilinearities-rectangular loops. During the past four years, our study has been by and large centered around the folloing topics:Further development of scalar and vector Preisacli-type models of hysteresis.e Experimental testing of Preisach-type models of hysteresis.Development of new models for viscosity (aftereffect) in hysteretic systems. Next, I shall briefly described the main scientific results obtained in the areas outlined A §T above.

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“…Rather, in some studies, QOL responses seem subject to adaptation and may return spontaneously to some provisionally stable set-point, despite a constant level of stress [20-22], due to habituation [23] and/or active coping [24]. Change in QOL may also follow a pattern described by engineers and economists as hysteresis [25]. That is, stress may be added without inducing apparent change in a system (or a person), up to a certain level of tolerance, beyond which the system may undergo permanent and profound change that makes it impossible to returning to earlier tolerances.…”

First order reversal curves and intrinsic parameter determination for magnetic materials; limitations of hysteron-based approaches in correlated systems

“…The recently developed identification schemes to extract the SFD based on the inverse problem solving approach include applications to assemblies of magnetic nanoparticles7, and Δ H(M , Δ M ) method for granular materials relevant in magnetic recording891011121314, which was motivated by the earlier Δ H c methodology15. Simpler approaches to identify the SFD with variable degree of consistency were based on the differentiation of hysteresis loop ‘de-sheared’ to remove the contribution from magneto-static interactions16, methods based on Preisach models17, and methods based on analysing the transformed first order reversal curves (FORC), i.e. magnetisation curves generated by reversing the external magnetic field starting from a point on a major hysteresis loop branch (Fig.…”

Memory of recessions

“…This is a manifestation of the famous wiping out principle of the Preisach model, as described in Mayergoyz (1986).…”