I. The Classical Preisach Model of Hysteresis.- 1 Definition of the Classical Preisach Model.- 2 Geometric Interpretation and Main Properties of the Preisach Model.- 3 Experimental Determination of µ(?, ?). Representation Theorem.- 4 Numerical Implementation of the Preisach Model.- 5 The Preisach Model and Hysteretic Energy Losses.- 6 Preisach Model with Stochastic Input as a Model for Viscosity.- II. Generalized Scalar Preisach Models of Hysteresis.- 1 Moving Preisach Model of Hysteresis.- 2 Nonlinear Preisach Model of Hysteresis.- 3 Restricted Preisach Models of Hysteresis.- 4 Dynamic Preisach Models of Hysteresis.- 5 Preisach Model of Hysteresis with Accommodation.- 6 Superconducting Hysteresis and Preisach-Type Models.- 7 Magnetostrictive Hysteresis and Preisach Models with Two Inputs.- 8 Experimental Testing of Preisach-Type Models of Hysteresis.- III. Vector Presiach Models of Hysteresis.- 1 Classical Stoner-Wohlfarth Model of Vector Hysteresis.- 2 Definition of Vector Preisach Models of Hysteresis and Their Numerical Implementation.- 3 Some Basic Properties of Vector Preisach Hysteresis Models.- 4 Identification Problem for Isotropic Vector Preisach Models.- 5 Identification Problem for Anisotropic Vector Preisach Models.- 6 Dynamic Vector Preisach Models of Hysteresis.- 7 Generalized Vector Preisach Models of Hysteresis.- References.
The purpose of this book is to describe in sufficient detail the mathematical models of hysteresis nonlinearities with "nonlocal memories. " The distinct feature of these nonlinearities is that their future states depend on past histories of input variations. It turns out that memories of hysteresis nonlinearities are quite selective. Indeed, experiments show that only some past input extrema (not the entire input variations) leave their marks upon future states of hysteresis nonlinearities. Thus, special mathematical tools are needed to describe nonlocal selective memories of hysteresis nonlinearities. The origin of such tools can be traced back to the landmark paper of Preisach. The book is primarily concerned with Preisach-type models of hysteresis. All these models have a common generic feature; they are constructed as superposi tions of simplest hysteresis nonlinearities-rectangular loops. The discussion is by and large centered around the following topics: various generalizations and extensions of the classical Preisach model (with special emphasis on vector generalizations), finding of necessary and sufficient conditions for the represen tation of actual hysteresis nonlinearities by various Preisach-type models, solution of identification problems for these models, and numerical implementa tion and experimental testing of Preisach-type models. Although the study of Preisach-type models constitutes the main subject of the book, some effort is also made to establish some interesting connections between these models and such topics as the critical state model for superconducting hysteresis, the classi cal Stoner-Wohlfarth model for vector magnetic hysteresis, thermal activation type models for viscosity, magnetostrictive hysteresis and neural networks.
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