On a low-dimensional model for ferromagnetism
type: Item
instance of: scholarly article
title: On a low-dimensional model for ferromagnetism
zbMATH Open document ID: 1099.34045
author: Ram V. Iyer
author: P. S. Krishnaprasad
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2005-06-13T00:00:00Z
review text: The authors suggest and study a new one-dimensional differential model of rate-independent hysteresis in ferromagnetic materials with two state variables. The model is systematically derived from thermodynamics and energy balance consideration (with some additional assumptions), where hysteresis losses are assumed to have the form postulated by Jiles and Atherton, which essentially means that the losses are proportional to the change of magnetization. Qualitative properties of the model are analyzed, including a proof of the existence and uniqueness of solutions. The main theorem states convergence to a periodic solution from the zero initial state for sinusoidal inputs provided some model parameter is small enough, which is for example the case for small hysteresis losses. This result is then extended to a larger class of inputs.
Mathematics Subject Classification ID: 34C55
Mathematics Subject Classification ID: 82D40
Mathematics Subject Classification ID: 47J40
Mathematics Subject Classification ID: 74M05
Mathematics Subject Classification ID: 34C25
zbMATH DE Number: 2175334
zbMATH Keywords: ferromagnetic hysteresis
zbMATH Keywords: low-dimensional model
zbMATH Keywords: periodic orbit
reviewed by: Dmitrii Rachinskii
MaRDI profile type: Publication
full work available at URL: j.na.2005.01.109
OpenAlex ID: W2166835262
cites work: Hysteresis and phase transitions
cites work: Q3994508
cites work: Q3871201
cites work: Q3029380
cites work: Q3997792
cites work: Differential models of hysteresis
DOI: 10.1016/J.NA.2005.01.109
description: scientific article; zbMATH DE number 2175334