A Semigroup Theory of Rate Independent Hysteresis
Disordered Systems and Neural Networks
2007-07-24 v1 Statistical Mechanics
Abstract
We explore a macroscopic, algebraic approach to rate independent hysteresis using semigroup theory. A macroscopic description of metastable states relevant to rate independent hysteresis is introduced using field history. The semigroup structure of the history space is identified. Using semigroup theory and related mathematical techniques, the general relation between return point memory (RPM) and partial order is discovered. For hysteresis system with RPM, a variational principle is identified. The erasing properties of field histories are also characterized. The connection between this semigroup approach and other models are also discussed.
Keywords
Cite
@article{arxiv.0707.3302,
title = {A Semigroup Theory of Rate Independent Hysteresis},
author = {Xiangjun Xing},
journal= {arXiv preprint arXiv:0707.3302},
year = {2007}
}
Comments
4 pages, 2 eps figures, submitted to physical review letters