2007/07/23 by Xiangjun Xing, Xing, Xiangjun
Engineering · Physics and Astronomy · #Disordered Systems and Neural Networks (cond-mat.dis-nn) #FOS: Physical sciences #Metallurgy and Material Forming #Statistical Mechanics (cond-mat.stat-mech) #cond-mat.dis-nn #cond-mat.stat-mech
paper · pdf · doi:10.48550/arxiv.0707.3302
4 pages, 2 eps figures, submitted to physical review letters
arxiv created 2007/07/23 · openalex publication_date 2007/07/23 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.