摘要翻译：
我们用半群理论探索了速率无关迟滞的一种宏观的代数方法。利用场史介绍了与速率无关迟滞相关的亚稳态的宏观描述。确定了历史空间的半群结构。利用半群理论和相关数学技巧，发现了返回点记忆(RPM)与偏序之间的一般关系。对于具有RPM的滞环系统，辨识出一个变分原理。对场历史的擦除特性也进行了表征。本文还讨论了该半群方法与其它模型的联系。
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英文标题：
《A Semigroup Theory of Rate Independent Hysteresis》
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作者：
Xiangjun Xing
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最新提交年份：
2007
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分类信息：

一级分类：Physics        物理学
二级分类：Disordered Systems and Neural Networks        无序系统与神经网络
分类描述：Glasses and spin glasses; properties of random, aperiodic and quasiperiodic systems; transport in disordered media; localization; phenomena mediated by defects and disorder; neural networks
眼镜和旋转眼镜；随机、非周期和准周期系统的性质；无序介质中的传输；本地化；由缺陷和无序介导的现象；神经网络
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一级分类：Physics        物理学
二级分类：Statistical Mechanics        统计力学
分类描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变，热力学，场论，非平衡现象，重整化群和标度，可积模型，湍流
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英文摘要：
  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.
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PDF链接：
https://arxiv.org/pdf/707.3302