速率无关滞后的半群理论
A Semigroup Theory of Rate Independent Hysteresis
摘要：
我们探索了一个宏观的，代数的方法，率独立滞后使用半群理论。利用场历史对与速率无关的滞后现象有关的亚稳态进行了宏观描述。确定了历史空间的半群结构。利用半群理论和相关的数学技巧，发现了返回点记忆（RPM）和偏序之间的一般关系。对于具有转速的迟滞系统，建立了一个变分原理。场历史的擦除特性也得到了表征。文中还讨论了该方法与其它模型的联系。
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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