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首页> 外文期刊>Annales Henri Poincare >The Structure of State Transition Graphs in Systems with Return Point Memory: I. General Theory
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The Structure of State Transition Graphs in Systems with Return Point Memory: I. General Theory

机译：返回点记忆系统中的状态转换图结构：I。一般理论

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We consider the athermal quasi-static dynamics (AQS) of disordered systems driven by an external field. Our interest is in an automaton description (AQS-A) that represents the AQS dynamics via a graph of state transitions triggered by the field and in the presence of return-point-memory (RPM) property, a tendency for the system to return to the same microstate upon cycling driving. The existence of three conditions, (1) a partial order on the set of configuration; (2) a no-passing property; and (3) an adiabatic response to monotonously changing fields, implies RPM. When periodically driven, such systems settle into a cyclic response after a transient of at most one period. While sufficient, conditions (1)-(3) are not necessary. We show that the AQS dynamics provides a more selective partial order which, due to its explicit connection to hysteresis loops, is a natural choice for establishing the RPM property. This enables us to consider AQS-A exhibiting RPM without necessarily possessing the no-passing property. We call such automata lAQS-A and work out the structure of their state transition graphs. We find that the RPM property constrains the intra-loop structure of hysteresis loops, namely its hierarchical organization into sub-loops, but not the inter-loop structure. We prove that the topology of the intra-loop structure can be represented as an ordered tree and show that the corresponding state transition graph is planar. On the other hand, the RPM property does not significantly restrict the inter-loop transitions. A system exhibiting RPM and subject to periodic forcing can undergo a large number of transient cycles before settling into a periodic response. Such systems can even exhibit subharmonic response.
机译：我们考虑由外部场驱动的无序系统的滴漏准静态动态（AQS）。我们的兴趣是在Automaton描述（AQS-A）中，它通过字段触发的状态转换图和在存在返回点内存（RPM）属性的情况下，返回的趋势骑行驾驶时的Microstate相同。存在三种条件，（1）集合上的部分顺序; （2）一个无越的财产; （3）对单调改变田地的绝热反应意味着rpm。当定期驱动时，这种系统在最多一个时期的瞬态后核对循环响应。虽然足够，条件（1） - （3）不是必需的。我们表明AQS动态提供了一种更具选择性的部分顺序，由于其与滞后环的显式连接，是建立RPM属性的自然选择。这使我们能够考虑AQS-A表现出RPM，同时不一定拥有无通过的财产。我们称之为Automata Laqs-A并解决其州过渡图的结构。我们发现RPM属性约束滞后循环的循环内结构，即其分层组织进入子环路，但不是环路循环结构。我们证明了跨内结构的拓扑结构可以表示为有序树，并显示相应的状态转换图是平面的。另一方面，RPM属性不会显着限制循环间转换。在定期响应之前，表现出RPM并经过周期性强制而经过周期性循环的系统可以进行大量的瞬态循环。这种系统甚至可以表现出次谐响应。

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