Bertotti G, Mayergoyz I D, Basso V, Magni A
Istituto Elettrotecnico Nazionale Galileo Ferraris, Corso Massimo d'Azeglio 42, I-10125 Torino, Italy.
Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 1999 Aug;60(2 Pt A):1428-40. doi: 10.1103/physreve.60.1428.
A general formulation of scalar hysteresis is proposed. This formulation is based on two steps. First, a generating function g(x) is associated with an individual system, and a hysteresis evolution operator is defined by an appropriate envelope construction applied to g(x), inspired by the overdamped dynamics of systems evolving in multistable free-energy landscapes. Second, the average hysteresis response of an ensemble of such systems is expressed as a functional integral over the space G of all admissible generating functions, under the assumption that an appropriate measure mu has been introduced in G. The consequences of the formulation are analyzed in detail in the case where the measure mu is generated by a continuous, Markovian stochastic process. The calculation of the hysteresis properties of the ensemble is reduced to the solution of the level-crossing problem for the stochastic process. In particular, it is shown that, when the process is translationally invariant (homogeneous), the ensuing hysteresis properties can be exactly described by the Preisach model of hysteresis, and the associated Preisach distribution is expressed in closed analytic form in terms of the drift and diffusion parameters of the Markovian process. Possible applications of the formulation are suggested, concerning the interpretation of magnetic hysteresis due to domain wall motion in quenched-in disorder and the interpretation of critical state models of superconducting hysteresis.
提出了标量磁滞的一般公式。该公式基于两个步骤。首先，一个生成函数g(x)与单个系统相关联，并且受在多稳态自由能景观中演化的系统的过阻尼动力学启发，通过对g(x)应用适当的包络构造来定义磁滞演化算子。其次，在假设已在G空间中引入适当测度μ的情况下，此类系统集合的平均磁滞响应表示为所有可允许生成函数的空间G上的泛函积分。在测度μ由连续的马尔可夫随机过程生成的情况下，详细分析了该公式的结果。集合的磁滞特性的计算简化为随机过程的水平穿越问题的求解。特别地，表明当过程是平移不变（均匀）时，随后的磁滞特性可以由磁滞的Preisach模型精确描述，并且相关的Preisach分布根据马尔可夫过程的漂移和扩散参数以封闭解析形式表示。提出了该公式的可能应用，涉及对由于淬火无序中的畴壁运动引起的磁滞的解释以及对超导磁滞的临界状态模型的解释。
