无序和应力竞争断裂过程中的相变和相关性
Phase transitions and correlations in fracture processes where disorder and stress compete
摘要：
我们研究的无序和应力增强的断裂过程中使用的本地负载共享纤维束模型，一个模型，徘徊在边界之间的分析易处理性和数值可访问性之间的竞争的效果。我们实现了一个可调参数的无序分布。该模型经历了一个本地化的过渡作为这个参数的函数。我们确定了一个序参量，这个过渡，并发现该系统是在本地化的相位在一个有限的范围内的参数值的范围内的过渡到非本地化的相位两侧。在较低的转变为一级转变，在较高的转变为二级转变。表征二级转变的临界指数与表征渗滤转变的临界指数接近。我们确定了局域相的时空关联函数。它的特点是两个幂律在入侵渗流。我们发现指数与该问题中的值一致。
英文摘要：
We study the effect of the competition between disorder and stress enhancement in fracture processes using the local load sharing fiber bundle model, a model that hovers on the border between analytical tractability and numerical accessibility. We implement a disorder distribution with one adjustable parameter. The model undergoes a localization transition as a function of this parameter. We identify an order parameter for this transition and find that the system is in the localized phase over a finite range of values of the parameter bounded by a transition to the non-localized phase on both sides. The transition is first order at the lower transition and second order at the upper transition. The critical exponents characterizing the second order transition are close to those characterizing the percolation transition. We determine the spatiotemporal correlation function in the localized phase. It is characterized by two power laws as in invasion percolation. We find exponents that are consistent with the values found in that problem.
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