论文标题
裂缝过程中的相位转变和相关性，而混乱和压力竞争
Phase transitions and correlations in fracture processes where disorder and stress compete
论文作者
论文摘要
我们研究了使用局部负载共享纤维束模型在断裂过程中竞争与应力增强之间的竞争效果，该模型徘徊在分析性障碍和数值可及性之间的边界上。我们用一个可调节参数实施疾病分布。该模型作为此参数的函数进行本地化过渡。我们确定了此过渡的顺序参数，并发现该系统位于局部阶段，这是在有限的参数值范围内，该值由两侧的过渡到非定位阶段界定。该过渡是在下部过渡时期的一阶，在上部过渡时进行了二阶。表征二阶转变的临界指数接近表征渗滤过渡的临界指数。我们确定局部阶段中的时空相关函数。它的特征是两种权力定律，如入侵渗透中。我们发现与该问题中发现的值一致的指数。
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.
