It has long been conjectured that (rapid) fracture propagation dynamics in materials and turbulent motion of fluids are two manifestations of the same physical process. The universality class of turbulence (Kolmogorov dispersion, in particular) is conjectured to be identifiable with the Flory statistics for linear polymers (self-avoiding walks on lattices). These help us to relate fracture statistics to those of linear polymers (Flory statistics). The statistics of fracture in the fiber bundle model (FBM) are now well studied and many exact results are now available for the equal-load-sharing (ELS) scheme. Yet, the correlation length exponent in this model was missing and we show here how the correspondence between fracture statistics and the Flory mapping of Kolmogorov statistics for turbulence helps us to make a conjecture about the value of the correlation length exponent for fracture in the ELS limit of FBM and, also, about the upper critical dimension. In addition, the fracture avalanche size exponent values at lower dimensions (as estimated from such mapping to Flory statistics) also compare well with the observations.

中文翻译：

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通过Kolmogorov弥散获得的湍流在纤维束模型中产生的类似于弗洛里断裂的统计数据：一个推测。

长期以来，人们一直认为，材料中的（快速）裂缝扩展动力学和流体的湍流运动是同一物理过程的两个体现。湍流的普遍性类别（尤其是Kolmogorov弥散度）被推测可以通过线性聚合物的弗洛里统计量来识别（晶格上的自规步道）。这些帮助我们将断裂统计与线性聚合物的断裂统计联系起来（Flory统计）。现在已经对纤维束模型（FBM）中的断裂统计进行了深入研究，并且对于等负载分担（ELS）方案，现在可以获得许多准确的结果。然而，该模型中的相关长度指数缺失，并且我们在此处显示了裂缝统计量和Kolmogorov统计数据对湍流的Flory映射之间的对应关系如何帮助我们猜想骨折的相关长度指数在FBM的ELS极限内的值以及关于上限临界尺寸。此外，较低尺寸的裂缝雪崩尺寸指数值（从此类映射到Flory统计数据估计）也与观测值比较好。