Turbulence纤维束模型中基于Kolmogorov色散的Flory-like断裂统计：一个猜想
Flory-like Statistics of Fracture in Fiber Bundle Model as obtained via Kolmogorov Dispersion for Turbulence: A conjecture
摘要：
长期以来，人们一直认为材料中的（快速）断裂扩展动力学和流体的湍流运动是同一物理过程的两种表现。湍流的普适性类（特别是Kolmogorov色散）已经被证明可以用线性聚合物的Flory统计（晶格上的自回避行走）来识别。这些有助于我们将断裂统计与线性聚合物的断裂统计（弗洛里统计）联系起来。纤维束模型（FBM）中的断裂统计现在已经得到了很好的研究，并且对于等载荷分配（ELS）方案，现在有许多精确的结果。然而，在这个模型中的相关长度指数是失踪，我们在这里展示了如何骨折统计和Flory映射的Kolmogorov统计湍流之间的对应关系，帮助我们做出一个猜想的相关长度指数的值骨折的ELS限制FBM，也约上临界尺寸。此外，在较低的维度的断裂雪崩尺寸指数值（估计从这样的映射到Flory统计）也比较好的观察。
英文摘要：
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) had been 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. Besides, the fracture avalanche size exponent values in lower dimensions (as estimated from such mapping to Flory statistics) also compare well with the observations.
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