论文标题

纤维束模型中裂缝的like状统计,通过kolmogorov湍流分散剂获得:一种猜想

Flory-like Statistics of Fracture in Fiber Bundle Model as obtained via Kolmogorov Dispersion for Turbulence: A conjecture

论文作者

Biswas, Soumyajyoti, Chakrabarti, Bikas K.

论文摘要

长期以来,人们一直猜想材料中(快速的)断裂传播动力学和流体的湍流运动是相同物理过程的两种表现。湍流的通用类别(尤其是kolmogorov分散体)被认为可以通过线性聚合物(晶格上的自我避免行走)的液化统计数据来识别。这些帮助我们将断裂统计数据与线性聚合物的统计数据联系起来(Flory Statistics)。现在已经对纤维束模型(FBM)中断裂的统计数据进行了充分的研究,现在可以使用相等的负载分享(ELS)方案进行许多确切的结果。然而,该模型中缺少相关长度指数,我们在这里展示了裂缝统计数据与Kolmogorov统计量的湍流统计量的对应关系如何有助于我们对FBM ELS极限中裂缝的相关长度指数的值进行猜想,以及FBM限制的裂缝的值。此外,较低维度的断裂雪崩大小指数值(从映射到弗洛里统计的估计)也与观测值很好地比较。

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.

扫码加入交流群

加入微信交流群

微信交流群二维码

扫码加入学术交流群,获取更多资源