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首页> 外文期刊>Physica, A. Statistical mechanics and its applications >Geometrical minimum units of fracture patterns in two-dimensional space: Lattice and discrete Walsh functions
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Geometrical minimum units of fracture patterns in two-dimensional space: Lattice and discrete Walsh functions

机译：二维空间中断裂模式的几何最小单位：晶格和离散沃尔什函数

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We present the geometrical minimum units of fracture patterns in two-dimensional space. For this analysis, a new method is developed from the algebraic approach: the concept of lattice (a type of partially ordered set) is applied to the discrete Walsh functions that have been used to measure symmetropy (an object related to symmetry and entropy) of fracture patterns. We concluded that the minimum units of fracture patterns can be expressed as three kinds of lattice. Our model is applied to the temporal change of the spatial pattern of acoustic-emission events in a rock-fracture experiment. As a result, the symmetropy of lattice decreases with the evolution of fracture process. We find that the pre-nucleation process of fracture corresponds to the subcritical states, and the propagation process to the critical states. Moreover, using a particular mathematical structure called sheaf on a lattice, we suggest the algebraic interpretation of fracture process, and provide justification to regard fracturing as an irreversible process. (C) 2008 Elsevier B.V. All Fights reserved.
机译：我们提出了二维空间中断裂模式的几何最小单位。为了进行此分析，从代数方法中开发出一种新方法：将晶格（部分有序集的一种类型）的概念应用于离散的Walsh函数，该函数已用于测量正交项（与对称性和熵有关的对象）断裂模式。我们得出的结论是，断裂模式的最小单位可以表示为三种晶格。我们的模型应用于岩石破裂实验中声发射事件的空间模式的时间变化。结果，随着断裂过程的发展，晶格的同向性降低。我们发现，断裂的预成核过程对应于亚临界状态，而传播过程则对应于临界状态。此外，我们使用一种称为网格的特殊数学结构，建议对断裂过程进行代数解释，并提供将断裂视为不可逆过程的理由。 （C）2008 Elsevier B.V.版权所有。

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