Scattering by Fractal Structures
Scattering by Fractal Structures
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分形结构的散射
DOI：
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发表时间：
1988
期刊：
影响因子：
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通讯作者：
J. Teixeira
中科院分区：
文献类型：
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作者：
J. Teixeira
自然界中的一些物体乍一看似乎是完全无序的。然而，它们的不规则结构与观测规模无关。换句话说，它们没有特征的长度标尺，但它们是自相似的。在物理学中，这些物体被归类为一大类：分形类。如果严格地取自相似，则得到正则结构，如Cantor集或Sierpinsky垫片。这种理想的情况在现实世界中并不存在。在物理上，一个分形物体的质量分布M(R)遵循长度为R的幂D，该长度小于嵌入该物体的空间的维度d。分形对象的经典示例是高斯聚合物(D=2)或自回避步行聚合物(D=5/3)。在聚集或不规则生长等过程中形成的其他物体，具有从1到d的各种不同的分维。已经推导出预测不同形成条件下的D值的理论。
Some objects in nature appear at first sight as completely disordered. However, their irregular structure is independent of the scale of observation. In other words, they have no characteristic length scale but they are self-similar. In physics, these objects are classified in a large class: the fractals /1/. If the self-similarity is taken in a strict sense, one obtains regular structures such as the Cantor sets or the Sierpinsky gasket. Such ideal situations are not present in the real world. Physically, a fractal object has its mass distribution M(R) following a power D of the length R, which is smaller than the dimension d of the space where the object is embedded. Classical examples of fractal objects are gaussian polymers (D=2) or self avoiding walk polymers (D=5/3). Other objects, formed in processes such as aggregation or irregular growth, have a large variety of fractal dimensions extending from 1 to d. Theories have been derived which predict the values of D for different conditions of formation of fractal objects.