Abstract

We study heterogeneous Diffusion Limited Aggregates (DLAs) i.e. those formed by a mixture, in different proportions, of 4-legged and 2-legged particles. We fixed the total number of particles, let the proportions vary, and computed their finite dimension, a recent addition to the list of “fractal” dimensions. At one extreme, when all particles are 4-legged, the corresponding DLAs are complex, fractal structures whose appearance resembles very much that of the DLAs that occur in Nature. At the other extreme, when almost all particles are 2-legged, the DLAs lose much of their complexity and acquire long rectilinear stretches so that their appearance resembles more and more the structure of the underlying lattice. We expected the complexity in between would decrease monotonically, and this would be reflected in the finite dimension of the corresponding DLAs. However, the finite dimension first increases and then, when the proportion of 4-legged to 2-legged particles is about 30 to 70, starts decreasing. In the paper, we study and explain the mechanisms behind this unexpected, counter-intuitive behaviour.

Graphical abstract

中文翻译：

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有限维和粒子异质 DLA

摘要

我们研究异质扩散受限聚集体 (DLA)，即由 4 条腿和 2 条腿粒子以不同比例混合而成的那些。我们固定了粒子的总数，让比例变化，并计算了它们的有限维数，最近添加到“分形”维度列表中。在一个极端情况下，当所有粒子都是四足时，相应的 DLA 是复杂的分形结构，其外观与自然界中出现的 DLA 非常相似。在另一个极端，当几乎所有粒子都是两条腿时，DLA 失去了大部分复杂性并获得了长的直线拉伸，因此它们的外观越来越类似于底层晶格的结构。我们预计两者之间的复杂性会单调下降，这将反映在相应 DLA 的有限维度上。然而，有限维数首先增加，然后，当 4 足粒子与 2 足粒子的比例约为 30 到 70 时，开始减少。在论文中，我们研究并解释了这种意外背后的机制，

图形概要