Dimension of diffusion-limited aggregates grown on a line
Dimension of diffusion-limited aggregates grown on a line
复制标题
在线生长的扩散限制聚集体的尺寸
DOI：
10.1103/physreve.103.l020101
复制
发表时间：
2021
影响因子：
2.4
通讯作者：
Procaccia, Itamar
中科院分区：
文献类型：
--
作者：
Procaccia, Eviatar B.;Procaccia, Itamar
扩散限制聚集(DLA)作为创造分形生长模式的范例已有40年之久。尽管参考了数千篇文献，但关于DLA的分维还没有确切的结果。在这封信中，我们宣布了一个关于非晶格DLA的精确结果，它生长在嵌入平面的直线上。其结果依赖于用迭代保角映射表示DLA，从而允许证明自亲和性、适当的标度极限和定义良好的分形维。主要结果的数学证明可在N.Berger，E.B.Procaccia和A.Turner，Growth of Static Hastings-Levitov，arxiv：2008.05792中找到。
Diffusion-limited aggregation (DLA) has served for 40 years as a paradigmatic example for the creation of fractal growth patterns. In spite of thousands of references, no exact result for the fractal dimensionof DLA is known. In this Letter we announce an exact result for off-lattice DLA grown on a line embedded in the plane. The result relies on representing DLA with iterated conformal maps, allowing one to prove self-affinity, a proper scaling limit, and a well-defined fractal dimension. Mathematical proofs of the main results are available in N. Berger, E. B. Procaccia, and A. Turner, Growth of stationary Hastings-Levitov, arXiv:2008.05792.