Dimension of diffusion-limited aggregates grown on a line

被引：4
|
作者：
Procaccia, Eviatar B. [1 ,4 ]
Procaccia, Itamar [2 ,3 ]
机构：
[1] Technion, Fac Ind Engn & Management, IL-32000 Haifa, Israel
[2] Weizmann Inst Sci, Dept Chem Phys, IL-76100 Rehovot, Israel
[3] Northwestern Polytech Univ, Ctr Opt Imagery Anal & Learning, Xian 710072, Peoples R China
[4] Texas A&M Univ, Dept Math, College Stn, TX 77840 USA
来源：
PHYSICAL REVIEW E | 2021年 / 103卷 / 02期
关键词：
Fractal dimension;
D O I：
10.1103/PhysRevE.103.L020101
中图分类号：
O35 [流体力学]; O53 [等离子体物理学];
学科分类号：
070204 ; 080103 ; 080704 ;
摘要：
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 dimension D of DLA is known. In this Letter we announce an exact result for off-lattice DLA grown on a line embedded in the plane D = 3/2. 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.
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收藏
页数：4
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