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.

引用

页数：4

共 50 条

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