平面内扩散驱动聚集体生长的形态图：各向异性和粘附力的竞争
Morphological diagram of diffusion driven aggregate growth in plane: competition of anisotropy and adhesion
摘要：
研究了用Witten和Sander算法生长的二维结构。我们用$N_{fp}=3,4,5,6,7$和8个允许的生长方向分析了离格生长的团簇和用天线方法生长的团簇。借助可变探针粒子技术，我们测量了这种团簇$D(N)$的分形维数与团簇尺寸$N$的关系。我们提出，在热力学极限的无限大的集群大小（$N_{fp}=3,4,5$）具有高的各向异性程度的聚集体往往有分形维数$D$等于3/2，而非晶格聚集体和聚集体与较低的各向异性（$N_{fp}>6$）有$D \approx 1.710$。降噪处理导致DLA普适性等级的改变。对于足够高的降噪值，具有$N_{fp} \ge 6$的聚类具有当$N\rightarrow\infty$时变为$3/2$的分形维数。
英文摘要：
Two-dimensional structures grown with Witten and Sander algorithm are investigated. We analyze clusters grown off-lattice and clusters grown with antenna method with $N_{fp}=3,4,5,6,7$ and 8 allowed growth directions. With the help of variable probe particles technique we measure fractal dimension of such clusters $D(N)$ as a function of their size $N$. We propose that in the thermodynamic limit of infinite cluster size the aggregates grown with high degree of anisotropy ($N_{fp}=3,4,5$) tend to have fractal dimension $D$ equal to 3/2, while off-lattice aggregates and aggregates with lower anisotropy ($N_{fp}>6$) have $D \approx 1.710$. Noise-reduction procedure results in the change of universality class for DLA. For high enough noise-reduction value clusters with $N_{fp} \ge 6$ have fractal dimension going to $3/2$ when $N\rightarrow\infty$.
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