扇形几何中Hastings-Levitov模式的分形结构
Fractal Structure of Hastings-Levitov Patterns Restricted in a Sector Geometry
摘要：
研究了Hastings和Levitov（HL）算法的推广形式，用于模拟扇形几何条件下的扩散限制聚集（DLA）问题。研究发现，这种统一测度的推广在物理空间中产生了“楔形”分形图案，其分形维数和各向异性指数显著依赖于扇形的张开角$β$.通过计算方向图的角两点密度关联函数，分析了方向图的形态特征和整体形状。我们还发现，具有正弦分布测度的图案的分形维数对$β$的依赖性很弱，与径向DLA团簇的维数几乎相同。在这种情况下的各向异性指数和图案的视觉外观示出与那些的对流扩散限制聚集（ADLA）集群兼容。
英文摘要：
A generalized form of the Hastings and Levitov (HL) algorithm for simulation of diffusion-limited aggregation (DLA) restricted in a sector geometry is studied. It is found that this generalization with uniform measure produces "wedge-like" fractal patterns in the physical space, whose fractal dimension and anisotropy exponent depend significantly on the opening angle $β$ of the sector. The morphological properties and the overall shape of the patterns are analyzed by computing the angular two-point density correlation function of the patterns. We also find that the fractal dimension of the patterns with sinusoidal distributed measure depend weakly on $β$ with almost the same dimension as the radial DLA cluster. The anisotropy exponent and the visual appearance of the patterns in this case are shown to be compatible with those of the advection-diffusion-limited aggregation (ADLA) clusters.
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