【摘要】 提出3种模型———小尺寸随机逐次成核生长模型和二维及三维代代聚集生长模型,在不同的近邻条件下和不同尺寸的网格中,通过蒙特卡罗模拟,系统地研究了一维、二维和三维分形聚集的逾渗性质.计算结果显示,分形聚集的逾渗阈值仅取决于空间维数和近邻条件,与模型的网格大小无关,是分形系统固有的临界属性;生长概率等于逾渗阈值时,聚集体可以无限生长并保持分形维数恒定,此时的分形维数只是空间维数的线性函数.更多还原

【Abstract】 We present a randomsuccessive nucleation growth model,a two-and a three-dimensional aggregation generation-by-generation model to investigate percolation properties of fractal aggregations with various neighbor conditions and lattice size.Itshows that the percolationthreshold of fractal aggregationisindependent of the lattice size.It dependents onspatial dimension andneighbor conditions,andis aninherent property of the fractal system.The fractal aggregate grows infinitely withthe same fractaldimension whenthe growth probabilityis equal tothe percolationthreshold.The fractal dimension is just a linear function of thespatial dimension.更多还原