论文标题
随机apollonian包装的平均场方法
Mean-field approach to Random Apollonian Packing
论文作者
论文摘要
我们使用平均场方法重新审查了在D = 2,3和4个维度中随机接种的生长球的缩放特性。我们在不假定半径分布的功能形式的情况下对插入概率进行建模。插入概率的功能形式显示了与d = 2、3和4维中数值模拟的前所未有的一致性。我们从插入概率推断出随机apollonian填料及其分形维度的缩放行为。我们的模型的有效性通过256个模拟集进行了评估，每个模拟都在2、3和4维度中包含2000万球。
We revisit the scaling properties of growing spheres randomly seeded in d=2,3 and 4 dimensions using a mean-field approach. We model the insertion probability without assuming a priori a functional form for the radius distribution. The functional form of the insertion probability shows an unprecedented agreement with numerical simulations in d=2, 3 and 4 dimensions. We infer from the insertion probability the scaling behavior of the Random Apollonian Packing and its fractal dimensions. The validity of our model is assessed with sets of 256 simulations each containing 20 million spheres in 2, 3 and 4 dimensions.
