d维Apollonian垫片的分维估计
Estimate for the fractal dimension of the Apollonian gasket in d dimensions
摘要：
我们采用了最近的理论在三维多分散球的随机紧密堆积[R。S. Farr和R. D. Groot，J. Chem. Phys. { \bf 131} 244104（2009）]，以便预测2维及以上的阿波罗垫圈的Hausdorff尺寸$d_{A}$。我们的近似结果同意在$2$和$3$尺寸内公布的值分别在$0.05%$和$0.6%$，我们提供尺寸$4$到$8$的预测。
英文摘要：
We adapt a recent theory for the random close packing of polydisperse spheres in three dimensions [R. S. Farr and R. D. Groot, J. Chem. Phys. {\bf 131} 244104 (2009)] in order to predict the Hausdorff dimension $d_{A}$ of the Apollonian gasket in dimensions 2 and above. Our approximate results agree with published values in $2$ and $3$ dimensions to within $0.05%$ and $0.6%$ respectively, and we provide predictions for dimensions $4$ to $8$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
