论文标题
根据ZIPF的缩放指数探索城市化水平
Exploring the Level of Urbanization Based on Zipf's Scaling Exponent
论文作者
论文摘要
城市的排名分布遵循ZIPF定律，ZIPF缩放指数通常趋于常数1。这似乎是一般规则。但是，最近的数值实验表明，在一个大人来说，ZIPF指数1与高城市化水平之间存在矛盾。在本文中，采用数学建模，计算分析和通过矛盾的证明方法来揭示城市化水平与ZIPF缩放指数之间的数值关系。主要发现如下。 （1）如果ZIPF缩放指数等于1，那么大人口群的城市化率几乎不超过50％。 （2）如果ZIPF缩放指数小于1，那么大人口群的城市化水平可能会超过80％。可以得出结论，ZIPF指数是城市化动力学的控制参数。为了提高大人口国家的城市化水平，有必要减少ZIPF缩放指数。使用异态增长法来解释ZIPF指数的变化，并采用缩放变换来证明城市的不同定义基本上没有影响上述分析结论。这项研究提供了一种新的方式来研究ZIPF的城市规模分布和城市化动态定律。
The rank-size distribution of cities follows Zipf's law, and the Zipf scaling exponent often tends to a constant 1. This seems to be a general rule. However, a recent numerical experiment shows that there exists a contradiction between the Zipf exponent 1 and high urbanization level in a large population country. In this paper, mathematical modeling, computational analysis, and the method of proof by contradiction are employed to reveal the numerical relationships between urbanization level and Zipf scaling exponent. The main findings are as follows. (1) If Zipf scaling exponent equals 1, the urbanization rate of a large populous country can hardly exceed 50%. (2) If Zipf scaling exponent is less than 1, the urbanization level of large populous countries can exceeds 80%. A conclusion can be drawn that the Zipf exponent is the control parameter for the urbanization dynamics. In order to improve the urbanization level of large population countries, it is necessary to reduce the Zipf scaling exponent. Allometric growth law is employed to interpret the change of Zipf exponent, and scaling transform is employed to prove that different definitions of cities do no influence the above analytical conclusion essentially. This study provides a new way of looking at Zipf's law of city-size distribution and urbanization dynamics.
