Birth, Annexation, and Squeezing of Cities in a Prefecture: Can the Ranking of Competitive Areas of Municipalities Obey the Authentic Power Law?

Kazuya Hayata

doi:10.3389/fphy.2021.789571

Abstract

As the first step for revealing potential rules inherent in cities that are closely squeezed in a sectioned domain, municipalities in the entire prefecture in Japan are considered and their distributions of the areas are analyzed in details according to a rank-size procedure. Computed results suggest that among the population, area, and population density, the last becomes the most important factor in finding the rank-size rule. Indeed, of the 47 Japanese prefectures the Metropolis of Tokyo and Fukuoka Prefecture exhibit the most typical rank-size rules, where the former possesses the exceptionally high population density as well as urbanized rate. The underlying mechanism of the rule can be supported by a toy model with a tournament game using a sequence of random numbers, where teams (municipalities) are highly competitive in gaining the final wins (broadest territory). A stability analysis implying perturbations due to global warming allows one to confirm unexpected robustness of the rank-size relation. Finally, the authenticity of the log-log relation in the rank-area data of Tokyo Metropolis is tested statistically.

Highlights

Cities, towns, and villages have long been regarded as an attractive object of scientific study [1,2,3]
In the context of applied statistical physics, their dynamics, configuration, geography, and population have been studied from a variety of viewpoints [4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20]
# The three frames in Figure 3 show a cross-sectional view of the three-dimensional scattergram of optimal solutions for the entire prefecture in Japan

Summary

Introduction

Towns, and villages have long been regarded as an attractive object of scientific study [1,2,3]. It should be noted here that in most literature the key term “size” has been employed implicitly as the meaning of population. That besides the population there are two meanings in the term, namely, area and population density. Areas of municipalities ( cities but towns and villages being included) that are squeezed in a prefecture of a country are considered. For an example we consider Japan because this country has been divided into 47 prefectures; in each prefecture, typically tens of municipalities are closely packed with a unique configuration that has been arranged according to a self-organized process over a long period.

Results

Discussion

Conclusion