The law of allometric scaling based on Zipf distributions can be employed to research hierarchies of cities in a geographical region. However, the allometric patterns are easily influenced by random disturbance from the noises in observational data. In theory, both the allometric growth law and Zipf's law are related to the hierarchical scaling laws associated with fractal structure. In this paper, the scaling laws of hierarchies with cascade structure are used to study Chinese cities, and the method of R/S analysis is applied to analyzing the change trend of the allometric scaling exponents. The results show that the hierarchical scaling relations of Chinese cities became clearer and clearer from 1991 to 2014 year; the global allometric scaling exponent values fluctuated around 0.85, and the local scaling exponent approached to 0.85. The Hurst exponent of the allometric parameter change is greater than 0.5, indicating persistence and a long-term memory of urban evolution. The main conclusions can be reached as follows: the allometric scaling law of cities represents an evolutionary order rather than an invariable rule, which emerges from self-organized process of urbanization, and the ideas from allometry and fractals can be combined to optimize spatial and hierarchical structure of urban systems in future city planning.
The development of public transportation networks and associated transit oriented development policies are efficient tools to mitigate urban sprawl and its negative environmental impacts, especially in terms of commuting emissions. We study in this paper the trajectories in terms of sprawl and public transport accessibility of the nine largest Chinese megacities, from 2000 to 2030 with projected transportation networks and populations. Using the radial profile methodology, we compare the evolution of population distribution with the evolution of accessibility profiles. We show a rebalancing of…
Multiple small- to middle-scale cities, mostly located in northern China, became epidemic hotspots during the second wave of the spread of COVID-19 in early 2021. Despite qualitative discussions of potential social-economic causes, it remains unclear how this pattern could be accounted for from a quantitative approach. Through the development of an urban epidemic hazard index (EpiRank), we came up with a mathematical explanation for this phenomenon. The index is constructed from epidemic simulations on a multi-layer transportation network model on top of local SEIR transmission dynamics, which…
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 …
Cities are centers for the integration of capital and incubators of invention, and attracting venture capital (VC) is of great importance for cities to advance in innovative technology and business models towards a sustainable and prosperous future. Yet we still lack a quantitative understanding of the relationship between urban characteristics and VC activities. In this paper, we find a clear nonlinear scaling relationship between VC activities and the urban population of Chinese cities. In such nonlinear systems, the widely applied linear per capita indicators would be either biased to large…
Traffic networks have been proved to be fractal systems. However, previous studies mainly focused on monofractal networks, while complex systems are of multifractal structure. This paper is devoted to exploring the general regularities of multifractal scaling processes in the street network of 12 Chinese cities. The city clustering algorithm is employed to identify urban boundaries for defining comparable study areas; box-counting method and the direct determination method are utilized to extract spatial data; the least squares calculation is employed to estimate the global and local multifrac…
Publicly traded companies are fundamental units of contemporary economies and markets and are important mechanisms through which humans interact with their environments. Understanding the general properties that underlie the processes of their growth has long been of interest, yet fundamental debates about the effects of firm size on growth have persisted. Here we develop a scaling framework that focuses on company size as the critical feature determining a variety of tradeoffs, and use this to reveal novel systematic behavior across the diversity of publicly-traded companies. Using a large da…
