Fractal-Based Modeling and Spatial Analysis of Urban Form and Growth: A Case Study of Shenzhen in China

Study on the structural characteristics of China's high-speed railway network and its coordination with economic growth based on Fractal theory

As one of the modern transportation modes, the high-speed railway network system has been a robust part of the comprehensive transportation system in China. An important topic emerges the exploration and optimization of its structural organization and coordinated relationship with the regional development, including urban form, land use, and economy. Therefore, supported by the integration of geographical information system (GIS) and fractal theory, this paper aims to carry out an investigation and discussion on the structural characteristics, including intensity (density), complexity, nonstationarity, and heterogeneity of the high-speed railway network in China (HSRNC) from the perspective of the whole country and specific regions, i.e., urban agglomerations. Moreover, based on the time-series data of network mileage expansion and economic output analysis, this study aims to evaluate and characterize the coordinated relationships between network development and economic growth in the context of the nationwide area and urban agglomerations. This study aims to explore and promote the spatial structural organization and morphology of the high-speed railway network in China, thus improving the coordinated development with the regional economic growth, for giving a new perspective to the future planning and evolution of the high-speed railway network in China.

Optimization of emergency allocation of necessities of life based on fractal perspective

The supply and reserves of emergency necessities of life are important for emergency management in disaster events. The scope of the necessities of life changes with social development, and their reserves and allocation in sudden disaster events continually face new challenges. Timely distribution of the necessities of life during disasters is critical to saving lives and maintaining social order. Therefore, this study proposes a fractal multi-level distribution network (FMDN) optimization model with multiple warehouse points, multiple emergency distribution centers, and multiple disaster points from the perspective of fractal theory. The FMDN model considers the influence of road damage on vehicle speed and the dynamic change in demand at the affected points. The FMDN model aims to minimize the operating costs of a distribution network, including the cost of building emergency reserve points, transportation costs, and penalty costs for lack of demand. Numerical experiments verify the feasibility of the model. The FMDN model is solved using LINGO software programming, and an optimal distribution path and quantity are obtained. Analyzing the numerical example results shows that the model is suitable for emergencies and has good applicability.

Modeling Urban Growth and Socio-Spatial Dynamics of Hangzhou, China: 1964–2010

Urban population density provides a good perspective for understanding urban growth and socio-spatial dynamics. Based on sub-district data of the five national censuses in 1964, 1982, 1990, 2000, and 2010, this paper is devoted to analyzing of urban growth and the spatial restructuring of the population in the city of Hangzhou, China. Research methods are based on mathematical modeling and field investigation. The modeling result shows that the negative exponential function and the power-exponential function can be well fitted to Hangzhou’s observational data of urban density. The negative exponential model reflects the expected state, while the power-exponential model reflects the real state of urban density distribution. The parameters of these models are linearly correlated to the spatial information entropy of population distribution. The fact that the density gradient in the negative exponential function flattened in the 1990s and 2000s is closely related to the development of suburbanization. In terms of investigation materials and the changing trend of model parameters, we can reveal the spatio-temporal features of Hangzhou’s urban growth. The main conclusions can be reached as follows. The policy of reformation and opening-up and the establishment of a market economy improved the development mode of Hangzhou. As long as a city has a good social and economic environment, it will automatically tend to the optimal state through self-organization.