Analyses Of Urban Patterns Based On Maximum Flux Principle

Since urban is the most centralized and the most active area of modern materialized civilization and spiritual civilization, there is important and profound implications to study this problem. Explanation for how urban patterns are shaped with the growth of economy will provide a fundamental instructive support for urban planning. Traditional researchers by economists and sociologists usually employed Euclidean geometry and reductive sciences, and great achievements have been made. Nevertheless, for complex urban systems, due to its numerous factors and being unable to carry out experiments and modeling like researches in natural science, it is difficult to make further progresses in this field except for appearance of new research thoughts and methods.Urban is a typical complex system, because it possesses all characteristics of other systems in complex science. Traditional achievements and unsolved problems are first summarized, which is the base of the new theoretical model presented in this paper. For urban systems, it shows that a complex urban system far away from equilibrium is always seeking an optimized process to obtain maximum generalized urban flux under given prices, so called maximum flux principle (MFP). It is proved that the MFP not only agrees with Hamiltonian principle and Darwin evolutionism in complex systems but also has intrinsic relationship with classical thermodynamic theories especially the second thermodynamic law. To study the development of urban structure and urban pattern, urbanization is defined as the aggregating of generalized urban flux here. With this point of view, a new theoretical model for urbanization based on statistical mechanics is presented. An ensemble of interacting micro urban agents is set up in this model, which leads to the renormalized equations of urban systems. The dynamic mechanism is thus found and a fractal structure accordingly appears. With two representative examples of Tianjin Binhai new regions and Guangzhou City, the evolutionary processes of their structures and patterns are analyzed. Then several suggestions on urban planning are put forward based on the problems found concerning two cities.A corresponding numerical simulation method from artificial neural network is developed and applied. Based on the framework of new statistical mechanics in the present model, the self-organizing map (SOM) is further explored. Basing on the same working mechanisms between MFP and SOM, new quantitative numerical simulation method of urban patterns is obtained, by which urban pattern evolution process as well as the corresponding fractal structure of the pattern can be calculated and analyzed. With the statistical data of examples, pattern parameters of urban are calculated in the Matlab simulation system, based on which suggestions on urban planning are proposed. Finally, the advantages and disadvantages of this research are analyzed, and perspectives for further study are also suggested.