城市中空间扩散的各向异性研究

STUDY ON THE ANISOTROPIC SPATIALDIFFUSION IN CITIES

由于哈格斯特朗（Ｔ．Ｈａｇｅｒｓｔｒａｎｄ）的空间扩散模型以均质地域为基础，而现实存在的绝大多数为非均质空间，因而需对非均质条件下的空间扩散问题进行探讨。以非均质空间扩散过程来考虑，对革新沿不同扩散轴及在相邻扩散轴间具有不同扩散情况的非均质、各向异性空间扩散问题进行了研究。在应用扩散介质随机游动模型的基础上，通过对扩散的理论模拟，首先建立了当扩散轴正交时的各向异性空间扩散方程。其次，将实平面上非正交的两扩散轴，通过复交换，映射成复平面上的实轴和虚轴，得到扩散概率表达式，再进行逆变换，得出非均质空间、各向异性扩散方程的一般表达式。并以城市住宅地的基准地价评估进行了实例分析。

A significant body of spatial diffusion theory exists as a result of the work of Hagerstrand and others. Spatial diffusion research has been important in understanding the spread of diseases, ideas, businesses,produCts, and people from an initial origin through time and space. But, existent diffusion models have beenfound to be parsimonious and inflexible in solving practical problems, because the Hagerstrand's models wereband on the homogeneous space and the diffusion of geographic environment was ignored.This paper gives out a concept of the nonhomogenous and anisotropic diffusion and points out that if diffusion axes exit, the spatial diffusion possesses anisotropism , such as the growth of morphology of cities. Innovation diffuses firstly along the diffusion axes, then, filling the area between two adjacent axes. Spatial diffusion is not of the same character not only in axes, but also in the area between two adjacent axes.On the basis of stochastic movement equation of the nonhomogenous spatial diffusion, this paper deducesa nonhomogenous and anisotropic spoilal diffusion equation about two orthogonal diffusion axes. Innovationdiffuses firstly along are X and Y. diffusion probability at any point which is in the area closed by X and Ycan be expressed into product of two independent diffusion probabilities along X and Y. The spatial diffusionconformes to a diffusion probability. If two adjacent axes are not vertical, a proper complex transformation istaken. This angled area in plane z is mapped to the retrangle area in plane w and two nonorthogonal axes aremapped to the orthogonal axes u and v. According to the characteristic of the conformal map, this mapping isconformal with the exception of dispersal centre. The spatial diffusion equation in plane w is just the same asthat of orthogonal axes. By using this equation, the diffusion probability at any point can be obtained. Withtaking inverse transformation from w to z, a general stochastic movement equation of the nonhomogenous andanisotropic spatial diffusion can be concluded.This paper also gives an example on appraisal of the basic price of city land. On the basis of this equation, we set up a land price equation and give three conclusions about the isoplethic curves of land price.