物理场多重分形谱理论模型的数值模拟研究

利用二维双标度三分非空集对物理场多重分形谱进行了理论模型的数值模拟研究。模拟结果表明：随着物理量空间分布不均匀性的增大，不同模型参数下的理论分形谱曲线变陡，Dq值域范围变宽。利用多重分形谱曲线的形态特征，可进一步了解是“稀疏区”还是“密集区”起主导作用，这对于从理论上把握物理和化学场分布特性具有重要意义。

A NUMERICAL SIMULATION STUDY ON THEORETICALMODELS OF MULTIFRACTAL SPECTRA FOR PHYSICAL FIELD

The theoretical models with different modeling parameters are studied for physical field using 2 dimensional, double scaled, non empty,three equally divided sets. The result shows that the multifractal spectra curves (D-q q curves) become steeper and value ranges of D-q wider with the increasing of the spatial inhomogeneity of modeling parameters. Furthermore, according to the behaviors of multifractal spectra curves in -q and q sections, it can be determined that the distribution feature of fractal structure dominated by "thinner sub sets" or "thicker sub sets". This will be important for grasping the distribution features of physical and chemical fields from the theory.