摘要
讨论了固体薄膜材料裂纹分形研究中出现的一类分维不确定性问题，指出实际分形体的近似分形结构是其产生的根本原因，并在数学上给予了证明，材料断裂行为中的多度域似分形结构维数测量、计算中也存在分维不确定性问题，文中也进行了讨论。
The fractal theory has been used widely for study of materials and surface and fractural study in particular. The uncertainty of fractal dimension is the key to the actual application of fractal theory. Lung et al. has reported the uncertainty of perimeter-area method used for fractal dimension calculation of actual fractals. We have discovered the uncertainty of capacity dimension equation used for the fractal structure of DLC films' cracks, ahd the effects of the measurement yardsticks on the fractal dimension in actual measurement. Based on the finite-level structure of actual fractals, the measurement yardsticks are not arbitrary values and within a certain size range beyond the range, fractal dimension will be varia ble and uncertain. We have completely interpreted the uncertainty of fractal dimension calculation of actual fractals by the means of mathematical method.
出处
《材料科学与工艺》
EI
CAS
CSCD
1998年第1期63-65,共3页
Materials Science and Technology
