According to the self-similarity of powder particle breakage, multi fractal model which could simulate the process of powder
particle breakage and aggregation has been built and also has been discussed the simulation process by using methods of number theory
and matrix. The comparative analysis of the simulation results and the statistical results, shows that the multi fractal model can be used to
accurately describe the breaking process and distribution of powder particles and may have the duality of static state (contribution of
powder particles) and dynamic state (fragmentizing course). According to the fractal dimension obtained from the expression of fractal
dimension have the uniqueness, which show multiple fractal about process of powder particle breakage and aggregation have the uniqueness.
Matrix model based on multi fractal parameters could describe and forecast the breaking process and distribution of powder particles,
and is expected to be insensitive to resolution and sampling length of measuring instrument, so this model is more reasonable and
effective than the traditional model based on statistical analysis.
Keywords: Fractal spectrum, multi fractal, particle distribution, powder.
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