| Summary: | 碩士 === 國立清華大學 === 物理系 === 103 === It has been reported that the distribution of crumpling noise obeys simple power law (SPL). But the analyses were baded on the Least Squares method which judges the goodness of fit by minimizing the residual sum of squares and error. We show that this method is flawed and may cause delusion when judging whether a set of data obeys SPL. By bridging the gap with mathematicians, we introduce a more rigorous statistical method: AIC (Akaike information criterion).
By use of AIC, we found the crumpling sound in fact obeys the Zipf-Mandelbrot distribution (ZMD), instead of SPL when the thin sheet is wringed. The delicacy of this difference is explained by a designed experiment and the attenuation effect.
To both test the robustness and SPL and simulate a system with more than one intrinsic mechanism, we also arranged for two different sheets to be crumpled together. By sorting the data according to different time order, we observed a subtle transition from Double power law (DPL) in the early phase to SPL when the crumpled ball is more compact. This result is consistent with the general belief and the prediction of a PNAS article [1] that enhanced interactions are capable of causing such a transition in statistical behavior.
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