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Scaling laws and fractality in the framework of a phenomenological approach

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  • Delsanto, Pier Paolo
  • Gliozzi, Antonio S.
  • Bruno, Caterina L.E.
  • Pugno, Nicola
  • Carpinteri, Alberto

Abstract

Phenomenological Universality (PUN) represents a new tool for the classification and interpretation of different non-linear phenomenologies in the context of cross-disciplinary research. Also, they can act as a “magnifying glass” to finetune the analysis and quantify the difference among similarly looking datasets. In particular, the class U2 is of special relevance since it includes, as subcases, most of the commonly used growth models proposed to date. In this contribution we consider two applications of special interest in two subfields of Elasto-dynamics, i.e. Fast- and Slow-Dynamics, respectively. The results suggest that new equations should be adopted for the fitting of the experimental results and that fractal-dimensioned variables should be used to recover the scaling invariance, which is invariably lost due to non-linearity.

Suggested Citation

  • Delsanto, Pier Paolo & Gliozzi, Antonio S. & Bruno, Caterina L.E. & Pugno, Nicola & Carpinteri, Alberto, 2009. "Scaling laws and fractality in the framework of a phenomenological approach," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2782-2786.
    • Handle: RePEc:eee:chsofr:v:41:y:2009:i:5:p:2782-2786
    DOI: 10.1016/j.chaos.2008.10.014
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    Cited by:

    1. Barberis, L. & Condat, C.A., 2012. "Describing interactive growth using vector universalities," Ecological Modelling, Elsevier, vol. 227(C), pages 56-63.
    2. Jia Liu & Fengshan Ma & Jie Guo & Guang Li & Yewei Song & Yang Wan, 2022. "A Field Study on the Law of Spatiotemporal Development of Rock Movement of Under-Sea Mining, Shandong, China," Sustainability, MDPI, vol. 14(10), pages 1-13, May.
    3. Barberis, L. & Condat, C.A. & Román, P., 2011. "Vector growth universalities," Chaos, Solitons & Fractals, Elsevier, vol. 44(12), pages 1100-1105.

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