Scaling laws and fractality in the framework of a phenomenological approach

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 U 2 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