In the present chapter, we show that the use of the nondifferentiable mathematical procedures, developed in the Scale Relativity Theory with constant arbitrary fractal dimension, simplifies very much the dynamics analyses in the case of complex systems. By applying such a procedure to various complex systems dynamics (biological structures, ablation or discharge plasmas, etc.), we are able to observe that it starts from a steady (oscillating state) and as the external factor is varied the system undergoes significant changes. The systems evolve asymptotically through various transition, toward a chaotic regime (like bifurcations or intermittencies), but never reaching it. Another important reveal from the study of the system’s dynamics was the presence of various steady states depending on the resolution scale at which the theoretical investigations are performed.
Part of the book: Fractal Analysis
Understanding the underline fundamental mechanism behind experimental and industrial technologies embodies one of the foundations of the advances and tailoring new materials. With the pulsed laser deposition being one of the key techniques for obtaining complex biocompatible materials with controllable stoichiometry, there is need for experimental and theoretical advancements towards understanding the dynamics of multi component plasmas. Here we investigate the laser ablation process on Cu-Mn-Al and Fe-Mn-Si by means of space-and time-resolved optical emission spectroscopy and fast camera imaging. In a fractal paradigm the space–time homographic transformations were correlated with the global dynamics of the ablation plasmas.
Part of the book: Practical Applications of Laser Ablation