Chapters authored
Complex Systems with Self‐Elimination of Dissipation with Implication in Bio‐Structural Behavior Via Nondifferentiability By Maricel Agop, Decebal Vasincu, Daniel Timofte, Elena Simona
Bacaita, Andrei Agop and Stefan Andrei Irimiciuc
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
Experimental and Theoretical Studies on the Dynamics of Transient Plasmas Generated by Laser Ablation in Various Temporal Regimes By Petru-Edward Nica, Stefan Andrei Irimiciuc, Maricel Agop, Silviu
Gurlui, Michael Ziskind and Cristian Focsa
During the last decade, our groups have performed systematic experimental studies on the characterization of plasma plumes generated by laser ablation in various temporal regimes (ns, ps, fs) on materials ranging from simple metals (Al, Cu, Mn, Ni, In, W, …) to more complex compounds (ceramics, chalcogenide glasses, ferrites). Optical (fast imaging and space- and time-resolved emission spectroscopy) and electrical (mainly Langmuir probe) methods have been applied to experimentally investigate the dynamics of the plasma plume and its constituents. Influence of the target physical (thermodynamic and electrical) parameters on the plasma dynamics has been studied. A mathematical correlation between the local and global plasma parameters and the physical properties of the target was proposed for the first time. Peculiar behaviors like plume splitting or plasma oscillations have been evidenced for high laser fluence ablation in vacuum. Along with results from the literature, our findings provide convincing arguments for the existence of multiple double-layers in the laser ablation plasma plume, in a scenario including two-temperature electrons. New fractal-based theoretical approaches have been developed to qualitatively and quantitatively account for the observed phenomena. The space and time evolution of expansion velocity, particle number, current density and plasma temperature were theoretically investigated.
Part of the book: Laser Ablation
Non-Linear Behaviours in the Dynamics of Some Biostructures By Emil Anton, Anna Gavrilut, Maricel Agop and Daniel Timofte
Various differentiable models are frequently used to describe the dynamics of complex systems (see the kinetic models, fluid models, etc.). Given the complexity of all the physical phenomena involved in the dynamics of such systems, it is required to introduce the dynamic variable dependencies both on the space-time coordinates and on the scale resolutions. Therefore, in this case an adequate theoretical approach may be the use of non-linear physical models either in the form of the Scale Relativity Theory or of the Extended Scale Relativity Theory, i.e., the Scale Relativity Theory with an arbitrary constant fractal dimension. In the framework of the Extended Scale Relativity Theory, fractal velocity field is described both by topological solitons of kink type and by non-topological soliton varieties of breather type. Applications for the blood flow are proposed. The results revealed the directional flow toward the walls, which can explain the thickening effect which is one of the source of arteriosclerosis.
Part of the book: Nonlinear Systems
Dynamics of Biostructures on a Fractal/Multifractal Space-Time Manifold By Maricel Agop, Calin Buzea, Decebal Vasincu and Daniel Timofte
A theory of space-time is built on a fractal/multifractal variety. Thus, considering that both the spatial coordinates and the time are fractal/multifractal, it is shown that both the energy and the non-differentiable mass of any biostructure depend on both the “state” of the biostructure and a speed limit of constant value. For the dynamics on Peano fractal/multifractal curves and Compton scale resolutions, it is shown that our results are reduced to those of Einstein relativity. In such a context, it has been shown that the “chameleon effect” of cholesterol corresponds to the HDL-LDL state transfer dictated by the spontaneous symmetry breaking through a fractal/multifractal tunnel effect. Then both HDL and LDL become distinct states of the same biostructure as in nuclear physics where proton and neutron are distinct states of the same nucleon.
Part of the book: Progress in Relativity
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