Fractal Modeling of Polymer Plasma Laser Ablation, Plasma Plume Tsallis Entropy and Its q-Statistics Interpretation, Part I: Theory

Abstract

Polymer plasma produced by laser ablation is investigated in a theoretical manner. In relation to the fact that the charge carrier circulation is assumed to take place on fractal curves, the so-called fractality type, electrical charge transport can be resolved by an extended scale relativity method. In addition, an elegant mathematical model, utilizing a conjecture of fractal space-time, is elaborated. The complete solution and its graphical representation for temperature distribution in two-dimensional and three-dimensional cases are successfully introduced. The discrete physical behavior and irrevocable transformation of nanoscale microdomain substructures by laser ablation are realistically examined. Further, benefiting from the interpretation of the fractal analysis, each of the experimental results can be fairly explained. On top of that, this paper presents a proof of Tsallis nonextensive q-statistics, especially for the plasma plume studied. Tsallis entropy in direct connection with fractal dynamics and chaotic-type mechanics of the plasma plume and time-series representation of plasma temperature is introduced for the first time in the present publication, and the q-statistics of the plume plasma temperature are also studied, among others.

On the Polymer Plasma Laser Ablation

“…According to the distinction in their expansion rate, by observing two apparent velocities of displacement, in papers of specialty publications, they could be justified as being the rapid plasma frame/composition (namely "first plasma structure") and sluggish plasma frame (namely "second plasma structure"), respectively. Evidently, both plasma structures extend with constant, but separate velocities values [9].…”

“…In Figure 3, the estimation of temperature versus x, position in the probe, and time t, is shown [9]. This is the graphic representation of complete solution for the temperature distribution in a two-dimensional case.…”

“…In Figure 4, the estimation of temperature function of t (time) and x (position in the probe) is presented. In the 3D graphs, the value of temperature is specified by a colormap bar [9]. In Figure 5, the evolution of the visible emission from the polymer plasma plume recorded using an ICCD PI MAX camera (gating time 20 ns) is listed.…”

Fractal Derivatives, Fractional Derivatives and q-Deformed Calculus

“…Establishing a clear connection between the Parvate-Gangal fractal derivative and Caputo's fractional derivative, this work opens the possibility for a deeper understanding of the use of fractional differential equations, which is so common in many different areas. In this respect, let us remark that fractal and fractional differential equations have been used in applications as dynamic of the system in porous or heterogeneous media [26][27][28], diffusive flow [29][30][31][32][33], solitons [34], control of complex systems [35], epidemic process [36], polymer plasma [37] and many others. The consequences of the present study for these physical systems deserve further investigation in the future.…”