Lorenz Type Behaviors in the Dynamics of Laser Produced Plasma
Abstract
:1. Introduction
2. Mathematical Model
2.1. Route to Non-Differentiability
- (i)
- Any variable used to describe the dynamics of a nondifferential Lorenz type system will be described through multifractal mathematical functions dependent on both the spatial and temporal coordinates, and on the scale resolution.
- (ii)
- The laws describing these dynamics are invariant with respect to the spatial coordinates and temporal transformation, and the scale resolution transformation.
- (iii)
- The constraints on the Lorenz type system dynamics, described through continuous and differentiable curves of a Euclidian space, are replaced by the dynamics of a system lacking any constraints, and being described by continuous and nondifferentiable curves in a multifractal space.
- (iv)
- Between any two points in the multifractal space there is an infinity of curves describing the dynamics of a systems (its geodesics). The indiscernibility between these curves is a natural property of multifractalization through stochasticization; meanwhile, their discernibility is the result of a selection process based on the principle of maximum informational energy [14]. From such a perspective, any Lorenz type system with dynamics described by continuous and differentiable curves has hidden dissipative information (lacks memory). Otherwise, Lorenz type systems described by continuous and nondifferentiable curves have explicit information (presents memory).
Scale Resolutions
2.2. Non-Differentiable Lorenz Type Systems
2.3. Motion Integration
3. Plasma Modelling
4. Experimental Confirmation
5. Conclusions
Author Contributions
Funding
Conflicts of Interest
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Irimiciuc, S.A.; Enescu, F.; Agop, A.; Agop, M. Lorenz Type Behaviors in the Dynamics of Laser Produced Plasma. Symmetry 2019, 11, 1135. https://doi.org/10.3390/sym11091135
Irimiciuc SA, Enescu F, Agop A, Agop M. Lorenz Type Behaviors in the Dynamics of Laser Produced Plasma. Symmetry. 2019; 11(9):1135. https://doi.org/10.3390/sym11091135
Chicago/Turabian StyleIrimiciuc, Stefan Andrei, Florin Enescu, Andrei Agop, and Maricel Agop. 2019. "Lorenz Type Behaviors in the Dynamics of Laser Produced Plasma" Symmetry 11, no. 9: 1135. https://doi.org/10.3390/sym11091135
APA StyleIrimiciuc, S. A., Enescu, F., Agop, A., & Agop, M. (2019). Lorenz Type Behaviors in the Dynamics of Laser Produced Plasma. Symmetry, 11(9), 1135. https://doi.org/10.3390/sym11091135