# Lorenz Type Behaviors in the Dynamics of Laser Produced Plasma

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## Abstract

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## 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

^{2}and background pressure of 10

^{−2}Torr). The choice of the relatively simple mineral comes from its composition, having elements with different physical properties (S, Cu and Fe) which will allow a better showcase of phenomena like: particle separation, ionic oscillations and plume splitting. Further details on the experimental set-up can be found in [6,12].

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**(

**a**) Particle velocity distribution for various scale resolutions, (

**b**) particle distribution with the scale resolution distribution at various moments in time.

**Figure 2.**(

**a**) Charged particles’ distribution at various moments in time, (

**b**) charge particle current induced by fluctuation current at the resolution scale.

**Figure 3.**(

**a**) Spatial mapping of Cu, S and Fe emission after 650 ns, (

**b**) bi-dimensional representation of atomic and ionic emission.

**Figure 4.**(

**a**) ICCD fast camera image of a LPP Chalcopyrite collected after 650 ns, (

**b**) cross section for a series of images extracted at various time delays.

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**MDPI and ACS Style**

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

**AMA Style**

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 Style**

Irimiciuc, 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