scholarly journals Lorenz Type Behaviors in the Dynamics of Laser Produced Plasma

Symmetry ◽  
2019 ◽  
Vol 11 (9) ◽  
pp. 1135 ◽  
Author(s):  
Stefan Andrei Irimiciuc ◽  
Florin Enescu ◽  
Andrei Agop ◽  
Maricel Agop
Keyword(s):  
Experimental Data ◽  
Lorenz System ◽  
Integral Form ◽  
Diagnostic Techniques ◽  
Oscillatory Behavior ◽  
Mathematical Representation ◽  
System A ◽  
Theoretical Predictions ◽  
Fractal Space ◽  
The Lorenz System

An innovative theoretical model is developed on the backbone of a classical Lorenz system. A mathematical representation of a differential Lorenz system is transposed into a fractal space and reduced to an integral form. In such a conjecture, the Lorenz variables will operate simultaneously on two manifolds, generating two transformation groups, one corresponding to the space coordinates transformation and another one to the scale resolution transformation. Since these groups are isomorphs various types isometries become functional. The Lorenz system was further adapted to describe the dynamics of ejected particles as a result of laser matter interaction in a fractal paradigm. The simulations were focused on the dynamics of charged particles, and showcase the presence of current oscillations, a heterogenous velocity distribution and multi-structuring at different interaction scales. The theoretical predictions were compared with the experimental data acquired with noninvasive diagnostic techniques. The experimental data confirm the multi-structure scenario and the oscillatory behavior predicted by the mathematical model.

CONTROL OF THE DIFFERENTIALLY FLAT LORENZ SYSTEM

2001 ◽  
Vol 11 (07) ◽  
pp. 1989-1996 ◽  
Author(s):  
JIN MAN JOO ◽  
JIN BAE PARK
Keyword(s):  
Equilibrium State ◽  
Lorenz System ◽  
Degree Of Freedom ◽  
Design Approach ◽  
State Trajectory ◽  
System A ◽  
Full State ◽  
Tracking Controller ◽  
The Lorenz System ◽  
Two Degree Of Freedom

This paper presents an approach for the control of the Lorenz system. We first show that the controlled Lorenz system is differentially flat and then compute the flat output of the Lorenz system. A two degree of freedom design approach is proposed such that the generation of full state feasible trajectory incorporates with the design of a tracking controller via the flat output. The stabilization of an equilibrium state and the tracking of a feasible state trajectory are illustrated.

Multistability in the Lorenz System: A Broken Butterfly

2014 ◽  
Vol 24 (10) ◽  
pp. 1450131 ◽  
Author(s):  
Chunbiao Li ◽  
Julien Clinton Sprott
Keyword(s):  
Parameter Space ◽  
Limit Cycles ◽  
Lorenz System ◽  
Dynamical Behavior ◽  
Symmetric Pair ◽  
Physical Systems ◽  
System A ◽  
Plausible Model ◽  
Fluid Convection ◽  
The Lorenz System

In this paper, the dynamical behavior of the Lorenz system is examined in a previously unexplored region of parameter space, in particular, where r is zero and b is negative. For certain values of the parameters, the classic butterfly attractor is broken into a symmetric pair of strange attractors, or it shrinks into a small attractor basin intermingled with the basins of a symmetric pair of limit cycles, which means that the system is bistable or tristable under certain conditions. Although the resulting system is no longer a plausible model of fluid convection, it may have application to other physical systems.

Feedback Linearization of the Lorenz System: Stabilization and Tracking Control

2002 ◽  
Author(s):  
L. G. Crespo ◽  
J. Q. Sun
Keyword(s):  
Feedback Linearization ◽  
Lorenz System ◽  
The State ◽  
Differential Flatness ◽  
State Transformation ◽  
System A ◽  
Excellent Control ◽  
High Control ◽  
The Lorenz System ◽  
Control Study

This paper presents a control study of the Lorenz system by using feedback linearization. The effects of the state transformation on the dynamics of the Lorenz system are studied first. Then, composite controllers are developed for both stabilization and tracking of the system. The controls are designed to overcome the barrier in controllability imposed by the state transformation. The transition through the manifold defined by such a singularity is achieved by inducing the chaotic response within a boundary layer that contains the singularity. Outside this region, a conventional feedback nonlinear control is applied. In this fashion, the authority of the control is enlarged to the whole state space and the need for high control efforts is substantially mitigated. Tracking problems that involve single and cooperative objectives are studied by using the differential flatness property of the system. A good understanding of the system dynamics proves to be invaluable in the design of better controls. In all numerical examples, the proposed approach led to excellent control performances.

scholarly journals Oscillating forcings and new regimes in the Lorenz system: a four-lobe attractor

2012 ◽  
Vol 19 (3) ◽  
pp. 315-322 ◽  
Author(s):  
V. Pelino ◽  
F. Maimone ◽  
A. Pasini
Keyword(s):  
Lorenz System ◽  
Climate Dynamics ◽  
System A ◽  
The Lorenz System

Abstract. It has been shown that forced Lorenz models generally maintain their two-lobe structure, just giving rise to changes in the occurrence of their regimes. Here, using the richness of a unified formalism for Kolmogorov-Lorenz systems, we show that introducing oscillating forcings can lead to the birth of new regimes and to a four-lobe attractor. Analogies within a climate dynamics framework are mentioned.

Shil’nikov Analysis of Homoclinic and Heteroclinic Orbits of the T System

2010 ◽  
Vol 6 (2) ◽  
Author(s):  
Robert A. Van Gorder ◽  
S. Roy Choudhury
Keyword(s):  
Lorenz System ◽  
Chaotic Behavior ◽  
Three Dimensional ◽  
Homoclinic Orbits ◽  
Heteroclinic Orbits ◽  
Secure Communications ◽  
Smale Horseshoe ◽  
System A ◽  
The Lorenz System ◽  
T System

We study the chaotic behavior of the T system, a three dimensional autonomous nonlinear system introduced by Tigan (2005, “Analysis of a Dynamical System Derived From the Lorenz System,” Scientific Bulletin Politehnica University of Timisoara, Tomul, 50, pp. 61–72), which has potential application in secure communications. Here, we first recount the heteroclinic orbits of Tigan and Dumitru (2008, “Analysis of a 3D Chaotic System,” Chaos, Solitons Fractals, 36, pp. 1315–1319), and then we analytically construct homoclinic orbits describing the observed Smale horseshoe chaos. In the parameter regimes identified by this rigorous Shil’nikov analysis, the occurrence of interesting behaviors thus predicted in the T system is verified by the use of numerical diagnostics.

Isothermal and isobaric vapour-liquid equilibrium data in the tetrachloromethane-sec-butyl alcohol system

1983 ◽  
Vol 48 (9) ◽  
pp. 2446-2453 ◽  
Author(s):  
Jan Linek
Keyword(s):  
Experimental Data ◽  
Boiling Point ◽  
Butyl Alcohol ◽  
Correlation Equations ◽  
Wilson Equation ◽  
Liquid Equilibrium ◽  
Raoult’S Law ◽  
System A ◽  
Equilibrium Data ◽  
Alcohol System

Isothermal vapour-liquid equilibrium data at 65, 73 and 80 °C and isobaric ones at 101.3 kPa were measured in the tetrachloromethane-sec-butyl alcohol system. A modified circulation still of the Gillespie type was used for the measurements. Under the conditions of measurement, the system exhibits positive deviations from Raoult's law and minimum boiling-point azeotropes. The experimental data were fitted to a number of correlation equations, the most suitable being the Wilson equation.

Dynamics, Synchronization and Electronic Implementations of a New Lorenz-like Chaotic System with Nonhyperbolic Equilibria

2019 ◽  
Vol 29 (14) ◽  
pp. 1950197 ◽  
Author(s):  
P. D. Kamdem Kuate ◽  
Qiang Lai ◽  
Hilaire Fotsin
Keyword(s):  
Chaotic System ◽  
Chaotic Systems ◽  
Lorenz System ◽  
Chaotic Behavior ◽  
Piecewise Linear ◽  
Period Doubling ◽  
Adaptive Synchronization ◽  
The Novel ◽  
Algebraic Equations ◽  
The Lorenz System

The Lorenz system has attracted increasing attention on the issue of its simplification in order to produce the simplest three-dimensional chaotic systems suitable for secure information processing. Meanwhile, Sprott’s work on elegant chaos has revealed a set of 19 chaotic systems all described by simple algebraic equations. This paper presents a new piecewise-linear chaotic system emerging from the simplification of the Lorenz system combined with the elegance of Sprott systems. Unlike the majority, the new system is a non-Shilnikov chaotic system with two nonhyperbolic equilibria. It is multiplier-free, variable-boostable and exclusively based on absolute value and signum nonlinearities. The use of familiar tools such as Lyapunov exponents spectra, bifurcation diagrams, frequency power spectra as well as Poincaré map help to demonstrate its chaotic behavior. The novel system exhibits inverse period doubling bifurcations and multistability. It has only five terms, one bifurcation parameter and a total amplitude controller. These features allow a simple and low cost electronic implementation. The adaptive synchronization of the novel system is investigated and the corresponding electronic circuit is presented to confirm its feasibility.

scholarly journals An Additive Model to Predict the Rheological and Mechanical Properties of Polypropylene Blends Made by Virgin and Reprocessed Components

Recycling ◽  
2021 ◽  
Vol 6 (1) ◽  
pp. 2
Author(s):  
Francesco Paolo La Mantia ◽  
Maria Chiara Mistretta ◽  
Vincenzo Titone
Keyword(s):  
Experimental Data ◽  
Mechanical Properties ◽  
Additive Model ◽  
Industrial Process ◽  
Theoretical Predictions ◽  
Experimental Values ◽  
Polypropylene Blends ◽  
Polypropylene Sample

In this work, an additive model for the prediction of the rheological and mechanical properties of monopolymer blends made by virgin and reprocessed components is proposed. A polypropylene sample has been reprocessed more times in an extruder and monopolymer blends have been prepared by simulating an industrial process. The scraps are exposed to regrinding and are melt reprocessed before mixing with the virgin polymer. The reprocessed polymer is, then, subjected to some thermomechanical degradation. Rheological and mechanical experimental data have been compared with the theoretical predictions. The results obtained showed that the values of this simple additive model are a very good fit for the experimental values of both rheological and mechanical properties.

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