Fractal structures in nonlinear plasma physics

2011 ◽  
Vol 369 (1935) ◽  
pp. 371-395 ◽  
Author(s):  
R. L. Viana ◽  
E. C. Da Silva ◽  
T. Kroetz ◽  
I. L. Caldas ◽  
M. Roberto ◽  
...  
Keyword(s):  
Dynamical Systems ◽  
Plasma Physics ◽  
Discrete Dynamical Systems ◽  
Plasma Edge ◽  
Fractal Structures ◽  
Nonlinear Plasma ◽  
Dissipative Dynamical Systems ◽  
Area Preserving ◽  
The Magnetic Field

Fractal structures appear in many situations related to the dynamics of conservative as well as dissipative dynamical systems, being a manifestation of chaotic behaviour. In open area-preserving discrete dynamical systems we can find fractal structures in the form of fractal boundaries, associated to escape basins, and even possessing the more general property of Wada. Such systems appear in certain applications in plasma physics, like the magnetic field line behaviour in tokamaks with ergodic limiters. The main purpose of this paper is to show how such fractal structures have observable consequences in terms of the transport properties in the plasma edge of tokamaks, some of which have been experimentally verified. We emphasize the role of the fractal structures in the understanding of mesoscale phenomena in plasmas, such as electromagnetic turbulence.

scholarly journals Coexisting Infinite Orbits in an Area-Preserving Lozi Map

Entropy ◽  
2020 ◽  
Vol 22 (10) ◽  
pp. 1119
Author(s):  
Houzhen Li ◽  
Kexin Li ◽  
Mo Chen ◽  
Bocheng Bao
Keyword(s):  
Dynamical Systems ◽  
Sample Entropy ◽  
Discrete Dynamical Systems ◽  
Spectral Entropy ◽  
Hardware Platform ◽  
Initial Values ◽  
Extreme Multistability ◽  
Specific Parameter ◽  
Different Types ◽  
Area Preserving

Extreme multistability with coexisting infinite orbits has been reported in many continuous memristor-based dynamical circuits and systems, but rarely in discrete dynamical systems. This paper reports the finding of initial values-related coexisting infinite orbits in an area-preserving Lozi map under specific parameter settings. We use the bifurcation diagram and phase orbit diagram to disclose the coexisting infinite orbits that include period, quasi-period and chaos with different types and topologies, and we employ the spectral entropy and sample entropy to depict the initial values-related complexity. Finally, a microprocessor-based hardware platform is developed to acquire four sets of four-channel voltage sequences by switching the initial values. The results show that the area-preserving Lozi map displays coexisting infinite orbits with complicated complexity distributions, which heavily rely on its initial values.

Instabilities in the solar wind

1980 ◽  
Vol 297 (1433) ◽  
pp. 555-563 ◽  
Keyword(s):  
Solar Wind ◽  
Plasma Physics ◽  
Linear Theory ◽  
Recent Progress ◽  
Collisionless Plasma ◽  
Plasma Turbulence ◽  
Physical Processes ◽  
Nonlinear Plasma ◽  
Present Understanding

We review recent progress in the possible role of micro turbulence in the solar wind. The solar wind is expected to excite plasma microinstabilities owing to its transition from a collision-dominated to a collisionless plasma, with potentially drastic consequences for thermal transport and other physical processes. We discuss both the extensive linear theory of this subject and also our present understanding of nonlinear plasma turbulence. The solar wind is an excellent laboratory for studying many aspects of solar and plasma physics, and may soon provide some answers to several fundamental questions.

DYNAMICAL SYSTEMS EXCITED BY TEMPORAL INPUTS: FRACTAL TRANSITION BETWEEN EXCITED ATTRACTORS

Fractals ◽  
1999 ◽  
Vol 07 (02) ◽  
pp. 205-220 ◽  
Author(s):  
KAZUTOSHI GOHARA ◽  
ARATA OKUYAMA
Keyword(s):  
Phase Space ◽  
Dynamical Systems ◽  
Vector Fields ◽  
Invariant Set ◽  
Discrete Dynamical Systems ◽  
Contraction Property ◽  
Cylindrical Phase ◽  
Iterated Functions ◽  
Dissipative Dynamical Systems ◽  
Cylindrical Phase Space

This paper presents a framework for dissipative dynamical systems excited by external temporal inputs. We introduce a set {Il} of temporal inputs with finite intervals. The set {Il} defines two other sets of dynamical systems. The first is the set of continuous dynamical systems that are defined by a set {fl} of vector fields on the hyper-cylindrical phase space ℳ. The second is the set of discrete dynamical systems that are defined by a set {gl} of iterated functions on the global Poincaré section Σ. When the inputs are switched stochastically, a trajectory in the space ℳ converges to an attractive invariant set with fractal-like structure. We can analytically prove this result when all of the iterated functions satisfy a contraction property. Even without this property, we can numerically show that an attractive invariant set with fractal-like structure exists.

scholarly journals Weighted power mean discrete dynamical systems: Fast convergence properties

2006 ◽  
Vol 2006 ◽  
pp. 1-9
Author(s):  
Francisco J. Solis
Keyword(s):  
Dynamical Systems ◽  
Discrete Dynamical Systems ◽  
Fast Convergence ◽  
Power Mean ◽  
Convergence Properties ◽  
New Concepts ◽  
Iteration Functions ◽  
Nonlinear Maps

We studied families of discrete dynamical systems obtained by using iteration functions given by weighted power mean in order to understand the role of hyperrapid convergence in nonlinear maps. Our interest resides in concepts related to the velocity of convergence. We introduce new concepts regarding the time of convergence and we provide an ordering of these families according to their dependence on parameters.

The Non-Causal Character of Renormalization Group Explanations

2018 ◽  
Author(s):  
Margaret Morrison
Keyword(s):  
Probability Theory ◽  
Renormalization Group ◽  
Dynamical Systems ◽  
Recent Literature ◽  
Mathematical Explanation ◽  
Causal Status ◽  
Physical Information ◽  
The Relationship ◽  
Structural Aspects

After reviewing some of the recent literature on non-causal and mathematical explanation, this chapter develops an argument as to why renormalization group (RG) methods should be seen as providing non-causal, yet physical, information about certain kinds of systems/phenomena. The argument centres on the structural character of RG explanations and the relationship between RG and probability theory. These features are crucial for the claim that the non-causal status of RG explanations involves something different from simply ignoring or “averaging over” microphysical details—the kind of explanations common to statistical mechanics. The chapter concludes with a discussion of the role of RG in treating dynamical systems and how that role exemplifies the structural aspects of RG explanations which in turn exemplifies the non-causal features.

scholarly journals Hidden Attractors in Discrete Dynamical Systems

Entropy ◽  
2021 ◽  
Vol 23 (5) ◽  
pp. 616
Author(s):  
Marek Berezowski ◽  
Marcin Lawnik
Keyword(s):  
Dynamical Systems ◽  
Chaos Theory ◽  
Scientific Literature ◽  
Discrete Systems ◽  
Discrete Dynamical Systems ◽  
Continuous Systems ◽  
Hidden Attractors ◽  
Negative Effects ◽  
Chemical Reactors ◽  
Points Of View

Research using chaos theory allows for a better understanding of many phenomena modeled by means of dynamical systems. The appearance of chaos in a given process can lead to very negative effects, e.g., in the construction of bridges or in systems based on chemical reactors. This problem is important, especially when in a given dynamic process there are so-called hidden attractors. In the scientific literature, we can find many works that deal with this issue from both the theoretical and practical points of view. The vast majority of these works concern multidimensional continuous systems. Our work shows these attractors in discrete systems. They can occur in Newton’s recursion and in numerical integration.

scholarly journals What Density of Magnetosheath Sodium Ions Can Provide the Observed Decrease in the Magnetic Field of the “Double Magnetopause” during the First MESSENGER Flyby?

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1168
Author(s):  
Elena Belenkaya ◽  
Ivan Pensionerov
Keyword(s):  
Magnetic Field ◽  
Analytical Approach ◽  
Field Structure ◽  
Sodium Ions ◽  
Plasma Parameters ◽  
Calculation Results ◽  
Magnetizing Current ◽  
The Magnetic Field ◽  
Density Excess

On 14 January 2008, the MESSENGER spacecraft, during its first flyby around Mercury, recorded the magnetic field structure, which was later called the “double magnetopause”. The role of sodium ions penetrating into the Hermean magnetosphere from the magnetosheath in generation of this structure has been discussed since then. The violation of the symmetry of the plasma parameters at the magnetopause is the cause of the magnetizing current generation. Here, we consider whether the change in the density of sodium ions on both sides of the Hermean magnetopause could be the cause of a wide diamagnetic current in the magnetosphere at its dawn-side boundary observed during the first MESSENGER flyby. In the present paper, we propose an analytical approach that made it possible to determine the magnetosheath Na+ density excess providing the best agreement between the calculation results and the observed magnetic field in the double magnetopause.

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