scholarly journals Evolution of fractality in magnetized plasmas

2017 ◽  
Author(s):  
Víctor Muñoz ◽  
Macarena Domínguez ◽  
Juan Alejandro Valdivia ◽  
Simon Good ◽  
Giuseppina Nigro ◽  
...  
Keyword(s):  
Solar Wind ◽  
Fractal Dimension ◽  
Shell Model ◽  
Geomagnetic Activity ◽  
Temporal Evolution ◽  
Fractal Dimensions ◽  
Magnetized Plasma ◽  
Magnetic Clouds ◽  
The Relationship ◽  
The Magnetic Field

Abstract. We studied the temporal evolution of fractality for geomagnetic activity, by calculating fractal dimensions from Dst data and from an MHD shell model for a turbulent magnetized plasma, which may be a useful model to study geomagnetic activity under solar wind forcing. We show that the shell model is able to reproduce the relationship between the fractal dimension and the occurrence of dissipative events, but only in a certain region of viscosity and resistivity values. We also present preliminary results of the application of these ideas to the study of the magnetic field time series in the solar wind during magnetic clouds. Results suggest that the fractal dimension is able to characterize the complexity of the magnetic cloud structure.

scholarly journals Evolution of fractality in space plasmas of interest to geomagnetic activity

2018 ◽  
Vol 25 (1) ◽  
pp. 207-216 ◽  
Author(s):  
Víctor Muñoz ◽  
Macarena Domínguez ◽  
Juan Alejandro Valdivia ◽  
Simon Good ◽  
Giuseppina Nigro ◽  
...  
Keyword(s):  
Solar Wind ◽  
Fractal Dimension ◽  
Shell Model ◽  
Geomagnetic Activity ◽  
Temporal Evolution ◽  
Fractal Dimensions ◽  
Magnetized Plasma ◽  
Magnetic Clouds ◽  
The Relationship ◽  
The Magnetic Field

Abstract. We studied the temporal evolution of fractality for geomagnetic activity, by calculating fractal dimensions from the Dst data and from a magnetohydrodynamic shell model for turbulent magnetized plasma, which may be a useful model to study geomagnetic activity under solar wind forcing. We show that the shell model is able to reproduce the relationship between the fractal dimension and the occurrence of dissipative events, but only in a certain region of viscosity and resistivity values. We also present preliminary results of the application of these ideas to the study of the magnetic field time series in the solar wind during magnetic clouds, which suggest that it is possible, by means of the fractal dimension, to characterize the complexity of the magnetic cloud structure.

scholarly journals Study of the fractality in a magnetohydrodynamic shell model forced by solar wind fluctuations

2020 ◽  
Vol 27 (2) ◽  
pp. 175-185 ◽  
Author(s):  
Macarena Domínguez ◽  
Giuseppina Nigro ◽  
Víctor Muñoz ◽  
Vincenzo Carbone ◽  
Mario Riquelme
Keyword(s):  
Solar Wind ◽  
Fractal Dimension ◽  
Energy Dissipation ◽  
Shell Model ◽  
Langevin Equation ◽  
Dissipation Rate ◽  
Solar Maximum ◽  
Magnetic Energy ◽  
Energy Dissipation Rate ◽  
The Magnetic Field

Abstract. The description of the relationship between interplanetary plasma and geomagnetic activity requires complex models. Drastically reducing the ambition of describing this detailed complex interaction and, if we are interested only in the fractality properties of the time series of its characteristic parameters, a magnetohydrodynamic (MHD) shell model forced using solar wind data might provide a possible novel approach. In this paper we study the relation between the activity of the magnetic energy dissipation rate obtained in one such model, which may describe geomagnetic activity, and the fractal dimension of the forcing. In different shell model simulations, the forcing is provided by the solution of a Langevin equation where a white noise is implemented. This forcing, however, has been shown to be unsuitable for describing the solar wind action on the model. Thus, we propose to consider the fluctuations of the product between the velocity and the magnetic field solar wind data as the noise in the Langevin equation, the solution of which provides the forcing in the magnetic field equation. We compare the fractal dimension of the magnetic energy dissipation rate obtained, of the magnetic forcing term, and of the fluctuations of v⋅bz, with the activity of the magnetic energy dissipation rate. We examine the dependence of these fractal dimensions on the solar cycle. We show that all measures of activity have a peak near solar maximum. Moreover, both the fractal dimension computed for the fluctuations of v⋅bz time series and the fractal dimension of the magnetic forcing have a minimum near solar maximum. This suggests that the complexity of the noise term in the Langevin equation may have a strong effect on the activity of the magnetic energy dissipation rate.

scholarly journals Study of the fractality in an MHD Shell model forced by solar wind fluctuations

2019 ◽  
Author(s):  
Macarena Domínguez ◽  
Giuseppina Nigro ◽  
Víctor Muñoz ◽  
Vincenzo Carbone ◽  
Mario Riquelme
Keyword(s):  
Solar Wind ◽  
Fractal Dimension ◽  
Energy Dissipation ◽  
Shell Model ◽  
Langevin Equation ◽  
Dissipation Rate ◽  
Solar Maximum ◽  
Magnetic Energy ◽  
Energy Dissipation Rate ◽  
The Magnetic Field

Abstract. The description of the relationship between interplanetary plasma and geomagnetic activity requires complex models. Drastically reducing the ambition of describing this detailed complex interaction, and if we are interested only in the fractality properties of the time-series of its characteristic parameters, a magnetohydrodynamic (MHD) shell model forced using solar wind data, might provide a possible novel approach. In this paper we study the relation between the activity of the magnetic energy dissipation rate obtained in one such model, which may describe geomagnetic activity, and the fractal dimension of the forcing. In different shell model simulations, the forcing is provided by the solution of a Langevin equation where a white noise is implemented. Since this forcing has shown its unsuitableness in describing the driver due to solar wind action, we propose to consider the fluctuations of the product between the velocity and the magnetic field solar wind data as the noise in Langevin equation, whose solution provides the forcing in the magnetic field equation. We compare the fractal dimension of the magnetic energy dissipation rate obtained, of the magnetic forcing term, and of the fluctuations of v · bz, with the activity of the magnetic energy dissipation rate. We examine the dependence of these fractal dimensions on the solar cycle. We show that all measures of activity have a peak near solar maximum. Moreover, both the fractal dimension computed for the fluctuations of v · bz time series and the fractal dimension of the magnetic forcing have a minimum near solar maximum. This suggests that the complexity of the noise term in the Langevin equation may have a strong effect in the activity of the magnetic energy dissipation rate.

Study of the fractality of magnetized plasma using an MHD shell model driven by solar wind data

2018 ◽  
Vol 25 (9) ◽  
pp. 092302 ◽  
Author(s):  
Macarena Domínguez ◽  
Giuseppina Nigro ◽  
Víctor Muñoz ◽  
Vincenzo Carbone
Keyword(s):  
Solar Wind ◽  
Shell Model ◽  
Magnetized Plasma ◽  
Wind Data ◽  
Model Driven

scholarly journals On Similarity of Seismo Magnetic Power Density and Pressure Head Fractal Dimension for Characterizing Shajara Reservoirs of the Permo-Carboniferous Shajara Formation, Saudi Arabia

2020 ◽  
pp. 1-8
Author(s):  
Khalid Elyas Mohamed Elameen Alkhidir ◽  
Keyword(s):  
Fractal Dimension ◽  
Power Density ◽  
Functional Relationship ◽  
Fractal Dimensions ◽  
Pressure Head ◽  
Density Maximum ◽  
Phase Saturation ◽  
Head Pressure ◽  
Second Procedure ◽  
The Relationship

The quality and assessment of a reservoir can be documented in details by the application of seismo magnetic power density. This research aims to calculate fractal dimension from the relationship among seismo magnetic power density, maximum seismo magnetic power density and wetting phase saturation and to approve it by the fractal dimension derived from the relationship among inverse pressure head * pressure head and wetting phase saturation. Two equations for calculating the fractal dimensions have been employed. The first one describes the functional relationship between wetting phase saturation, seismo magnetic power density, maximum seismo magnetic power density and fractal dimension. The second equation implies to the wetting phase saturation as a function of pressure head and the fractal dimension. Two procedures for obtaining the fractal dimension have been utilized. The first procedure was done by plotting the logarithm of the ratio between seismo magnetic power density and maximum seismo magnetic power density versus logarithm wetting phase saturation. The slope of the first procedure = 3- Df (fractal dimension). The second procedure for obtaining the fractal dimension was determined by plotting the logarithm (inverse of pressure head and pressure head) versus the logarithm of wetting phase saturation. The slope of the second procedure = Df -3. On the basis of the obtained results of the fabricated stratigraphic column and the attained values of the fractal dimension, the sandstones of the Shajara reservoirs of the Shajara Formation were divided here into three units

scholarly journals Magnetic clouds' structure in the magnetosheath as observed by Cluster and Geotail: four case studies

2014 ◽  
Vol 32 (10) ◽  
pp. 1247-1261 ◽  
Author(s):  
L. Turc ◽  
D. Fontaine ◽  
P. Savoini ◽  
E. K. J. Kilpua
Keyword(s):  
Magnetic Field ◽  
Solar Wind ◽  
Magnetic Fields ◽  
Bow Shock ◽  
Field Direction ◽  
Magnetic Clouds ◽  
Magnetic Field Direction ◽  
Field Orientation ◽  
The Impact ◽  
The Magnetic Field

Abstract. Magnetic clouds (MCs) are large-scale magnetic flux ropes ejected from the Sun into the interplanetary space. They play a central role in solar–terrestrial relations as they can efficiently drive magnetic activity in the near-Earth environment. Their impact on the Earth's magnetosphere is often attributed to the presence of southward magnetic fields inside the MC, as observed in the upstream solar wind. However, when they arrive in the vicinity of the Earth, MCs first encounter the bow shock, which is expected to modify their properties, including their magnetic field strength and direction. If these changes are significant, they can in turn affect the interaction of the MC with the magnetosphere. In this paper, we use data from the Cluster and Geotail spacecraft inside the magnetosheath and from the Advanced Composition Explorer (ACE) upstream of the Earth's environment to investigate the impact of the bow shock's crossing on the magnetic structure of MCs. Through four example MCs, we show that the evolution of the MC's structure from the solar wind to the magnetosheath differs largely from one event to another. The smooth rotation of the MC can either be preserved inside the magnetosheath, be modified, i.e. the magnetic field still rotates slowly but at different angles, or even disappear. The alteration of the magnetic field orientation across the bow shock can vary with time during the MC's passage and with the location inside the magnetosheath. We examine the conditions encountered at the bow shock from direct observations, when Cluster or Geotail cross it, or indirectly by applying a magnetosheath model. We obtain a good agreement between the observed and modelled magnetic field direction and shock configuration, which varies from quasi-perpendicular to quasi-parallel in our study. We find that the variations in the angle between the magnetic fields in the solar wind and in the magnetosheath are anti-correlated with the variations in the shock obliquity. When the shock is in a quasi-parallel regime, the magnetic field direction varies significantly from the solar wind to the magnetosheath. In such cases, the magnetic field reaching the magnetopause cannot be approximated by the upstream magnetic field. Therefore, it is important to take into account the conditions at the bow shock when estimating the impact of an MC with the Earth's environment because these conditions are crucial in determining the magnetosheath magnetic field, which then interacts with the magnetosphere.

Neural network classification of substorm geomagnetic activity caused by solar wind magnetic clouds

2020 ◽  
Vol 205 ◽  
pp. 105301
Author(s):  
N.A. Barkhatov ◽  
V.G. Vorobjev ◽  
S.E. Revunov ◽  
O.M. Barkhatova ◽  
E.A. Revunova ◽  
...  
Keyword(s):  
Neural Network ◽  
Solar Wind ◽  
Geomagnetic Activity ◽  
Magnetic Clouds ◽  
Neural Network Classification

scholarly journals Resistive evolution of toroidal field distributions and their relation to magnetic clouds

2019 ◽  
Vol 85 (1) ◽  
Author(s):  
C. B. Smiet ◽  
H. J. de Blank ◽  
T. A. de Jong ◽  
D. N. L. Kok ◽  
D. Bouwmeester
Keyword(s):  
Magnetic Field ◽  
Solar Wind ◽  
Field Strength ◽  
Magnetic Field Strength ◽  
Magnetic Clouds ◽  
Twisted Field ◽  
Field Lines ◽  
Rotational Transform ◽  
Universal Pattern ◽  
The Magnetic Field

We study the resistive evolution of a localized self-organizing magnetohydrodynamic equilibrium. In this configuration the magnetic forces are balanced by a pressure force caused by a toroidal depression in the pressure. Equilibrium is attained when this low-pressure region prevents further expansion into the higher-pressure external plasma. We find that, for the parameters investigated, the resistive evolution of the structures follows a universal pattern when rescaled to resistive time. The finite resistivity causes both a decrease in the magnetic field strength and a finite slip of the plasma fluid against the static equilibrium. This slip is caused by a Pfirsch–Schlüter-type diffusion, similar to what is seen in tokamak equilibria. The net effect is that the configuration remains in magnetostatic equilibrium whilst it slowly grows in size. The rotational transform of the structure becomes nearly constant throughout the entire structure, and decreases according to a power law. In simulations this equilibrium is observed when highly tangled field lines relax in a high-pressure (relative to the magnetic field strength) environment, a situation that occurs when the twisted field of a coronal loop is ejected into the interplanetary solar wind. In this paper we relate this localized magnetohydrodynamic equilibrium to magnetic clouds in the solar wind.

scholarly journals Cluster-C1 observations on the geometrical structure of linear magnetic holes in the solar wind at 1 AU

2010 ◽  
Vol 28 (9) ◽  
pp. 1695-1702 ◽  
Author(s):  
T. Xiao ◽  
Q. Q. Shi ◽  
T. L. Zhang ◽  
S. Y. Fu ◽  
L. Li ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Solar Wind ◽  
Geometrical Structure ◽  
Occurrence Rate ◽  
Geometrical Shape ◽  
Magnetic Field Data ◽  
Magnetic Field Magnitude ◽  
The Relationship ◽  
Plasma Measurements ◽  
The Magnetic Field

Abstract. Interplanetary linear magnetic holes (LMHs) are structures in which the magnetic field magnitude decreases with little change in the field direction. They are a 10–30% subset of all interplanetary magnetic holes (MHs). Using magnetic field and plasma measurements obtained by Cluster-C1, we surveyed the LMHs in the solar wind at 1 AU. In total 567 interplanetary LMHs are identified from the magnetic field data when Cluster-C1 was in the solar wind from 2001 to 2004. We studied the relationship between the durations and the magnetic field orientations, as well as that of the scales and the field orientations of LMHs in the solar wind. It is found that the geometrical structure of the LMHs in the solar wind at 1 AU is consistent with rotational ellipsoid and the ratio of scales along and across the magnetic field is about 1.93:1. In other words, the structure is elongated along the magnetic field at 1 AU. The occurrence rate of LMHs in the solar wind at 1 AU is about 3.7 per day. It is shown that not only the occurrence rate but also the geometrical shape of interplanetary LMHs has no significant change from 0.72 AU to 1 AU in comparison with previous studies. It is thus inferred that most of interplanetary LMHs observed at 1 AU are formed and fully developed before 0.72 AU. The present results help us to study the formation mechanism of the LMHs in the solar wind.

THE RELATIONSHIP BETWEEN FRACTIONAL CALCULUS AND FRACTALS

Fractals ◽  
1995 ◽  
Vol 03 (01) ◽  
pp. 217-229 ◽  
Author(s):  
FRANK B. TATOM
Keyword(s):  
Time Series ◽  
Fractal Dimension ◽  
Fractional Calculus ◽  
Fractal Dimensions ◽  
Linear Functions ◽  
Fractal Curve ◽  
Random Fractal ◽  
Fractal Functions ◽  
Decay Exponent ◽  
The Relationship

The general relationship between fractional calculus and fractals is explored. Based on prior investigations dealing with random fractal processes, the fractal dimension of the function is shown to be a linear function of the order of fractional integro-differentiation. Emphasis is placed on the proper application of fractional calculus to the function of the random fractal, as opposed to the trail. For fractional Brownian motion, the basic relations between the spectral decay exponent, Hurst exponent, fractal dimension of the function and the trail, and the order of the fractional integro-differentiation are developed. Based on an understanding of fractional calculus applied to random fractal functions, consideration is given to an analogous application to deterministic or nonrandom fractals. The concept of expressing each coordinate of a deterministic fractal curve as a “pseudo-time” series is investigated. Fractional integro-differentiation of such series is numerically carried out for the case of quadric Koch curves. The resulting time series produces self-similar patterns with fractal dimensions which are linear functions of the order of the fractional integro-differentiation. These curves are assigned the name, fractional Koch curves. The general conclusion is reached that fractional calculus can be used to precisely change or control the fractal dimension of any random or deterministic fractal with coordinates which can be expressed as functions of one independent variable, which is typically time (or pseudo-time).

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