Statistical analysis of stochastic magnetic fluctuations in space plasma based on the MMS mission

Based on the Magnetospheric Multiscale (MMS) mission we look at magnetic field fluctuations in the Earth's magnetosheath. We apply the statistical analysis using a Fokker-Planck equation to investigate processes responsible for stochastic fluctuations in space plasmas. As already known, turbulence in the inertial range of hydromagnetic scales exhibits Markovian features. We have extended the statistical approach to much smaller scales in space, where kinetic theory should be applied. Here we study in detail and compare the characteristics of magnetic fluctuations behind the bow shock, inside the magnetosheath, and near the magnetopause. It appears that the first Kramers- Moyal coefficient is linear and the second term is quadratic function of magnetic increments, which describe drift and diffusion, correspondingly, in the entire magnetosheath. This should correspond to a generalization of Ornstein-Uhlenbeck process. We demonstrate that the second order approximation of the Fokker-Planck equation leads to non-Gaussian kappa distributions of the probability density functions. In all cases in the magnetosheath, the approximate power-law distributions are recovered. For some moderate scales we have the kappa distributions described by various peaked shapes with heavy tails. In particular, for large values of the kappa parameter this shape is reduced to the normal Gaussian distribution. It is worth noting that for smaller kinetic scales the rescaled distributions exhibit a universal global scale-invariance, consistently with the stationary solution of the Fokker-Planck equation. These results, especially on kinetic scales, could be important for a better understanding of the physical mechanism governing turbulent systems in space and astrophysical plasmas.Comment: 13 pages, 7 figure

Testing for Markovian Character and Modeling of Intermittency in Solar Wind Turbulence

We present results of statistical analysis of solar wind turbulence using an approach based on the theory of Markov processes. It is shown that the Chapman-Kolmogorov equation is approximately satisfied for the turbulent cascade. We evaluate the first two Kramers-Moyal coefficients from experimental data and show that the solution of the resulting Fokker-Planck equation agrees well with experimental probability distributions. Our results suggest the presence of a local transfer mechanism for magnetic field fluctuations in solar wind turbulence

On the Origin and Evolution of the Universe: Chaos or Cosmos? Plan of Presentation

Abstract We consider evolution of the Universe based on the standard Big Bang model, quantum models of creation, and recent theory of nonlinear dynamics, including deterministic chaos and fractals. We show that by looking for an order and harmony in the the complex surrounding real world these modern studies give also new insight into the most important philosophical issues exceeding the classical ontological principles, e.g., providing a deeper understanding of an old philosophical question: why does something exist instead of nothing? We postulate that the origin of Universe is based on a simple but nonlinear law. Finally, it is worth noting that in mathematical-natural sciences we ought to look for the sense of the world in the mystery of rationality; the sense of every existence is the justification of the Universe. Finally, we argue that this scientific view provides also sense and hope to a human existence

On the Origin and Evolution of the Universe: Chaos or Cosmos? Plan of Presentation

Abstract We consider evolution of the Universe based on the standard Big Bang model, quantum models of creation, and recent theory of nonlinear dynamics, including deterministic chaos and fractals. We show that by looking for an order and harmony in the the complex surrounding real world these modern studies give also new insight into the most important philosophical issues exceeding the classical ontological principles, e.g., providing a deeper understanding of an old philosophical question: why does something exist instead of nothing? We postulate that the origin of Universe is based on a simple but nonlinear law. Finally, it is worth noting that in mathematical-natural sciences we ought to look for the sense of the world in the mystery of rationality; the sense of every existence is the justification of the Universe. Finally, we argue that this scientific view provides also sense and hope to a human existence

On the Origin and Evolution of the Universe: Chaos or Cosmos? Plan of Presentation

Abstract We consider evolution of the Universe based on the standard Big Bang model, quantum models of creation, and recent theory of nonlinear dynamics, including deterministic chaos and fractals. We show that by looking for an order and harmony in the the complex surrounding real world these modern studies give also new insight into the most important philosophical issues exceeding the classical ontological principles, e.g., providing a deeper understanding of an old philosophical question: why does something exist instead of nothing? We postulate that the origin of Universe is based on a simple but nonlinear law. Finally, it is worth noting that in mathematical-natural sciences we ought to look for the sense of the world in the mystery of rationality; the sense of every existence is the justification of the Universe. Finally, we argue that this scientific view provides also sense and hope to a human existence

Ακαδημία Θεσμών και Πολιτισμών Academy of Institutions and Cultures On the Origin and Evolution of the Universe: Chaos or Cosmos?

Xρώμεθα γαρ πολιτείαι ου ζηλούσηι τους των πέλας νόμους, παράδειγμα δε μάλλον αυτοί όντες τισίν ή μιμούμενοι ετέρους· και όνομα μεν δια το μη ες ολίγους αλλ ABSTRACT We consider evolution of the Universe based on the standard Big Bang model, quantum models of creation, and recent theory of nonlinear dynamics, including deterministic chaos and fractals. We show that by looking for an order and harmony in the the complex surrounding real world these modern studies give also new insight into the most important philosophical issues exceeding the classical ontological principles, e.g., providing a deeper understanding of an old philosophical questions: why does something exist instead of nothing? We postulate that the origin of Universe is based on a simple but nonlinear law. Finally, it is worth noting that in mathematical-natural sciences we ought to look for the sense of the world in the mystery of rationality; the sense of every existence is the justification of the Universe. Therefore, we argue that this scientific view provides also sense and hope to a human existence

Testing for multifractality of the slow solar wind

Abstract We analyse a time series of the radial component of the Elsässer variable for the low-speed stream of the solar wind plasma representing Alfvénic fluctuations propagating downstream as measured in situ by the Helios spacecraft in the inner heliosphere. We demonstrate that the influence of noise in the data can be efficiently reduced by moving average and singular-value decomposition filters. We calculate the multifractal spectrum for the flow of the solar wind directly from the cleaned experimental signal. The resulting spectrum of dimensions shows a multifractal structure of the solar wind in the inner heliosphere. The obtained multifractal spectrum is consistent with that for the multifractal measure on the self-similar weighted Cantor set with the degree of multifractality of $10 À1