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This paper is an overview of studying the solar features in a complex network approach. First, we introduce the structural features of complex networks and important network parameters. Applying the detrended fluctuation and rescaled range analysis and nodes degree power-law distributions confirmed the non-randomness of the solar features complex networks. Using the HEALPix pixelization and considering all parts of the solar surface under the same conditions, as well as applying centrality parameters (the nodes with the highest connectivity, closeness, betweenness, and Pagerank) showed that the active areas on the solar surface were correctly identified and were consistent with observations. A review of the complex structure of the solar proton flux and active regions also showed that in these networks, the average clustering coefficient and Page-rank parameters are suitable criteria to use in event prediction methods. The complex network of sunspots has also shown that sunspots and sunspot groups are formed through complex nonlinear dynamics.

Due to the saturation of the body ($m_b$) and surface ($M_S$) earthquake magnitudes, the moment magnitude ($M_W$) is a more convenient parameter for representing earthquake energies. We use the HRVD data, including 18,569 earthquakes recorded from 1976 January 1 to 2010 December 31, for five regions on the Earth (\textbf{Asia}-Oceania, Europe, Africa, North America, and South America). Applying the error propagation technique on the moment tensor, we estimate the standard error for $M_W$ showing a distribution that deviates from Gaussian errors which recommends using the Monte Carlo Markov chain (MCMC) to obtain model parameters instead of the least square approach. We investigate the linear relationship between the body and surface waves in small ($\le$ 6.1) and large ($>$6.1) magnitudes via MCMC. The slope varies from 0.811 to 1.565 ($m_b - M_W$) and 0.566 to 0.971 ($M_S - M_W$) across five regions. For 18,569 global earthquakes, we obtained the slope for $m_b \le 6.1$ ($m_b>$6.1) 0.863 (1.374), while we find the slope for $M_S\le$6.1 ($M_S >$ 6.1) 0.581 (0.921). These transition relationships of the magnitude moments are useful for increasing earthquake monitoring capacity.

Modeling fast solar wind based on the kinetic theory is an important task for scientists. In this paper, we present a two-fluid model for fast solar wind with anisotropic Kappa-Maxwellian electrons and Bi-Maxwellian protons. In the simulation, the energy exchange between the plasma particles and low-frequency Alfv\'en waves is considered. A set of eleven coupled equations is derived by applying the zeroth- to fourth-order moments of the Vlasov equation and the modified electromagnetic Maxwell equations. A characteristic of the Kappa distribution (indicated by $\kappa$ index) is explicit in the equation for the parallel component of the electron heat flux (parallel to the ambient magnetic field line) and differs from the equation derived for the proton heat flux due to the different nature of the distributions. Within the large $\kappa$ index, the equations for the two-fluid model tend to the equations obtained by the Maxwellian distribution. Using an iterated Crank-Nicolson method, the coupled equations are numerically solved for the fast solar wind conditions. We show that at (0.3 - 1) AU from the Sun, the electron density, components of temperature, and components of heat flux follow the power-law behavior. We also showed that near the Earth, the flow speed (electron or proton) increases with decreasing $\kappa$. We concluded that applying the small $\kappa$ index (the non-Maxwellian distribution), the extraordinary nature of the solar atmosphere, with its temperature of several million kelvin temperature for electrons, has been captured., Comment: 37 pages, 7 figures