We investigate the characteristics of the solar flare complex network. The limited predictability, nonlinearity, and self-organized criticality of the flares allow us to study systems of flares in the field of the complex systems. Both the occurrence time and the location of flares detected from 2006 January 1 to 2016 July 21 are used to design the growing flares network. The solar surface is divided into cells with equal areas. The cells, which include flares, are considered nodes of the network. The related links are equivalent to sympathetic flaring. The extracted features demonstrate that the network of flares follows quantitative measures of complexity. The power-law nature of the connectivity distribution with a degree exponent greater than three reveals that flares form a scale-free and small-world network. A large value for the clustering coefficient, a small characteristic path length, and a slow change of the diameter are all characteristics of the flares network. We show that the degree correlation of the flares network has the characteristics of a disassortative network. About 11% of the large energetic flares (M and X types in GOES classification) that occurred in the network hubs cover 3% of the solar surface.

A constructive approach is developed to build the solar flare complex network by utilizing a visibility graph condition alongside the Abe–Suzuki method. Solar flare information such as position, start time, and peak flux is used for this purpose. The obtained characteristics of the topological features (such as the characteristic path length, power-law behavior of the probability distribution function of degrees, and the clustering coefficient) demonstrate the scale-free and small-world properties of the solar flare modified network. To explain the complexity of the constructed network, Omori’s law as well as the universal scaling features are investigated. Furthermore, a nonextensive modification of the Gutenberg–Richter law is examined for the solar flare modified network using a q-stretched exponential model. Establishing a two-dimensional map for the configuration of 118 energetic main flares observed between 2006 and 2016, it is found that the main flares are located within the regions consisting of hubs (high-connectivity regions) of the network. A fractal dimension of the solar flare network of about 0.79 is also obtained.

We introduce analogue black holes (BHs) based on ideal magnetohydrodynamic equations. Similar to acoustic BHs, which trap phonons and emit Hawking radiation (HR) at the sonic horizon where the flow speed changes from super-to sub-sonic, in the horizon of magnetoacoustic and Alfvénic BHs, the magnetoacoustic and Alfvén waves will be trapped and emit HR made of quantized vibrations similar to phonons which we call magnephonons and Alphonons. We proposed that magnetoacoustic and Alfvénic BHs may be created in the laboratory using a tube with variable cross section embedded in a uniform magnetic field, and a supermagnetoacoustic or a super-Alfvénic flow. We show that the Hawking temperature for both BHs is a function of the background magnetic field, number density of fluid, and radius of the tube. For a typical setup, the temperature is estimated to be about 0.0266 K.

We introduce analogue black holes (BHs) based on ideal magnetohydrodynamic equations. Similar to acoustic BHs, which trap phonons and emit Hawking radiation (HR) at the sonic horizon where the flow speed changes from super-to sub-sonic, in the horizon of magnetoacoustic and Alfvénic BHs, the magnetoacoustic and Alfvén waves will be trapped and emit HR made of quantized vibrations similar to phonons which we call magnephonons and Alphonons. We proposed that magnetoacoustic and Alfvénic BHs may be created in the laboratory using a tube with variable cross section embedded in a uniform magnetic field, and a super-magnetoacoustic or a super-Alfvénic flow. We show that the Hawking temperature for both BHs is a function of the background magnetic field, number density of fluid, and radius of the tube. For a typical setup, the temperature is estimated to be about 0.0266 K.