Equation of state under nuclear statistical equilibrium conditions

We investigate a three-parameter equation of state for stellar matter under nuclear statistical equilibrium conditions in the ranges of temperatures 3×10⁹–10¹¹ K and densities 10⁴–10¹³ g cm^?3 and for various ratios of the total number of neutrons to the total number of protons within the range 1–1.5. These conditions correspond to the initial stages of the gravitational collapse of iron stellar cores that are accompanied by nonequilibrium matter neutronization. We analyze the effect of the excited levels of atomic nuclei on the thermodynamic properties of the matter. We show that this effect is insignificant at low densities, ρ?10¹⁰ g cm^?3, but it leads to an expansion of the instability region, γ<4/3, at higher densities. The incorporated effects of the Fermi degeneracy of free nucleons prove to be insignificant, because their concentrations are low at low temperatures. In the future, we plan to investigate the effects of Coulomb interactions and neutron-rich nuclei on the thermodynamic properties of the matter.     

A semianalytical method for calculating the parameters of the electromagnetic halos around extragalactic gamma-ray sources

The ultrahigh-energy (>20 TeV ) gamma rays emitted by active galactic nuclei can be absorbed in intergalactic space through the production of electron-positron pairs during their interaction with extragalactic background photon fields. The electrons and positrons produced by this interaction form an electromagnetic halo. We have studied the halo formation and calculated the halo radiation spectrum. The magnetic field in the halo formation region is assumed to be strong enough for the electron velocities to be isotropized. For such fields, the halo formation process can be described by the method of generations. We calculated the synchrotron and Compton backscattering radiation spectra for the total halo luminosity. We obtained the spatial distribution of the radiation for a point gamma-ray source.     

Adapted Fuzzy Controller for Astronomical Telescope Tracking

This paper presents a novel application of fuzzy logic (FL) controller driven by an adaptive fuzzy set (AFS) for position tracking of the telescope driven by electric motor. Also, the proposed FL controller, driven by AFS, is compared with a classical FL control, driven by a static fuzzy set (SFS). Both FL controllers algorithm use the position error and its rate of change as an input vector. The mathematical model of the telescope driven by electric motor is highly nonlinear differential equations. Therefore the use of the artificial intelligent controller, such as FL is much better than the conventional controller, to cover a wide range of operating conditions. So, the output of FL control is utilized to force the electric drives, of the telescope, to satisfy a perfect matching of the predefined desired position of the telescope arms. Both of FL controllers, using AFS and SFS, are simulated and tested when the system is subjected to a step change in reference value. In addition, these simulation results are compared with the conventional Proportional-Derivative (PD) controller, driven by fixed gain. The proposed FL, using an adaptive fuzzy set, improve the dynamic response of the overall system by improving the damping coefficient and decreasing the rise time and settling time compared with other two controllers.     

The method of a two-point conditional column density for estimating the fractal dimension of the distribution of galaxies

We suggest a new method for estimating the fractal dimension of the spatial distribution of galaxies: the method of selected cylinders. We show the capabilities of this method by constructing a two-point conditional column density for galaxies with known redshifts from the LEDA database. The fractal dimension of a sample of LEDA and EDR SDSS galaxies has been estimated to be 2.1±0.1 for cylinder lengths of 200 Mpc. A major advantage of the suggested method is that it allows scales comparable to the catalog depth to be analyzed for galaxy surveys in the form of conical sectors and small fields in the sky.