Generalization of the Grad method in plasma physics

The Grad method is generalized based on the Bogolyubov idea of the functional hypothesis for states at the end of relaxation processes in a system. The Grad problem (i.e., description of the Maxwell relaxation) for a completely ionized spatially uniform two-component electron-ion plasma is investigated using the Landau kinetic equation. The component distribution functions and time evolution equations for parameters describing the state of a system are calculated, and corrections are obtained to the known results in a perturbation theory in a small electron-to-ion mass ratio.Comment: 10 pages, 2 table

On relaxation phenomena in a two-component plasma

The relaxation of temperatures and velocities of the components of a quasi-equilibrium two-component homogeneous completely ionized plasma is investigated on the basis of a generalization of the Chapman-Enskog method applied to the Landau kinetic equation. The generalization is based on the functional hypothesis in order to account for the presence of kinetic modes of the system. In the approximation of a small difference of the component temperatures and velocities, it is shown that relaxation really exists (the relaxation rates are positive). The proof is based on the arguments that are valid for an arbitrary two-component system. The equations describing the temperature and velocity kinetic modes of the system are investigated in a perturbation theory in the square root of the small electron-to-ion mass ratio. The equations of each order of this perturbation theory are solved with the help of the Sonine polynomial expansion. Corrections to the known Landau results related to the distribution functions of the plasma and relaxation rates are obtained. The hydrodynamic theory based on these results should take into account a violation of local equilibrium in the presence of relaxation processes.Comment: 18 page

Modeled Heavy-Tail Process Prediction Based on the Chebyshev Polynomials of the Second Kind

Nowadays telecommunication traffic in systems with data packet transfer is considered to be a heavy-tail process. The traffic prediction is an urgent problem for telecommunications, see, for example. There are many different approaches to traffic prediction. Some recent papers of the author were devoted to the investigation of the Kolmogorov–Wiener filter approach to the investigation if stationary heavy-tail data prediction, see, for example

On the accuracy of some polynomial approximations for the kolmogorov–wiener filter weight function

The problem of telecommunication traffic prediction is important for telecommunications and cyber security, see [1]. In paper [2] telecommunication traffic is described as a continuous stationary random process with a power-law structure function. In the framework of this model in papers [3–6] we proposed to use the Kolmogorov–Wiener filter for telecommunication traffic prediction. An approximate solution of the corresponding integral equation for the unknown weight function was obtained on the basis of the truncated polynomial expansion method

The effect of the probe magnetic moment orientation of magnetic resonance force microscope on the spectra of spin wave resonances

This work was supported by the Russian Science Foundation (project 16-12-10254)

Magnetic resonance force microscopy of individual domain wall

The sample preparation and micromagnetic simulations were supported by Russian Science Foundation (project # 16-12-10254)

Thermal expansion and polarization of (1-x)PNNxPT solid solutions

The paper presents the results of detailed studies of the thermal expansion of (1-x)PbNi1/3Nb2/3O3-xPbTiO3 solid solutions with x¼0- 0.8. The anomalous and lattice contributions to deformation and the thermal expansion coefficient are analyzed and the mean square polarization Pd is determined. The results obtained are discussed within the framework of the thermodynamic theory and the Landau 2-4-6 coefficients for solid solutions are estimate

The leading-order hydrodynamics of the Landau-Vlasov kinectic equation with the nonlocal collision integral

This paper is devoted to the hydrodynamics of a one-component gas with small potential interaction. The basis of investigation is the kinetic equation in case of small potential interaction which contains general nonlocal collision integral [1] and describes arbitrary non-uniform states. In the local approximation this equation coincides with the well-known Landau–Vlasov kinetic equation. In hydrodynamics the system is supposed to be weakly non-uniform

THE LEADING–ORDER HYDRODYNAMICS OF THE LANDAU-VLASOV KINECTIC EQUATION WITH THE NONLOCAL COLLISION INTEGRAL

This paper is devoted to the hydrodynamics of a one-component gas with small potential interaction. The basis of investigation is the kinetic equation in case of small potential interaction which contains general nonlocal collision integral [1] and describes arbitrary non-uniform states. In the local approximation this equation coincides with the well-known Landau–Vlasov kinetic equation. In hydrodynamics the system is supposed to be weakly non-uniform