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## Atomistic modelling and simulation of warm dense matter. Conductivity and reflectivity

Warm dense matter conductivity and reflectivity are investigated by means of density functional theory. Both one- and two-temperature cases are considered. One-temperature mode is related to equilibrium state where temperature of electrons and ions are equal. As an example of one-temperature system xenon plasma is studied. The reflectivity of shock-compressed dense xenon plasma is calculated and compared with experimental data. Two-temperature mode is associated with different temperature of electrons and ions. The thermal conductivity of aluminum and gold in such mode is examined. The comparison of obtained results with theoretical model based on Boltzmann equation is conducted.

The contribution of electron–phonon scattering to conductivity of a quantum cylinder in a lon-gitudinal magnetic field has been studied. It has been shown that the conductivity of the nanotube undergoes Aharonov–Bohm oscillations with variations in the magnetic flux through the nanotube cross section. The formulas describing the temperature dependence of the resistance of the nanostructure both in the case of an isotropic phonon spectrum and with allowance for the effects of phonon confinement have been obtained in the analytical form.

Warm dense matter (WDM) is a state of a substance with a solid-state density and temperature from 1 to 100 eV. Researchers believe that such a state exists in the cores of giant planets. Investigation of WDM is important for some applications, such as surface treatment on the nanometer scale, laser ablation, and the formation of the plasma sources of the X-ray radiation into the inertial synthesis. In this study, the conductivity and the thermal conductivity are calculated based on density functional theory and the Kubo-Greenwood theory. This approach was already used to simulate the transport properties in a broad range of densities and temperatures, and its efficiency has been demonstrated. The conductivity and the thermal conductivity of aluminum and gold are investigated. Both the isothermal state, when the electron temperature equals the ion temperature, and the two-temperature state, when the electron temperature exceeds the ion temperature, are considered. The calculations were performed for a solid body and liquid in the range of electron temperatures from 0 to 6 eV.

The photoemission of excess charge carriers into high-ohmic gallium arsenide was investigated. It was revealed, that the illumination even small local sample areas located far from contacts, influences both on contacts transition resistance and on volume conductivity of the crystal. On Suite-voltage dependencies there is a linear plot, angular coefficient which is directly proportional to the diameter of the illuminated surface. The model qualitatively explain the experimental results.

Investigated the effect of annealing on the optical properties of metallic films obtained by setting the plasma-focus "PF-4" on glass substrates. The transmission spectra of these films before and after annealing in air at about 900 K for about 10 minutes. Shows the effect of carbon on the optical properties and electrical conductivity of the films.

In operation results of computer simulation of characteristics of the standard analog device - the heterodyne executed on the printed circuit board from the composite dielectric having feeble conductivity are explained. Results of simulation showed that increase in specific bulk conductivity of material of the printed circuit board to 2·10 -7 Ohm -1 -m -1 practically does not change operating characteristics of a heterodyne. The possibility of effective use of the composite poorly carrying out dielectrics in standard radio engineering devices allowing to prevent origin of electrostatic discharges is set.

A contribution of the electron-phonon scattering to the conductivity of a quantum cylinder in a magnetic field is calculated. It is demonstrated that the nanotube conductivity undergoes the Aharonov–Bohm oscillations with changes of the magnetic flux through the nanotube cross section.

The dynamics of a two-component Davydov-Scott (DS) soliton with a small mismatch of the initial location or velocity of the high-frequency (HF) component was investigated within the framework of the Zakharov-type system of two coupled equations for the HF and low-frequency (LF) fields. In this system, the HF field is described by the linear Schrödinger equation with the potential generated by the LF component varying in time and space. The LF component in this system is described by the Korteweg-de Vries equation with a term of quadratic influence of the HF field on the LF field. The frequency of the DS soliton`s component oscillation was found analytically using the balance equation. The perturbed DS soliton was shown to be stable. The analytical results were confirmed by numerical simulations.

Radiation conditions are described for various space regions, radiation-induced effects in spacecraft materials and equipment components are considered and information on theoretical, computational, and experimental methods for studying radiation effects are presented. The peculiarities of radiation effects on nanostructures and some problems related to modeling and radiation testing of such structures are considered.

Let G be a semisimple algebraic group whose decomposition into the product of simple components does not contain simple groups of type A, and P⊆G be a parabolic subgroup. Extending the results of Popov [7], we enumerate all triples (G, P, n) such that (a) there exists an open G-orbit on the multiple flag variety G/P × G/P × . . . × G/P (n factors), (b) the number of G-orbits on the multiple flag variety is finite.

I give the explicit formula for the (set-theoretical) system of Resultants of m+1 homogeneous polynomials in n+1 variables