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## Interatomic potential for uranium in a wide range of pressures and temperatures

Using the force-matching method we develop an interatomic potential that allows us to study the structure and properties of alpha-U, gamma-U and liquid uranium. The potential is fitted to the forces, energies and stresses obtained from ab initio calculations. The model gives a good comparison with the experimental and ab initio data for the lattice constants of alpha-U and gamma-U, the elastic constants, the room-temperature isotherm, the normal density isochore, the bond-angle distribution functions and the vacancy formation energies. The calculated melting line of uranium at pressures up to 80 GPa and the temperature of the alpha–gamma transition at 3 GPa agree well with the experimental phase diagram of uranium.

The process of ablation of a gold target by femto- and picosecond laser radiation pulses has been studied by numerical simulations using an atomistic model with allowance for the electron subsystem and the dependence of the ion–ion interaction potential on the electron temperature. Using this potential, it is possible to take into account the change in the physical properties of the ion subsystem as a result of heating of the electron subsystem. The results of simulations reveal a significant difference between the characteristics of metal ablation by laser pulses of various durations. For ablation with subpicosecond pulses, two mechanisms of metal fracture related to the evolution of electronic pressure in the system are established.

A multiscale concept for irradiated materials simulation is formulated based on coupling molecular dynamics simulations (MD) where the potential was obtained from ab initio data of energies of the basic defect structures, with kinetic mesoscale models. The evolution of a system containing self-interstitial atoms (SIAs) and vacancies in crystalline molybdenum is investigated by means of MD. The kinetics of formation of di-SIA clusters and SIA–vacancy recombination is analyzed via approaches used in the kinetic theory of radiation ageing. The effects of 1D diffusion of SIAs, temperature, and defect concentrations on the reaction rates are also studied. This approach can validate both the kinetic mechanisms and the appropriate kinetic coefficients, offering the potential to significantly reduce the uncertainty of the kinetic methodology and providing a powerful predictive tool for simulating irradiation behavior of nuclear materials.

A simple set of equations is derived to determine the Morse interatomic interaction potential parameters without any assumptions. These parameters are calculated for a model fcc crystal represented as 30 configuration spheres made of 1060 atoms surrounding a central atom. The dependences of these parameters on the number of surrounding atoms are obtained. The found parameters are used to calculate the energies of vacancy migration in 11 fcc metals using the proposed configuration sphere method.

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