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## Molecular dynamics simulation of graphite melting

Questions on the behavior of the graphite melting curve have remained open during the last fifty years. The process of graphite melting in the pressure range of 2–14 GPa is investigated by the method of molecular dynamics using the model of reactive interatomic potential; the dynamics of meltingfront prop agation upon crystal superheating is considered, and the melting curve is plotted. The selfdiffusion coefficient in the liquid phase is determined for the aforementioned pressure range, and the question of the existence of the liquid–liquid phase transition in carbon is considered.

The solution energy of H and He in various interstitial and substitution positions in the hcp lattice of α-Ti has been calculated based on the method of electron density functional. The lowest solution energy of He corresponds to the basal octahedral position and that of H corresponds to the octahedral position (next in energy is the tetrahedral position). The calculated vibration frequencies of H in various positions are used for identification of lines in the vibration spectrum obtained by the method of neutron inelastic scattering. Taking into account these spectra, it can be concluded that hydrogen atoms occupy in the hcp lattice of Ti both the octahedral and tetrahedral positions even at 600 K. The available experimental data do not contradict the conclusion that the octahedral position is more preferable in α-Ti. The energy barriers are estimated for various diffusion paths of H and He.

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 new mathematical model of heat transfer in silicon field emission pointed cathode of small dimensions is constructed which permits taking its partial melting into account. This mathematical model is based on the phase field system, i.e., on a contemporary generalization of Stefan-type problems. The approach used by the authors is not purely mathematical but is based on the understanding of the solution structure (construction and study of asymptotic solutions) and computer calculations. The book presents an algorithm for numerical solution of the equations of the obtained mathematical model including its parallel implementation. The results of numerical simulation conclude the book.

The book is intended for specialists in the field of heat transfer and field emission processes and can be useful for senior students and postgraduates.

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