International Scientific Conference of Students, Postgraduates and Young Scientists "Lomonosov-2021"

Mathematical modeling

Memoirs of the Faculty of Physics 2022. N 1.

Gold thermodynamic properties were examined by molecular dynamics with use of the embedded atom model. The LAMMPS package was used. Equilibrium melting temperature and specific heat as function of pressure were determined in range from 0 to 100 kbar. Density and specific heat as function of temperature were determined in range from 300 to 5000 K that included melting region. The modeling results were consistent with those from other authors both experimental and determined with other methods. These dependences and quantities can be used as input data for the continuum model of pulsed laser heating of matter.

Show AbstractMemoirs of the Faculty of Physics 2022. N 1.

This paper presents the results of a numerical and analytical study of 2-layer explicit and implicit difference schemes for the KdV equation. On Eulerian computational grids, a satisfactory numerical solution was obtained only when using an explicit-implicit difference scheme of the Crank-Nichols type of the second order of approximation in time t and spatial x variables. A completely implicit 2-layer scheme of the 1st order in time t and 2nd in the space x, although it is absolutely stable, but the presence of a high schematic viscosity leads to a significant distortion of the solution. The use of moving grids with dynamic adaptation made it possible to obtain high-precision numerical solutions not only for Crank-Nichols-type schemes, but also for a family of completely implicit 2-layer schemes of the 1st order in time t and 2nd in space x. An important advantage of the considered schemes is their simplicity and transparency of the basic mathematical constructions.

Show AbstractRadiophysics

Memoirs of the Faculty of Physics 2022. N 1.

The results of modeling the interaction of a tubular electron beam and a field in an oversized axisymmetric relativistic diffraction generator on a periodic sequence of tori are presented. A numerical analysis of the generator response to the effect of an electron beam modulated at a given frequency in resonant modes is carried out. The diffraction boundary value problem was solved by the method of integral equations. The influence of the structure parameters by resonant frequencies upon the distributions of the components of the electromagnetic field in the space of interaction between the flow and the field were studied.

Show AbstractTheoretical physics

Memoirs of the Faculty of Physics 2022. N 1.

For a singular hypersurface of arbitrary type in quadratic gravity equations of motion were obtained using the principle of least action. The equations containing the components of the surface energy-momentum tensor corresponding to the “external pressure” and “external flow” together with the Lichnerowicz conditions are necessary to find the hypersurface itself, while the rest of the equations define “arbitrary” functions that arise due to the implicit presence of derivative of the delta function. It turned out that there are no double layers or thin shells for the Gauss-Bonnet quadratic term. It was demonstrated that there is no “external pressure” for null singular hypersurfaces. For spherically symmetric lightlike singular hypersurfaces the “external flux” is additionally equal to zero; therefore, such hypersurfaces can only be thin shells. In this case the system of equations of motion is reduced to one, which is expressed through the invariants of spherical geometry along with the Lichnerowicz conditions.

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