Van Ostaay J.A.M., Mukhin S.I. «Phonon-kink scattering effect on the low-temperature thermal transport in solids» Физика низких температур, 44, № 6, с. 647-757 (2018)

We consider contribution to the phonon scattering, in the temperature range of 1 K, by the dislocation kinks pinned in the random stress fields in a crystal. The effect of electron-kink scattering on the thermal transport in the normal metals was considered much earlier. The phonon thermal transport anomaly at low temperature was demonstrated by experiments in the deformed (bent) superconducting lead samples and in helium-4 crystals and was ascribed to the dislocation dynamics. Previously, we had discussed semi-qualitatively the phonon-kink scattering effects on the thermal conductivity of insulating crystals in a series of papers _5,6. In this work it is demonstrated explicitly that exponent of the power low in the temperature dependence of the phonon thermal conductivity depends, due to kinks, on the distribution of the random elastic stresses in the crystal, that pin the kinks motion along the dislocation lines. We found that one of the random matrix distributions of the well known Wigner–Dyson theory is most suitable to fit the lead samples experimental data. We also demonstrate that depending on the distribution function of the oscillation frequencies of the kinks, the power low-temperature dependences of the phonon thermal conductivity, in principle, may possess exponents in the range of 2–5.

Vilke V.G., Osipova L.S., Shatina A.V. «The effect of the mutual gravitational interactions on the perihelia displacement of the orbits of the Solar system's planets» Нелинейная динамика, 14, № 3, с. 291-300 (2018)

The classical N-body problem in the case when one of the bodies (the Sun) has a much larger mass than the rest of the mutually gravitating bodies is considered. The system of equations in canonical Delaunay variables describing the motion of the system relative to the barycentric coordinate system is derived via the methods of analitical dynamics. The procedure of averaging over the fast angular variables (mean anomalies) leads to the equation describing the evolution of a single Solar system planet’s perihelion as the sum of two terms. The first term corresponds to the gravitational disturbances caused by the rest of the planets, as in the case of a motionless Sun. The second appears because the problem is considered in the barycentric coordinate system and the orbits’ inclinations are taken into account. This term vanishes if all planets are assumed to be moving in one static plane. This term contributes substantially to the Mercury’s and Venus’s perihelion evolutions. For the rest of the planet this term is small compared to the first one. For example, for Mercury the values of the two terms in question were calculated to be 528.67 and 39.64 angular seconds per century, respectively.