Rjelka M., Pupyrev P.D., Koehler B., Mayer A.P. «Nonlinear effects of micro-cracks on acoustic surface and wedge waves» Физика низких температур, 44, № 7, с. 946-953 (2018)

Micro-cracks give rise to non-analytic behavior of the stress-strain relation. For the case of a homogeneous spatial distribution of aligned flat micro-cracks, the influence of this property of the stress-strain relation on harmonic generation is analyzed for Rayleigh waves and for acoustic wedge waves with the help of a simple micro-mechanical model adopted from the literature. For the efficiencies of harmonic generation of these guided waves, explicit expressions are derived in terms of the corresponding linear wave fields. The initial growth rates of the second harmonic, i.e., the acoustic nonlinearity parameter, has been evaluated numerically for steel as matrix material. The growth rate of the second harmonic of Rayleigh waves has also been determined for micro-crack distributions with random orientation, using a model expression for the strain energy in terms of strain invariants known in a geophysical context.

Mera Azal, Stepanenko Vitaly A., Tarkhanov Nikolai «Successive approximation for the inhomogeneous Burgers equation» Журнал Сибирского Федерального университета. Математика и физика, 11, № 4, с. 519-531 (2018)

Неоднородное уравнение Бюргерса представляет собой простой вид уравнений Навье–Стокса. С аналитической точки зрения неоднородная форма плохо изучена, а полное аналитическое решение тесно зависит от формы неоднородного члена.

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.