19 citations · 105 across the 10 of their papers we have counts for
10 papers
On the adiabatic invariance of the action of a trapped wave
Ekaterina V. Shishkina, Serge N. Gavrilov
Recently, it has been shown (Gavrilov et al., Nonlinear Dyn, 112, 2024) that in a linear solid discrete-continuous system with several slowly time-varying parameters, the amplitude…
The anti-localization of non-stationary linear waves and its relation to the localization. The simplest illustrative problem
Ekaterina V. Shishkina, Serge N. Gavrilov, Yulia A. Mochalova
We introduce a new wave phenomenon, which can be observed in continuum and discrete systems, where a trapped mode exists under certain conditions, namely, the anti-localization of…
Unsteady ballistic heat transport in a 1D harmonic crystal due to a source on an isotopic defect
Ekaterina V. Shishkina, Serge N. Gavrilov
In the paper we apply asymptotic technique based on the method of stationary phase and obtain the approximate analytical description of thermal motions caused by a source on an iso…
Steady-state ballistic thermal transport associated with transversal motions in a damped graphene lattice subjected to a point heat source
Serge N. Gavrilov, Anton M. Krivtsov
In the paper we deal with ballistic heat transport in a graphene lattice subjected to a point heat source. It is assumed that a graphene sheet is suspended under tension in a visco…
Discrete and continuum fundamental solutions describing heat conduction in 1D harmonic crystal: Discrete-to-continuum limit and slow-and-fast motions decoupling
Serge N. Gavrilov
In the recent paper by Sokolov et al. (Int. J. of Heat and Mass Transfer 176, 2021, 121442) ballistic heat propagation in 1D harmonic crystal is considered and the properties of th…
Passage through a resonance for a mechanical system, having time-varying parameters and possessing a single trapped mode. The principal term of the resonant solution
Ekaterina V. Shishkina, Serge N. Gavrilov, Yulia A. Mochalova
We consider a forced oscillation and passage through resonance for an infinite-length system, having time-varying parameters and possessing a single trapped mode. The system is a s…
Thermal equilibration in a one-dimensional damped harmonic crystal
Serge N. Gavrilov, Anton M. Krivtsov
The features for the unsteady process of thermal equilibration ("the fast motions") in a one-dimensional harmonic crystal lying in a viscous environment (e.g., a gas) are under inv…
Steady-state kinetic temperature distribution in a two-dimensional square harmonic scalar lattice lying in a viscous environment and subjected to a point heat source
Serge N. Gavrilov, Anton M. Krivtsov
We consider heat transfer in an infinite two-dimensional square harmonic scalar lattice lying in a viscous environment and subjected to a heat source. The basic equations for the p…
Non-stationary localized oscillations of an infinite Bernoulli-Euler beam lying on the Winkler foundation with a point elastic inhomogeneity of time-varying stiffness
E. V. Shishkina, S. N. Gavrilov, Yu. A. Mochalova
We consider non-stationary localized oscillations of an infinite Bernoulli-Euler beam. The beam lies on the Winkler foundation with a point inhomogeneity (a concentrated spring wit…
Non-stationary localized oscillations of an infinite string, with time-varying tension, lying on the Winkler foundation with a point elastic inhomogeneity
S. N. Gavrilov, E. V. Shishkina, Yu. A. Mochalova
We consider non-stationary oscillations of an infinite string with time-varying tension. The string lies on the Winkler foundation with a point inhomogeneity (a concentrated spring…