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Ч. 4: Информационные технологии и телекоммуникации. , М.: Энергоатомиздат, 2013.
Burov N.A., Gaydukov R.K., Russian Journal of Mathematical Physics 2026 Vol. 33 No. 2 P. 263–275
The spreading of a droplet of incompressible fluid over a substrate under the action of capillary forces and gravity is studied within a phase-field framework. An asymptotic analysis shows that the solution of the phase-field system (regularized problem) converges to the solution of the corresponding limiting problem when a regularization parameter tends to zero. The ...
Added: April 11, 2026
Danilov V., Borisov V., IEEE Transactions on Electron Devices 2025 Vol. 72 No. 3 P. 1462–1468
In this article, we propose a numerical method for calculating solutions of the PDE (the heat equation for the cathode temperature and the continuity equation for the current density inside and outside the cathode) with discontinuous flux at the emission surface of a cathode placed in a vacuum. The discontinuity of the flux appears because ...
Added: March 3, 2025
Ioanna N. Trunova, Vitaly A. Kuzkin, Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 2025 Vol. 111 No. 1 Article 014227
We investigate thermoelastic behavior of nonlinear chains with an instantaneously created temperature profile.
We focus on a regime, further referred to as the ballistic thermoelasticity. In this regime, macroscopic strains are
small, thermal expansion is linear, conversion of mechanical energy into heat is negligible, and heat transfer
is almost ballistic. Equations describing ballistic thermoelasticity of the chains in ...
Added: January 30, 2025
Krivtsov A., Vitaly A. Kuzkin, Tsaplin V., Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 2024 Vol. 110 No. 5 Article 054123
The transition from a ballistic to a diffusive regime of heat transfer is studied using two models. The first model is a one-dimensional chain with bonds, capable of dissociation. Interparticle forces in the chain are harmonic for bond deformations below a critical value, corresponding to the dissociation, and zero above this value. A kinetic description ...
Added: January 30, 2025
Dmitriev S., Vitaly A. Kuzkin, Krivtsov A., Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 2023 Vol. 108 No. 5 Article 054221
A thermal diode or rectifier is a system that transmits heat or energy in one direction better than in the opposite
direction. We investigate the influence of the distribution of energy among wave numbers on the diode effect for
the junction of two dissimilar harmonic chains. An analytical expression for the diode coefficient, characterizing
the difference between heat ...
Added: January 30, 2025
Gaydukov R. K., Indian Journal of Pure and Applied Mathematics 2026 Vol. 57 No. 3 P. 808–825
The paper is deals with the heat transfer in the laminar flow of a viscous incompressible fluid along a plate with a small heated localized irregularity. It is well known that double- and triple-deck structures of the boundary layer arise in such flow problems. These structures make it possible, among other things, to describe the phenomenon of ...
Added: May 21, 2024
R. K. Gaydukov, V. G. Danilov, Computational Mathematics and Mathematical Physics 2024 Vol. 64 No. 6 P. 1317–1325
Mathematical modeling of the ice–water phase transition during liquid flow inside a pipe
with a small ice buildup on the wall at high Reynolds numbers is considered. As a mathematical model
describing the dynamics of the phase transition, a double-deck boundary layer model and a phase field
system are used. Results of numerical simulation are presented. ...
Added: February 17, 2024
Gaydukov R., Danilov V., Fonaryova A., Известия РАН. Механика жидкости и газа 2023 № 5 С. 82–94
В работе исследуется фазовый переход при обтекании жидкостью ледяной поверхности с малой локализованной неровностью при больших числах Рейнольдса. В рамках двухпалубной структуры пограничного слоя, на основе системы фазового поля построена математическая модель, описывающая динамику фазового перехода, и приведены результаты численного моделирования. ...
Added: May 10, 2023
Gaydukov R., Danilov V., Fonaryova A., В кн.: Волны и вихри в сложных средах: 13-ая международная конференция – школа молодых ученых; 30 ноября – 02 декабря 2022 г.: М.: ООО «ИСПО-принт», 2022. С. 68–71.
Рассмотрена задача о фазовом переходе (лед-вода) в подвижной среде. ...
Added: December 14, 2022
Danilov V., Gaydukov R., Vadim Kretov, Springer, 2020.
This book deals with mathematical modeling, namely, it describes the mathematical model of heat transfer in a silicon cathode of small (nano) dimensions with the possibility of partial melting taken into account. This mathematical model is based on the phase field system, i.e., on a contemporary generalization of Stefan-type free boundary problems. The approach used ...
Added: September 12, 2019
Danilov V., Gaydukov R., Vadim Kretov et al., IEEE Transactions on Electron Devices 2014 Vol. 61 No. 12 P. 4232–4239
This paper presents the results of mathematical modeling of heat transfer in the field emission process in a conic cathode of small dimensions with its possible melting considered. It is shown that the possibility of melting is determined by the cathode vertex angle. The melting is modeled in the framework of the phase field system ...
Added: October 24, 2014
Danilov V., Rudnev V., Gaydukov R. et al., М.: Научно-техническое издательство «Горячая линия – Телеком», 2014.
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 ...
Added: September 23, 2014