Наукові роботи. Факультет комп'ютерних наук

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Dissipative instabilities and superradiation regimes (classic models)
(2021) Kuklin, V.M.; Poklonskiy, E.V.; Куклін, Володимир Михайлович; Поклонський, Євген Васильович
The generation of an electromagnetic field by oscillators in an open resonator is discussed in a one-dimensional approximation. In this case, the development of the so-called dissipative instability  the dissipative generation regime. Such an instability with the generation of electromagnetic oscillations arises when the decrement of oscillations in an open resonator in the absence of oscillators turns out to be greater than the increment of the resulting instability of the system of oscillators placed in this resonator. It is assumed that the oscillators do not interact with each other, and only the resonator field affects their behavior. If the resonator field is absent or small, the superradiance regime is possible, when the radiation of each oscillator is essential and the field in the system is the sum of all the eigenfields of the oscillators. In the dissipative regime of instability generation, the system of oscillators is synchronized by the induced resonator field. The synchronization of the oscillators in the superradiance mode owes its existence to the integral field of the entire system of oscillators. With a weak nonlinearity of the oscillators, a small initiating external field is required to excite the generation regime. It is noteworthy that the maximum value of the superradiance field is approximately two times less than the maximum field that the same particles could generate if they were at the same point. In all cases, for a given open resonator, the superradiance field turned out to be somewhat larger than the resonator field. Nevertheless, for the same resonator, the increments and attainable field amplitudes in both cases are of the same order of magnitude.
On frequency and spatial periodicity of the waves of the anomalous amplitude in the ocean
(2019) Kuklin, V.M.; Poklonskiy, E.V.; Куклін, Володимир Михайлович; Поклонський, Євген Васильович
The paper shows that the waves of anomalous amplitude are long-lived formations. They drift in the direction of the wave motion with the group velocity of the wave packet, which is half the phase velocity of the main wave. The swing of the wave (the distance from the hump to the trough) of the anomalous amplitude is more than three times the average value of the sweep of the wave motion. The modulation instability of this wave form a perturbation spectrum, the energy of which is twice the energy of the main wave in the developed process mode. The spatial size of the wave packet practically does not change, the amplitude of the swing in the maximum first increases, then gradually decreases. The number of such waves in areas of strong wind exposure is much larger than the statistics of random interference processes allow. This is due to the influence of the main wave (its amplitude remains noticeably greater than the amplitudes of each of the modes of the wave packet) on the behavior of each pair of modes from the wave packet of the perturbation. In the laboratory system, the duration of the anomalous wave coincides qualitatively with the time of existence of the Peregrin autowave. Although the Peregrin autowave corresponds to a different physical reality, where the dispersion of the wave is weak. Gravitational surface waves have a strong dispersion, and the NSE equation in this case is noticeably modified. However, in rest system of the wave packet (moving relative to the laboratory system) the abnormal amplitude wave lifetime is much longer. The distance that the wave packet travels with a persisting anomalous sweep is at least equal to several hundred wavelengths and can reach hundreds of kilometers. A simple calculation of such waves by means of space monitoring due to the small viewing area (frame) may be inaccurate. Once formed, such waves are able to drift over considerable distances. However, they may well get into the next frame of view. That is, estimates of the number of such waves can be overestimated.
On the periodic change of the luminosity of the cosmic sources with an active medium
(2020) Kostenko, V.V.; Kuklin, V.M.; Poklonskiy, E.V.; Костенко, В.В.; Куклін, В.М.; Поклонський, Є.В.
The presence of an internal layer with an active medium in a hot radiation source is considered, which can be described by a quantum two-level system located near equilibrium. The population of the upper and lower levels is approximately equal. It is shown that during convection from deeper hot layers, which supports the inversion of the populations of the active system, generation of induced radiation pulses is possible, the intensity of which is comparable to or greater than the intensity of the background spontaneous radiation of the source. With a sufficient thickness of the surface layers due to the effects of radiation scattering in them, the emission spectrum of a completely black body may well form there. Pulse generation near a previously detected new threshold of induced radiation can lead to a periodic change in the radiation intensity of the source as a whole. This threshold is determined by the equality of the squared population inversion to the total number of states. The generation of pulses of induced radiation is considered both in Einstein's representation, on the basis of balanced equations, and using a semiclassical description for small values of population inversion and for low levels of electric field intensity, when the Rabi frequency is less than the line width. The description of the induced radiation process is reduced to a one-parameter system of equations. Periodic solutions are represented by closed trajectories on the phase plane (relative density of quanta, relative density of population inversion). A similar layer with an active medium, which can be described by a quantum two-level system located near equilibrium, can exist in stars and is most likely localized in the photosphere. If there is significant convection in the star’s atmosphere, conditions can be realized for generating pulses of induced radiation. It turns out that one can see the similarity of the obtained solutions with known observations of changes in the luminosity of Cepheid stars (Cepheus delta and the North Star).
Phase transitions in convection
(2019) Gushchin, I.V.; Kuklin, V.M.; Poklonskiy, E.V.; Гущин, Іван Валерійович; Куклін, Володимир Михайлович; Поклонський, Євген Васильович
The paper presents the results of the study of the models of convective instability near its threshold of thin layers of liquid and gas bounded by poorly conducting walls. These models single out one spatial scale of interaction, leaving the possibility for the evolution of the system to choose the symmetry character. This is due to the fact that the conditions for the realization of the modes of convective instability near the threshold are chosen. All spatial perturbations of the same spatial scale, but of different orientations, interact with each other. It turned out that the presence of minima of the interaction potential of the Proctor-Sivashinsky equation modes, the absolute value of the wave number vectors of which is unchanged, determines the choice of symmetry and, accordingly, the characteristics of the spatial structure. In the case of a more realistic model of convection described by the Proctor-Sivashinsky equation, it was possible to observe both the first-order phase transition and the second-order phase transition and detect the form of the state function, which is responsible for the topology of the resulting convective structures: metastable rolls and stable square cells. In this paper, it is shown that the nature of the structural-phase transition in a liquid when taking into account the dependence of viscosity on temperature in the Proctor-Sivashinsky model is similar to the case of the absence of such a dependence. The transition time turns out to be the same, despite the fact that a different structure is formed - hexagonal convective cells. As in the Swift-Hohenberg model, a hard mode for the formation of hexagonal cells in a gas medium is possible only for a sufficiently noticeable dependence of its viscosity on temperature. The phase transition times are inversely proportional to the difference in the values of this function for two consecutive states. A similar description of phase transitions did not use phenomenological approaches and various speculative considerations, which allows for a closer look at the nature of transients.
Semiclassic models of the dissipative regime of instability and superradiation of a quantum radiator system
(2021) Kuklin, V.M.; Lazurik, V.T.; Poklonskiy, E.V.; Куклін, В.М.; Лазурик, В.Т.; Поклонский, Є.В.
The paper discusses the similarity between dissipative generation and superradiance regimes for systems of excited quantum emitters placed in an open cavity. In the case of the existence of a resonator field due to reflections from the ends of the system, a dissipative generation regime is usually realized. In this case, the decrement of oscillations in the waveguide in the absence of radiators turns out to be greater than the increment of the arising instability of the system of radiators placed in the resonator. When describing this mode, the influence of the emitters on each other and the sum of their own fields is neglected. The resonator field forces the oscillators to emit or absorb quanta synchronously with it, depending on the local value of the population inversion. Lasing takes on a weakly oscillatory character due to an asynchronous change in the population inversion of the system of emitting dipoles (nutations), which have a ground and excited energy levels. To describe the process, the equations of the semiclassical theory based on the use of the density matrix are quite sufficient. In the case when there is no resonator or waveguide field, taking into account the eigenfields of the oscillators becomes essential. To simulate the superradiance process, large emitting particles are used, to describe which one should use the equations for the density matrix. It is shown that the interaction of quantum emitters in this case is due to electromagnetic fields under conditions when the overlap of their wave functions is insignificant. Equations are obtained that allow considering the process of interaction of emitters. When the emitters interact, an integral field is formed in the resonator, an increase in the intensity of which leads to synchronization of the emitters. It is shown that the characteristic times of the development of the process, as well as the attainable amplitudes of the excited fields for dissipative regimes of generation and regimes of superradiance of emitters filling an open resonator, are comparable.