Известия ВУЗов.Радиофизика

We consider a dynamic system that consists of two coupled self-excited oscillators with delayed feedback. Such models occur in applied problems of radio physics and optics. It is assumed that the nonlinear function, which is responsible for the feedback, is finite and contains a great parameter. This reveals the possibility to use a special analytical method to study relaxation oscillations. It is shown that the dynamics of two such oscillators in the case of their asymptotically weak coupling is described by a special finite-dimension mapping and can be rather sophisticated.

We consider oscillations of a clamped liquid drop in an alternating electric field. The frequencies and damping rates of the drop eigenmodes are studied as functions of the problem parameters. The fundamental frequency of free oscillations can vanish in a certain interval of values of the Hocking parameter. The length of this interval depends on the ratio of the drop dimensions. Frequencies of other drop eigenmodes decrease monotonically with increasing Hocking parameter. Well-pronounced resonance effects are observed when studying forced oscillations. For any unequal values of the Hocking parameter, the amplitude of oscillations of the side surface is always finite. However, for identical Hocking parameters, the amplitude increases indefinitely in the case of low dissipation. It is shown that traveling capillary waves propagate on the side surface of the drop.

We study the structure and properties of the chimera states in the ensembles of chaotic oscillators with nonlocal coupling. It is shown that the phase and amplitude chimera states in the ensembles of chaotic oscillators with nonhyperbolic and hyperbolic attractors can be obtained using the models in the forms of two-dimensional Hénon and Lozi maps. The mechanisms of birth, the structure, and the lifetime of the phase and amplitude chimeras and the regime of solitary states are studied. The chimera states in two coupled ensembles of chaotic maps are considered. The possibility of realizing a new type of the chimera structure, namely, the chimera consisting of the solitary states is demonstrated. The effects of the external and mutual synchronizations of the chimera states are described by an example of two coupled ensembles of logistic maps with nonlocal coupling. A qualitative analogy of the obtained results with the classical effect of synchronization of periodic self-sustained oscillations is discussed.

We consider typical approaches to modeling of geodynamo processes in the liquid core of the Earth. Some features of magnetohydrodynamic turbulence under rapid rotation conditions are presented. On the example of net helicities, it is shown how rapid rotation facilitates the generation of a large-scale magnetic field and how the mechanism of the inverse effect of the magnetic field on the flow under geostrophy conditions is implemented. The arguments, based on the symmetry properties, in favor of the existence of a connection between the rapid rotation and the inversion frequency, as well as a number of other large-scale characteristics of the dynamo system, are given.

We propose a new algorithm for determining the basic significant points of various electrocardiographic-signal waves taking into account information from all available leads and ensuring a similar or higher accuracy compared with that of other up-to-date technologies. The test results of the algorithm efficiency for the QT data base [1] show a sensitivity above 97% when detecting the electrocardiographic-signal peaks, and 96% for their onsets and offsets, as well as the positive predictive value exceeding 97% for the peaks of the complexes, which is the best result compared with those of the previously known algorithms. As distinct from them, the proposed approach also allows one to determine the wave morphology. For the proposed algorithm, the delineation errors of all significant points are below the tolerances specified by the Committee of General Standards for Electrocardiography.

We have developed a method for deriving systems of closed equations for the dynamics of order parameters in the ensembles of phase oscillators. The Ott–Antonsen equation for the complex order parameter is a particular case of such equations. The simplest nontrivial extension of the Ott–Antonsen equation corresponds to two-bunch states of the ensemble. Based on the equations obtained, we study the dynamics of multi-bunch chimera states in coupled Kuramoto–Sakaguchi ensembles. We show an increase in the dimensionality of the system dynamics for two-bunch chimeras in the case of identical phase elements and a transition to one-bunch “Abrams chimeras” for imperfect identity (in the latter case, the one-bunch chimeras become attractive).

We consider the dynamics of the Kuramoto ensemble oscillators not included in a common synchronized cluster, where the mean field is subject to fluctuations. The fluctuations can be either related to the finite size of the ensemble or superimposed on the mean field in the form of common noise due to the constructive features of the system. It is shown that the states of such oscillators with close natural frequencies appear correlated with each other, since the mean-field fluctuations act as common noise. We quantify the effect with the synchronization index of two oscillators, which is calculated numerically and analytically as a function of the frequency difference and noise intensity. The results are rigorous for large ensembles with additional noise superimposed on the mean field and are qualitatively true for the systems where the mean-field fluctuations are due to the finite size of the ensemble. In the latter case, the effect is found to be independent of the number of oscillators in the ensemble.

We describe the main regimes of the wind wave dynamics, which correspond to the continuity of the fluxes of the wave momentum, energy, and action, on the basis of the wave turbulence theory. Basing on the experimental data about the wave growth, the energy flux into the largescale range (inverse cascade within the wave turbulence theory) is evaluated. The intensity of the direct energy cascade to the short-wave range is estimated basing on experimental parameterization of the wind wave frequency spectra, which corresponds to the Kolmogorov—Zakharov spectrum E(ω) ∝ ω−4. The obtained estimates show that intensity of the direct cascade exceeds that of the inverse one by two orders of magnitude. An approximate solution for the direct energy cascade is found as a perturbation of the classical Zakharov—Zaslavsky solution for the inverse cascade with a zero energy flux. The results are discussed in correlation with the development of spectral wind wave models.

We study the statistical moments of the soliton gas (mean field, variance, skewness, and kurtosis), which is described within the framework of the Gardner equation with negative cubic nonlinearity. The influence of the limiting (thick or table-like) soliton on the statistical moments of the soliton gas is considered. It is shown to be substantial if the thick-soliton intensity is comparable with that of the moderate-amplitude solitons.

The paper discusses the features of the previously published method of the Bayesian statistical evaluation of simultaneous satellite measurements of the minor species OH, HO2, and O3 at the mesospheric altitudes. These features are due to the introduction of a priori constraints on true concentration values (masked by measurement noise), which are determined by the condition of photochemical equilibrium of the species. The method is based on the probabilistic view of the satellite measurement process where the true concentrations of OH, HO2, and O3 are considered as random variables. In such a technique, we construct the a posteriori probability density of these variables and compare its statistical characteristics with the initial measurement data. It is shown that there is ambiguity in the construction of the a posteriori probability density of OH, HO2, and O3, which is due to the different ways of limiting transition from the three-dimensional probability distribution to the surface one. The ambiguity significantly affects the statistical means and leads to an inevitable systematic error. We present the main options for choosing the probability density, depending on the type of the transition. To estimate the systematic error, we tested the method by using artificial noisy model data on OH, HO2, and O3 that simulate perfect (unbiased) measurements. It is shown that choosing a patch transition leads to the least systematic error. Applying the method to MLS/Aura data of July 2005 confirmed the conclusion made earlier that the satellite measurements of the HO2 concentration have a significant bias greatly exceeding the systematic error of the method. This leads, in particular, to a significant error in the localization of the concentration maximum of this component at the mesospheric altitudes.

In this work, we propose a scenario of appearance of mixed dynamics in reversible two-dimensional diffeomorphisms. A jump-like increase in the sizes of the strange attractor and strange repeller, which is due to the heteroclinic intersections of the invariant manifolds of the saddle points belonging to the attractor and the repeller, is the key point of the scenario. Such heteroclinic intersections appear immediately after the collisions of the strange attractor and the strange repeller with the boundaries of their attraction and repulsion basins, respectively, after which the attractor and the repeller intersect. Then the dissipative chaotic dynamics related to the existence of the mutually separable strange attractor and strange repeller immediately becomes mixed when the attractor and the repeller are essentially inseparable. The possibility of realizing the proposed scenario is demonstrated using a well-known problem of the rigid-body dynamics, namely, the nonholonomic model of the Suslov top.

In this work, we experimentally study the heart rate variability, photoplethysmograms, and electroencephalograms of healthy subjects in the course of active experiments with respiration, whose rate varied according to a known law. On the basis of the experimentally measured signals of the heart rate variability, photoplethysmograms, and electroencephalograms, it is shown that the low-frequency regulation processes with frequencies below 1 Hz interact with each other and are significantly influenced by the respiration process. The obtained results are indicative of the presence of several vegetative-regulation centers whose activity is manifested in the low-frequency dynamics of the signals of the heart rate variability, photoplethysmograms, and electroencephalograms.

We study the convective diffusion of passive admixtures in the course of forced fluid filtration through a porous medium with frozen random inhomogeneities of macroscopic parameters. During the fluid filtration, the parameter inhomogeneities lead to spatially irregular flows and are responsible for dispersion of the fluid particles, which causes convective diffusion that is additional to molecular diffusion. In contrast to the molecular diffusion, this diffusion is anisotropic and directly proportional to the filtration flow velocity. We consider the inhomogeneities of both permeability and porosity of the medium and report on analytical results for the most common options of their statistical properties. It was assumed that the inhomogeneities are relatively small and their autocorrelation function decays with the distance r not slower than 1/rβ, where β > 1. Direct numerical simulation for different cases confirmed the validity of the restrictions we adopted and the correctness of the analytical findings.

We study the effects of turbulence on the electrification of thunderclouds. Analytical estimates of the disturbances of electrical parameters (in particular, charging current) stipulated by turbulent effects are performed for different parameters of turbulence and hydrometeors. The obtained results are used to improve the parameterization of electrical processes. A detailed comparison of the results of numerical simulation of thunderstorm events with and without taking into account turbulent effects revealed some characteristic features in the change of the electric parameter distributions in a thundercloud. Various scenarios of the electric parameter variations due to taking into account a high level of turbulence in thunderclouds are found and analyzed. They are (i) general intensification of the electrical processes without any significant change in the structure of the electrically active areas; (ii) an increase in the electric potential near the maximum values with the simultaneous decrease in potentials at the periphery; (iii) an increase in the electric potential with the coalescence of nearby areas of the maximum values of the potential.

We consider nanosecond subterahertz waveguide switches based on a 3D resonator with an active element made of a semiconductor, whose conductivity is controlled by a laser. Recently discovered possibilities to use these switches to obtain pulses with very long durations (up to tens of seconds) along with nanosecond pulses in one and the same device prototype are discussed. Switching with no distortion of the coherent radiation of promising subterahertz gyrotrons, which have powers of about several watts and pulse durations of up to ten seconds are demonstrated experimentally. The theoretical estimate of limiting powers of the switched subterahertz waves, which was proposed earlier, is confirmed and generalized. For this purpose, we perform a measurement of the powers by reducing it to a trivial measurement of the power of radiation of an industrial IR laser. Improvement of the resonance characteristics of the developed switch after switching several sequential long subterahertz pulses has been revealed. Most probably, it is due to “burning-off” of microscopic manufacturing defects and the approach of the actual frequency-amplitude characteristic to the calculated one. It has been predicted theoretically and partially confirmed experimentally that it is not possible to disable the switch being in the fundamental equilibrium state upon switching arbitrarily high powers of subteraheratz waves near the resonance band.

We theoretically study nonlinear acoustic effects (amplitude-dependent loss, resonant-frequency shift, and the second-harmonic generation) and determine the thresholds of parametric generation of subharmonic oscillations at fractional frequencies in the rod resonators with rigid boundaries and various nonlinearity types (elastic, hysteretic, different-modulus, etc.).

We propose an analytical solution of the problem of diffraction of a plane electromagnetic wave by a multilayer dielectric (including plasmon) sphere. The solution is obtained using the method of separation of variables. New efficient recurrence relationships are obtained for calculations of the fields in layers, as well as formulas for the fields in the near and far diffraction zones. The novelty of the proposed solution is connected with the way of representing its radial part in the form of normalized functions. It is shown that as the number of the lens layers, which approximate the smooth profile of dielectric permittivity, grows, the electric field at the focusing point increases and reaches the maximum value. This allows one to determine the minimum required number of layers in practical problems. Resonance properties of metal-dielectric nanoparticles are studied in the optical band.

The shadowing of some regions of a wavy water surface by other regions can significantly influence the backscattered signal not only in the problem of remote monitoring of a water reservoir at grazing angles (e.g., in radar), but also in the problems of underwater vision. In this work, we present the results of a theoretical study of this phenomenon with respect to the model of underwater imaging of the sky (Snell’s window) near the image boundary. The numerical-simulation method is used to develop the statistically mean image of Snell’s window, which allows for the shadowing effects, and the corrected formula of the estimate of a wave parameter, namely, the water-surface slope variance, is obtained using the value of blurring of the boundary of Snell’s window.

Features of detection of a single crack in a plate are experimentally studied by the nonlinear acoustic modulation method provided that single defects (cracks and cavities) are located between a low-frequency (tens of kilohertz) ultrasonic transducer of Lamb waves and a high-frequency (units of megahertz) ultrasonic transducer. It is shown that using modulation of the defect characteristics by a sequence of phase-inverted Lamb waves, by the level of modulation of the high-frequency wave reflected from the defect one can determine its type (a crack or a cavity). Changing step by step the interaction region of low-frequency and high-frequency waves by varying a delay between their radiation, it is possible to study selectively the nonlinear acoustic characteristics of the defects arranged in series on the location path. Based on the obtained results, we created a combined transducer which scans a defect and modulates its characteristics simultaneously in the preset area and which is suitable for moving it by hand on the surface of a plate for seeking hidden cracks.

We consider the method of formation of adaptive threshold of signal detection against the background of receiver inherent noise using the nonparametric algorithms on the basis of ordered statistics. The simulation results and the efficiency of using this method on the basis of estimating the quantiles of the statistical distribution of the process compared with the classical methods of “moving average” in the case of complicated signal-interference environment (weak-signal masking by intense interference, mutual masking of several signals simultaneously staying in the sliding data window, and the useful-signal presence in the region of the jump-like variation of interference) are shown. A mathematical model of estimating the loss introduced when detecting a useful signal by the threshold device based on the method of ordered statistics is developed.