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Introduction. Since nowadays ballast-free track structures are most often used in combination with continuous welded track solutions for organizing a rail string, it should be emphasized that stresses arising in the rail string affect the stress-strain state of the entire construction of the track superstructure; therefore, it is necessary to monitor the current state of the continuous welded track. Nevertheless, kinks are formed and assembled rails and sleepers lose stability during the operational period of a continuous welded track, and methods are needed to determine the pre-failure conditions related to the temperature range of operation of a continuous track. Materials and methods. In this study, we propose a model of a flat structure made of a material having anisotropic properties, which makes it possible to take account of initiation and propagation of wave processes under the action of an external dynamic load. Results. The considered methods of simulating the propagation of elastic waves in a plate will make it possible to identify the points where direct and reflected waves of various orders converge; these waves can both increase and reduce the overall intensity of wave processes, leading to an increase or reduction in stresses and deformations in the characteristic points of a structure. Conclusions. The proposed solutions are most relevant for the structural elements of transport infrastructure facilities, since they are the ones that are exposed to alternating dynamic loads having varying intensity and time distribution of characteristic values.

The results of studying a variability of internal-gravity-wave characteristics and their signatures based on satellite data are presented. Observations of the wave processes under study over the Russian Federation Pacific coast in the period from 2015 to 2017 are considered. High-periodic Himawari-8 satellite images and thematic products of their processing are used. The methods and algorithms for retrieving parameters of internal gravity waves and their cloud manifestations are described. Trends for various characteristics of wave processes under study are constructed. The typical variability of parameters of internal gravity waves and their signatures is revealed on the basis of the longest lasting episodes of their observation. The results of analysis of coefficients of correlation between the various characteristics of the wave processes under study are presented. Similar episodes of observing signatures of internal gravity waves for the time period under study are established. The processes occurring in the “atmosphere–underlying surface” system and their influence on the creation of favorable conditions for the generation and propagation of wave processes under study are discussed.

The paper presents the results of a numerical study of the fracture of concrete structures — the protective shell of a nuclear power plant (NPP), under impulse loads. The model of concrete behavior takes into account differences in the limits of compressive and tensile strength, dependence of tensile strengths on the strain rate, plastic properties of concrete, fracture, fragmentation of the shell. Numerical modeling is carried out by finite element method in a three-dimensional statement as part of a phenomenological approach of the mechanics of a continuous medium, using the authors computational software. The dynamics of the fracture of the nuclear power plant protective shell, which has a complex cellular structure and the role of wave processes, is investigated.

The review summarizes information on the effect of wave effects on various processes in chemistry and petrochemistry. Their classification by nature and by the physical bases of the processes taking place in this process is given. The main stages in the technology of oil refining (production, primary and deep oil refining, the use of fuels, environmental problems), in which wave processing plays a significant role, are considered. The questions of the mechanism of the effect of wave processes on oil systems are discussed.

The article shows the relevance of the application of discrete models of rod structures of radio-electronic means (REM) for the study of their behaviour under transient loading. A discrete model of the propagation of harmonic waves in the rod and the study of standing waves are proposed. Computational experiments using the proposed model are conducted. The results show that the model accurately reflects qualitative dynamics of the physical processes in the elastic rod while the waves of elastic deformations are passing through. The proposed models are used for software implementations of systems of mechanical simulation of the behaviour of rod structures.

In this paper, we developed and tested new protective devices, such as resonant stabilizers of wave processes, which allow completely neutralizing the negative impact of vibrations and hydraulic shocks in pipelines. The resonant stabilizer has significantly smaller (by 5–10 times) dimensions, material consumption, and competitive cost and does not require the use of additional pumping equipment, automation systems, and tanks, which, along with the simplification of operations, significantly increases the efficiency and reliability of the pipeline systems.

The authors substantiate the necessity of creating a generalized pile model, which would allow obtaining more plausible signalograms of wave processes in reinforced concrete piles. Using currently available models does not allow detecting defects in piles with sufficient accuracy. Several wave models of signalograms are developed, which are based on the finite difference method and take into account different types of oscillatory processes in reinforced concrete piles in the ground. The models are able to describe different types and locations of defects by length of the pile, take into account ground conditions of the construction site, etc. They allow simulating the echo of defects with specified increments on the signalogram. Now it will be possible not only to determine the length of the pile and location of defects, but also to identify small defects (less than 30% of the cross-sectional area of the pile). In the one-dimensional case, the obtained models coincide with those already known, and in three-dimensional case the obtained models are a generalization of the already known ones.

Today, the exploration of the Arctic region is one of the most important direction of research in our country, because large amounts of unexplored oil and gas deposits are located there. Large hydrocarbon deposits are situated within the Northern seas. Their development is complicated by gas explosions resulting from an accidental opening and further spread of the gas. Since the region with gas layers cannot be frequently monitored, an area with already detected gas deposits is numerically modeled instead. In this work, seismic waves propagating in multilayered geological models with gas-containing inclusions were numerically modeled over a four-year interval by applying the grid-characteristic method. Wave patterns of seismic reflections and seismograms for the described problem were obtained. The wave patterns and seismograms obtained in the two- and three-dimensional cases were compared. The results were found to be in good agreement.

The possible potentials and touch voltages in substations may reach several tens of kV even at low grounding resistances for the case of flowing of pulse lightning current in the earthing grids. The paper presents an approach to define the permitted values of the touch voltages in earthing grids at impulse lightning currents influences. For the determination of the permissible body current an energy limit of 10 J was accepted. Using the simulation model, developed for the study of wave processes in the earthing grids, comparison of the maximum values of the received touch voltages and the permitted touch voltages has done.

This paper focuses on further development of the non-destructive shock wave method used in structural engineering to control the state of reinforced concrete (RC) structures subjected to loading, which frequently leads the formation of cracks in these structures. Our version of this method implies registration of wave processes occurred in concrete due to impact loading and comparison of these processes for undamaged and cracked structures. The parameters of elastic shock waves are recorded at instants when they are practically independent of fastening conditions and responded best to the presence of a crack. Numerical simulations provide a means of analyzing parameter changes in the wave front passing through the region of cracking. A qualitative criterion is formulated to assess whether the examined concrete is undamaged or there are cracks in it and how the structure condition changes at increased load and during the elimination of cracks. This criterion is defined as the ratio of acceleration amplitudes of first half-waves registered in areas on both sides of the crack. A comparison of computational results and experimental data supports the validity of the criterion. Analysis of the results obtained from a series of numerical experiments makes it possible to compute optimal points for applying impulse loading and to determine sensor positions for recording accelerations needed to compute the criterion.

A comprehensive approach to studying nonlinear wave processes in the human cardiovascular system is overviewed based on the combination of high-precision methods for pulse wave measurements, mathematical analysis methods for empirical data, and direct numerical simulation of hemodynamic processes in the arterial tree. Combined application of high-precision recording devices and the developed mathematical apparatus is the basis for creating effective a new generation functional diagnostic base.

The description of the dynamics and fluctuations of macro variables remains one of the most exciting problems of financial economics. This paper models macro variables via the description of transactions between agents. We use risk ratings x of agents as their coordinates in the economic space. Transactions like buy-sell, investment, credits, etc., between agents change their extensive financial and economic variables. Aggregates of transactions between all agents with risk ratings x and y define the macro transactions between points x and y. Macro transactions determine the evolution of macro variables. Interactions between different transactions outline their dynamics and fluctuations. We model macro transactions and the interactions between them by economic hydrodynamic-like equations in the economic space. As an example, for simple model interactions between credit-loans and loans-repayment transactions we derive economic hydrodynamic-like equations and wave equations for near perturbations of macro transactions and study simple wave solutions and their consequences. Waves of macro transactions in the economic space propagate from high to low risk agents or vice versa and define the fluctuations of macro financial variables. The existence and diversity of waves and fluctuations of macro transactions in simple models clarifies the importance of wave processes for macro financial modeling and forecasting.

The principles of adapting wave techniques for fault location in electrical transmission lines with dynamically changing parameters are studied by simulation modelling. Pseudo-ranging and difference-ranging algorithms for fault location by wave techniques are developed. Results are presented from a study of the prospects for raising the accuracy of the wave method for fault location in transmission lines using these algorithms.

A calculation model has been developed to describe the propagation of magnetostatic waves in a periodic structure consisting of two one-dimensional magnonic crystals, the periods of which are shifted relative to each other in the wave propagation direction. It is shown that, depending on the shift between the magnonic crystals, up to three bandgaps can be formed in this structure in the first Bragg resonance.

Delamination caused by low-velocity strike is considered as one of the most dangerous failure types. The destruction of contact between the plies or composite components significantly lowers the residual strength of the material but cannot be determined by visual inspection. These failures can mostly be determined by ultrasound testing, however, it requires a long time and cannot be carried out on site, which increases the maintenance cost. Both delamination emergence and ultrasound diagnostic results are determined by wave processes in viscoelastic media. The grid-characteristic method used in this chapter shows good results verified on various experimental data. The results of numerical modelling of delamination and its diagnostics are given in this chapter.

Though Fano resonances were originally discovered in quantum physics, they can emerge in the variety of wave processes including photonic systems. In this chapter, we demonstrate how the concept of Fano resonances can be applied in topological photonics to describe photonic topological states supported by metasurfaces. As we prove, leaky nature of metasurface’s modes allows one to probe them from the far field, while the observed Fano-type features in transmittance spectrum can be unequivocally related to the topological properties of photonic bands. This fundamental link between Fano resonances in transmittance and photonic topological states opens an appealing perspective to control scattering of light through the topological characteristics of metasurface.

One of the new kind of apparatus massage is massage by the elastic «pseudo-boiling» layer (EPBL-massage). «Pseudoboiling» effect is created on the surface of the elastic membrane. It occurs by the multiple impacts of the metal small ball. This action results in origin and spreading wave processes in the organism. Such wave acoustical field improves blood circulation and increases metabolism. The aim was to assess of EPBL-massage influence to the children condition with diseases of the musculoskeletal system. Studies have been conducted in 82 children with posture disturbances, flat feet and spastic forms of cerebral palsy. We used clinical examination, carpal dynamometry and surface cutaneous electromyography, plantography. Analisis of the data revealed the increase carpal force, decrease higher electromyographic activity and improvement of static indurance. It was revealed a favourable effect of EPBL-massage on the clinical symptoms of these disorders: decreased pain, increased physical activity, increased strength and strength endurance muscles of the trunk, extremities, decreased their spasticity. The effectiveness of treatment, good tolerance, simplicity and comfort of the EPBL-massage allow to recommend its using in children with disorders of the musculoskeletal system.

It is demonstrated that pump complexes pipeline networks are characterized by a high degree of breakdown rate because of leakages accompanied by complicated wave processes in the hydrosystem. It is found out that pipeline network wave processes depend on localization place and amount of the leakage, hydronetwork structural parameters as well as the properties of the transported liquid. Leakage influence on technological, electromechanical and energy characteristics of the pump complex is determined. It is stated that to identify the leakage it is expedient to use a signal of hydraulic power, whose frequency analysis makes it possible to obtain a wider spectrum of diagnostic signs of non-stationary condition. It is shown that leakage is accompanied by growth of hydraulic power variable component, in particular, its sine component.

Analytical expressions for determining the complex slowing factor and reflection coefficient are obtained using a general form of the dispersion equation of the slow-wave system and taking into account the properties of the medium surrounding it. These parameters can also be measured experimentally. It is shown that the determination of these quantities enables a simplified analysis of the transformation of waves, and the structure and space charge of the electron beam in microwave devices with prolonged interaction to be carried out, using the example of a waveguide model of a traveling-wave tube.

A technique for calculation of wave parameters and overvoltages in one- and two-layer windings of an induction motor powered by a pulse-width modulation converter is introduced. A mathematical model and simulation results for wave processes in these windings are presented.

A mathematical model of wave hydrodynamics has been constructed that describes the wave setup on the coast and includes physical parameters such as turbulence exchange, the complex geometry of the bottom and coastal line, and friction with the bottom. For this mathematical model, a discrete model has been constructed, taking into account the dynamic change of the geometry of the calculated domain. A procedure to construct discrete mathematical models is proposed that reflects the occupancy of control cells, improving the real accuracy of the solution in the case of the complex geometry of the domain due to better approximation of the boundary. The software of this task of wave hydrodynamics has been implemented and numerical experiments staged.

New results of experimental studies performed at the Scientific Center of Nonlinear Wave Mechanics and Technology of the Russian Academy of Sciences (NTs NVMT RAN) on the investigation of wave processes in dispersed media, aimed at the application of wave effects for processing and obtaining microheterogeneous emulsions, are presented. The possibility of controlling the drop sizes of the dispersed phase due to variations in the wave processing mode is shown using the example of cosmetic creams. The energy efficiency of the wave method for processing and obtaining the microheterogeneous emulsions is presented.

This paper describes continuous time macro-finance via dynamics of financial transactions between economic agents. Risk ratings of agents play role of their coordinates x on economic space. Financial variables of agents like Investment or Assets, Profits or Credits allow describe corresponding macro financial variables. Aggregates of financial variables of all agents allocated near x define macro variables as functions of time and x. Integrals of financial variables over economic space equal common variables of entire macro-finance as functions of time only. Financial transactions between agents define evolution of their financial variables. Aggregates of financial transactions between agents allocated at points x and y define macro transactions that describe financial "action-at-a-distance" between points x and y. Dynamics of macro transactions define evolution of macro financial variables. To model macro financial transactions and their mutual interactions we obtain hydrodynamic-like equations. For simple model of interactions between two macro transactions like Assets-Liabilities and Income-on-Assets we derive hydrodynamic-like equations in a closed form. That allows model relations between two macro transactions in a self-consistent manner. For that model we derive wave equations on perturbations of macro transactions and study simple solutions and consequences. Existence and diversities of financial waves in simple models clarifies importance of wave processes for macro-finance modeling.

This paper describes evolution of economic and financial transactions between agents as ground for modelling fluctuations of economic and financial variables. We use risk ratings x of agents as their coordinates x on economic space. Transactions between agents define evolution of their economic and financial variables. Aggregates of agent’s variables like Investment or Assets, Profits or Credits allocated near point x on economic space describe corresponding macro variables as functions of time and x. Aggregates of economic and financial transactions between agents at points x and y define corresponding macro transactions between points of economic space as function of x and y. Dynamics of macro transactions define evolution of macro variables of entire economics. To describe macro transactions and interactions between them we derive hydrodynamic-like equations on economic space. As example, for simple interaction between two macro transactions as Assets-Liabilities and Income-on-Assets we derive hydrodynamic-like equations in a closed form. That allows model relations between two macro transactions in a self-consistent manner, derive economic wave equations on perturbations of macro transactions and study simple solutions and consequences. Economic waves of macro transactions describe propagation of their disturbances on economic space from high to low risk agents or vise versa and define evolution of macro variables of entire economics. Existence and diversities of economic waves in simple models clarifies importance of wave processes for economic modelling.

The influence of localization of vibrations on film exfoliation from an elastic basis is investigated. A model is suggested that makes it possible to find an approximate analytical solution and to analyze the conditions of increasing and decreasing exfoliation.

The results of investigations of wave processes in dispersed media for application of wave effects in the development of a new class of wave machines, including the mixer-activator to produce modifying additives, are presented. The results of experimental investigations into the wave effect on various types of dry multicomponent dispersed systems to apply similar wave machines and aggregates in various branches of industry are presented.

The influence of the number of winding parallel branches, steel sheets thickness in the magnetic system and the size of air gap on the overvoltage in the induction motor operating from power-width modulation converters is investigated. The mathematical model and the results of simulation of the wave processes that take place in the multiturn mush winding of a squirrel-cage motor are presented.

An acoustic system that poorly scatters an incident field and contains an area of acoustic shadow where the field is much weakened is theoretically considered. An object placed in this area becomes “invisible.” Double-negative materials are used to construct the system. Wave processes are simulated on the basis of the ray-tracing and wave approaches.

Using the results of numerical modeling of nonstationary gas hydrodynamic working processes in the gas conduit variable section channel when removing and cooling hot gases of different purpose technical plants, an engineering technique has been developed to provide the gas conduit operation under limitations on the flow temperature in the outlet plant section. A multiparametric area of permissible gas conduit operation connecting the characteristics of technical plants, gas conduit and water feeding system is presented.

Spatiotemporal distributions of local components of the distortion tensor of quasi-plastic materials—saliferous rocks (sylvinite)—have been studied under active compressive straining conditions using double-exposure speckle photography techniques. The strain localization patterns are presented and the features of macroscopic strain inhomogeneity are considered for inelastic behavior of the material. Results obtained for the slow wave processes in deformed saliferous rocks are compared to analogous data available for ionic crystals.

The paper explains a number of phenomena that are observed in the surface vibrational treatment of oil and gas reservoirs based on the thriving theory of pendulum waves, e.g., a ring-shape response of a productive stratum and a time lag in the response, seismic luminescence and its spectrum, etc. The authors give data on velocity groups of pendulum waves in stressed block hierarchy of rock masses and substantiate the choice of the wave velocity group to be generated by the powerful surface vibro-sources designed at the Institute of Mining. The theoretical and phenomenological formulas given in the paper are of assistance in the development and improvement of the surface vibrational technologies for the enhancement of oil and gas recovery.

The impact of a liquid drop in the region between rivulets on the surface of a locally heated falling liquid film and the effect of this disturbance on the development of wave processes in the film have been studied. It is established that perturbations caused by the incident drop are spreading downstream and not going beyond the region bounded by the adjacent side rivulets. The maximum increase in the amplitude of waves in the film is observed in the same region between rivulets. At a distance of 70 mm downstream from the site of impact, the amplitude of waves in this region exhibits a 40–60% increase in comparison to the undisturbed film.

The propagation of stress waves in a column of rods of a rocker machine during a lift is considered at an arbitrary time instant. Using an integral transformation of time, the second-degree differential equation for displacement is solved where the force of the column dead weight is taken into account. It is shown that the stress variation is of a pulsating type; parameters and a form of the pulsation cycle are given. The fatigue strength of a thread in the union joint of rods and the lifetime of rods having an initial fracture are determined.

Electrodynamic characteristics of an open waveguide formed by two diffraction gratings with distributed radiation sources have been studied by the method of experimental simulation. Such system was shown to give a good promise for creating hardware components and amplifiers operating in the millimeter wavelength range.

The paper analyzes the approaches to the problem of information-wave processes in the social education activity of a contemporary university. The possibilities to apply the wave approach in the social education activity of a university by focusing on such social education technology as “interactions wave” are considered. The paper presents a step-by-step realization of this technology in the social education activity of a university.

Analysis of oscillation processes in a blocky medium is fulfilled using models, wherein elastic blocks interact via inter-layers with different mechanical properties. To describe wave processes, three different models are applied. First model considers elastic interaction between blocks; second one is the viscoelastic Pointing-Thomson model, that combines both Maxwell and Kelvin-Voigt models, and third one, named as the model with a rigid contact, excludes a possibility of blocks interpenetration. The dissipationless Ivanov scheme is applied in interlayers, while in blocks the Godunov gap decay scheme is used. It is shown that additional enclosing equations, which guarantee absence of energy dissipation in the Ivanov scheme, provide thermodynamic consistency of the model, meaning that the difference analogue of the energy conservation law for blocky structures is performed. Using the MPI technology, a parallel software is designed for simulation of the elastic waves propagation in a two-dimensional blocky...

Waveguide properties of a block geomedium are studied by using a regular structure composed of elastic layers with elastic inertialess interlayers. The analytical solution of the problem is derived.

In the nature there are a lot of substances containing cavities, moreover, there are also artificially created materials, which are used in various devices, for example, in nanoengineering. In this connection, theoretical and practical interest arises to investigate physical processes in such media. In particular, it is possible to use results of studying of wave processes in them for nondestructive testing of properties of such media.

A mathematical model intended for research of wave processes in high-voltage two-windings transformers was developed. The variable separation method was used to solve the integral-differential equations describing the process under research. The voltage distribution in the transformer windings under the influence of the impulse overvoltages was analyzed.

A one-dimensional problem of the interaction between a pulsed pressure wave and a plane shield separating two media with different acoustic impedances is solved. The exact solution is derived and used for establishing the applicability criteria for different approximate solutions of the problem under consideration.

Periodic structures of the resonance type are investigated with a focus on the utilization of structure dispersion to achieve a wide-band operation for the surface-wave suppression. Both approximate and exact formulations are presented to illustrate wave processes involved in the resonant structure and to develop useful criteria for design purpose. In addition, experiments are performed to verify the phenomena with stopband and leakage associated with the resonance-type periodic structures.

Theoretical and experimental research of electrical responses under pulsed mechanical excitation of different size concrete products was carried out. Comparison of calculated and experimental data shows very close agreement. The obtained results will help to develop new opportunities to improve the method of non-destructive testing of concrete by creating a bank of calculated electrical responses from products of different geometrical arrangement and elastic response and using them as standard samples for defectiveness evaluation of products according to previously established criteria.

The equations of motion of sandwich shells of revolution with a discrete core are analyzed within the framework of the geometrically nonlinear theory of shells and plates. An efficient numerical algorithm is constructed to investigate nonstationary wave processes in elastic structures that are discrete-inhomogeneous across the thickness. Numerical examples are given

The first part of this paper gives a short description of wave processes on a dike, on what we know, including recent new knowledge. These wave processes are wave impacts, wave run-up and wave overtopping. The second part focuses on description of three Simulators, each of them simulating one of the wave processes and which have been and are being used to test the strength of grass covers on a dike under severe storm conditions.