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We suggest a possible mechanism for the transition from standing waves with a wavelength λ_SW to traveling waves with a half wavelength: λ_TW ≅λ_SW / 2. This phenomenon was observed in the Belousov–Zhabotinsky reaction dispersed in a water-in-oil aerosol OT/Span-20 microemulsion. The problem is solved in a spatially one-dimensional case using amplitude equations approach. We demonstrate that a transition is possible under certain conditions. We obtain conditions for the mode coupling strength parameters, under which the scenario of transition from a standing wave to a half-period traveling wave, observed experimentally, is realized. The result of theoretical analysis is confirmed by numerical simulations.

Comets and asteroids are recognized by the scientists and the governments of all countries in the world to be one of the most significant threats to the development and even the existence of our civilization. Preventing this threat includes studying the motion of large meteors through the atmosphere that is accompanied by various physical and chemical phenomena. Of particular interest to such studies are the meteors whose trajectories have been recorded and whose fragments have been found on Earth. Here, we study one of such cases. We develop a model for the motion and destruction of natural bodies in the Earth’s atmosphere, focusing on the Benešov bolid (EN070591), a bright meteor registered in 1991 in the Czech Republic by the European Observation System. Unique data, that includes the radiation spectra, is available for this bolid. We simulate the aeroballistics of the Benešov meteoroid and of its fragments, taking into account destruction due to thermal and mechanical processes. We compute the velocity of the meteoroid and its mass ablation using the equations of the classical theory of meteor motion, taking into account the variability of the mass ablation along the trajectory. The fragmentation of the meteoroid is considered using the model of sequential splitting and the statistical stress theory, that takes into account the dependency of the mechanical strength on the length scale. We compute air flows around a system of bodies (shards of the meteoroid) in the regime where mutual interplay between them is essential. To that end, we develop a method of simulating air flows based on a set of grids that allows us to consider fragments of various shapes, sizes, and masses, as well as arbitrary positions of the fragments relative to each other. Due to inaccuracies in the early simulations of the motion of this bolid, its fragments could not be located for about 23 years. Later and more accurate simulations have allowed researchers to locate four of its fragments rather far from the location expected earlier. Our simulations of the motion and destruction of the Benešov bolid show that its interaction with the atmosphere is affected by multiple factors, such as the mass and the mechanical strength of the bolid, the parameters of its motion, the mechanisms of destruction, and the interplay between its fragments.

In the work is numerically investigated the influence of elastic and strength characteristics of hard materials with coatings of refractory compounds, received electric-spark doping, at influence of temperature and power factors using the finite element method.

Calculations of radiation transport in the shockwave layer of a descent space vehicle cause essential difficulties due to complex multi-resonance dependence of the absorption macroscopic cross sections from the photon energy. The convergence of two approximate spectrum averaging methods to the results of exact pointwise spectrum calculations is investigated. The first one is the well known multigroup method, the second one is the Lebesgue averaging method belonging to methods of the reduction of calculation points by means of aggregation of spectral points which are characterized by equal absorption strength. It is shown that convergence of the Lebesgue averaging method is significantly faster than the multigroup approach as the number of groups is increased. The only 100–150 Lebesgue groups are required to achieve the accuracy of pointwise calculations even in the shock layer at upper atmosphere with sharp absorption lines. At the same time the number of calculations is reduced by more than four order. Series of calculations of the radiation distribution function in 2D shock layer around a sphere and a blunt cone were performed using the local flat layer approximation and the Lebesgue averaging method. It is shown that the shock wave radiation becomes more significant both in value of the energy flux incident on the body surface and in the rate of energy exchange with the gas-dynamic flow in the case of increasing of the vehicle’s size.

Use of algorithms based on neural networks can be inefficient for small amounts of experimental data. Authors consider a solution of this problem in the context of modelling of properties of ceramic composite materials reinforced with carbon nanotubes using perceptron complex. This approach allowed us to obtain a mathematical description of the object of study with a minimal amount of input data (the amount of necessary experimental samples decreased 2–3.3 times). Authors considered different versions of perceptron complex structures. They found that the most appropriate structure has perceptron complex with breakthrough of two input variables. The relative error was only 6%. The selected perceptron complex was shown to be effective for predicting the properties of ceramic composites. The relative errors for output components were 0.3%, 4.2%, 0.4%, 2.9%, and 11.8%.

The results of verification carried out for investigations of hydrodynamic effect on reentry conicalsegmental space vehicle are presented in the paper. The program complex Flow Vision is used for this analysis. The purpose of the study is verification of using Flow Vision program complex for problem solving mentioned above on the base of comparison between calculated and experimental data, obtained on the Apollo landing models and new development reentry spacecraft of manned transporting spaceship designed by RSC Energia. The comparison was carried out through the data of pressure values on spacecraft model surfaces during its water landing and inertia center motion parameters.

The results of study show good agreement between experimental and calculated data of force effects on vehicle construction during water landing and its motion parameters in the water medium. Computer simulation sufficiently well reproduces influence of initial velocities & water entry angles variations on water landing process.

Using of computer simulation provides simultaneous acquisition of all data information needed for investigation of water landing peculiarities during construction design, notably, hydrodynamic effects for structural strength calculations, parameters and dynamics of center mass motion and vehicle revolution around center mass for estimation water landing conditions, as well as vehicle stability after landing.

Obtained results confirm suitability of using Flow Vision program complex for water landing vehicle investigations and investigations of influence of different landing regimes through wide initial condition change range, that permits considerably decrease extent of expensive experimental tests and realize landing conditions which are sufficiently complicated for realizing in model physical experiments.

In this paper we consider statistical estimates of threshold and strength of percolation clusters on square lattices. The percolation threshold p_c and the strength of percolation clusters P_∞ for a square lattice with (1,π)-neighborhood depends not only on the lattice dimension, but also on the Minkowski exponent d. To estimate the strength of percolation clusters P_∞ proposed a new method of averaging the relative frequencies of the target subset of lattice sites. The implementation of this method is based on the SPSL package, released under GNU GPL-3 using the free programming language R.

The paper presents the results of numerical simulation and experimental data on the high-speed penetration of the impactor into the obstacle. In the calculations, a discrete-element model has been used, based on the representation of the impactor and the target by a set of close packed interconnected particles. This class of models finds an increasingly wide application in the problems of high-speed interaction of bodies. In the previous works of the authors, the questions of application of the discrete-element model to the problem of the penetration of spherical impactors into massive targets were considered. On the basis of a comparative analysis of the data of computational and physical experiments, it was found out that for a wide class of high-speed penetration problems, a high accuracy of discrete-element modeling can be achieved using the two-parameter Lennard–Jones potential. The binding energy was identified as a function of the dynamic hardness of materials. It was shown that the use of this approach makes it possible to describe accurately the penetration process in the range of impactor velocities 500–2500 m/c.

In this paper, we compare the results of discrete-element modeling with experimental data on penetration of high-strength targets of different thickness by steel impactors. The use of computational parallelization technologies on graphic processors in combination with 3D visualization and animation of the results makes it possible to obtain detailed spatio-temporal patterns of the penetration process and compare them with experimental data.

A comparative analysis of the experimental and calculated data has shown a sufficiently high accuracy of discrete-element modeling for a wide range of target thicknesses: for thin targets pierced with preservation of the integrity of the deformed impactor, for targets of medium thickness, pierced with practically complete fragmentation of the impactor at the exit from the target, and for thick impenetrable targets.

Ultrasound examination of material properties is a precision method for determining their elastic and strength properties in connection with the small wavelength formed in the material after impact of a laser beam. In this paper, the wave processes arising during these measurements are considered in detail. It is shown that full-wave numerical modeling allows us to study in detail the types of waves, topological characteristics of their profile, speed of arrival of waves at various points, identification the types of waves whose measurements are most optimal for examining a sample made of a specific material of a particular shape, and to develop measurement procedures.

To carry out full-wave modeling, a grid-characteristic method on structured grids was used in this work and a hyperbolic system of equations that describes the propagation of elastic waves in the material of the thin plate under consideration on a specific example of a ratio of thickness to width of 1:10 was solved.

To simulate an elastic front that arose in the plate due to a laser beam, a model of the corresponding initial conditions was proposed. A comparison of the wave effects that arise during its use in the case of a point source and with the data of physical experiments on the propagation of laser ultrasound in metal plates was made.

A study was made on the basis of which the characteristic topological features of the wave processes under consideration were identified and revealed. The main types of elastic waves arising due to a laser beam are investigated, the possibility of their use for studying the properties of materials is analyzed. A method based on the analysis of multiple waves is proposed. The proposed method for studying the properties of a plate with the help of multiple waves on synthetic data was tested, and it showed good results.

It should be noted that most of the studies of multiple waves are aimed at developing methods for their suppression. Multiple waves are not used to process the results of ultrasound studies due to the complexity of their detection in the recorded data of a physical experiment.

Due to the use of full wave modeling and analysis of spatial dynamic wave processes, multiple waves are considered in detail in this work and it is proposed to divide materials into three classes, which allows using multiple waves to obtain information about the material of the plate.

The main results of the work are the developed problem statements for the numerical simulation of the study of plates of a finite thickness by laser ultrasound; the revealed features of the wave phenomena arising in plates of a finite thickness; the developed method for studying the properties of the plate on the basis of multiple waves; the developed classification of materials.

The results of the studies presented in this paper may be of interest not only for developments in the field of ultrasonic non-destructive testing, but also in the field of seismic exploration of the earth's interior, since the proposed approach can be extended to more complex cases of heterogeneous media and applied in geophysics.

The article proposes a model for assessing the potential strength of a composite material based on modern fibers with brittle fracture.

Materials consisting of parallel cylindrical fibers that are quasi-statically stretched in one direction are simulated. It is assumed that the sample is not less than 100 pieces, which corresponds to almost significant cases. It is known that the fibers have a distribution of ultimate deformation in the sample and are not destroyed at the same moment. Usually the distribution of their properties is described by the Weibull–Gnedenko statistical distribution. To simulate the strength of the composite, a model of fiber breaks accumulation is used. It is assumed that the fibers united by the polymer matrix are crushed to twice the inefficient length — the distance at which the stresses increase from the end of the broken fiber to the middle one. However, this model greatly overestimates the strength of composites with brittle fibers. For example, carbon and glass fibers are destroyed in this way.

In some cases, earlier attempts were made to take into account the stress concentration near the broken fiber (Hedgepest model, Ermolenko model, shear analysis), but such models either required a lot of initial data or did not coincide with the experiment. In addition, such models idealize the packing of fibers in the composite to the regular hexagonal packing.

The model combines the shear analysis approach to stress distribution near the destroyed fiber and the statistical approach of fiber strength based on the Weibull–Gnedenko distribution, while introducing a number of assumptions that simplify the calculation without loss of accuracy.

It is assumed that the stress concentration on the adjacent fiber increases the probability of its destruction in accordance with the Weibull distribution, and the number of such fibers with an increased probability of destruction is directly related to the number already destroyed before. All initial data can be obtained from simple experiments. It is shown that accounting for redistribution only for the nearest fibers gives an accurate forecast.

This allowed a complete calculation of the strength of the composite. The experimental data obtained by us on carbon fibers, glass fibers and model composites based on them (CFRP, GFRP), confirm some of the conclusions of the model.