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In the autosoliton view, the complete mathematical model of the seismic process taken as the deformation and fracture process of a loaded geomedium combines dynamic equations of solid mechanics and specific constitutive equations for geomedium rheology. These equations describe both the conventional stress-strain evolution due to the stress wave propagation with sound velocities, which are governed by special features of constitutive equations, and slow dynamics of the loaded strong medium. Numerical investigation is given to the generation of deformation autosolitons, front structure, and propagation of intra- and interfault deformation disturbances. Slow deformation disturbances in real geomedium elements are numerically modeled.

Doppler laser interferometry is used to measure the transient time between the slow quasi-stationary stage of damage accumulation in rock samples to the ultrafast catastrophic stage of failure as well as the duration of the autocatalytic stage of macroscopic fracture. Small rock samples are tested for compression and three-point bending, and the velocity of displacement of their lateral surfaces is measured up to macroscopic fracture. The surface velocity at the catastrophic stage proves to be three orders of magnitude higher than the average surface velocity at the quasi-stationary stage of damage accumulation. The transient time to catastrophic failure is estimated at 60–100 ms, and the duration of the ultrafast catastrophic failure stage is 15–20 ms for small marble samples. The transient stage is the process of self-organization of individual acts of fracture into the state of self-organized criticality. At this stage, the distribution of individual acts of fracture evolves into power-law distributions. A simple fracture model with power laws is proposed, which is in full agreement with the experimental data. The developed mathematical model is used to calculate fracture of small rock samples, reproducing uniaxial compression and three-point bending tests, as well as fracture in rock masses with mine openings. We also model the process of faulting and fracturing in the mountains of Central Altai, including the foreshock process, main event (the Chuya earthquake of September 27, 2003) and aftershock process. The calculated seismic process fully corresponds to the Gutenberg–Richter recurrence law, and the calculated aftershock process conforms to the Omori law.

The necessity to develop an innovative economy to maintain global competitiveness remains an urgent task for the economy of Russia and its regions. The purpose of the work is to study the role of digitalization in the process of knowledge diffusion. This paper presents the results of a study of patent documents registered in the Pskov region for the period from 2012 to 2019. Based on the data obtained, a knowledge network was built and a correlation analysis of the characteristics of the resulting network with the digitalization indicators of the Pskov region was carried out.

In the modern economy, innovations appear as the main competitive strength. At the same time, there are some problems with the transformation of the raw-materials export model of development into an innovative one. In this context, the task of the transition of the RF organizations to innovation-based development is number one at present, the solution of which will ensure the sustainable economic growth and competitive ability of the national economy. The paper aims at the study of possibilities to promote innovative activity in the context of the digital economy through the creation of partner networks. The research proves the prospects of the application of digital platforms enabling the cooperation of organizations. The system analysis allowed identifying the following problems of development of the innovation sphere of Russia: the low innovation potential of organizations, the deficiency of own sources of financing, the lack of skilled personnel, and the low demand for the results of innovative activity. The paper considers the current situation with the development of partner networks in Russia. The analysis showed that, in general, the networking cooperation of the enterprises is on a low level. At the same time, the innovatively active organizations rather energetically participate in the partner networks when implementing co-projects. Russian enterprises as the partners are mainly oriented at their countrymen. Besides, they cooperate with European organizations and USA partners. Recently, Russian enterprises develop networking cooperation with the organizations of India and China.

The paper presents the calculation of modern tectonic flow fields in the Yenisei Ridge located on the stable Siberian Craton. At the first stage, we solve the problem of calculating the average field of tectonic flows due to collisional processes at the southern and northeastern margins of the Eurasian Plate with Indian and Arabian and with North American plates, respectively. These calculations clarify the state of stress and the structure of tectonic flows on the territory of the Siberian Craton. The subtraction of the average displacements of the Siberian Craton as a whole in the northeast direction reveals the detailed structure of tectonic flows. Structural models are built along the Batolit-1982 and Shpat geological profiles crossing the Yenisei Ridge. At the second stage, we numerically study the state of stress and strain along these profiles determined by the global tectonics of Central and Southeast Asia, as well as their structural organization and interaction with the neighboring crustal elements. &nbsp

In this paper, we present the results of numerical modeling of propagation of slow intrafault deformation disturbances in constrained conditions. It is shown that deformation disturbances propagating along the fault zone originate from the boundaries where the gradient of strength and elastic properties is maximum. The propagation pattern of deformation disturbances along the fault is of a pulsating nature.

Here we provide a review of research on slow motions and strain waves in the Earth and propose a substantiated hypothesis that all stress-strain perturbations in the form of slow waves propagating in solids and geomedia, including plastic waves in metals and waves in faults of different scales, are of common physical nature. Loaded solids and geomedia are active hierarchically organized multiscale systems that display nonlinear dynamics and lose their stability when disturbed by any dynamic processes at block boundaries, e.g., displacements in fault zones. Such a medium cooperatively responds to parametric excitation by generating slow strain waves (autowaves) as a way of its self-organization. In support of the proposed concept, a consistent mathematical model is suggested for describing the evolution of stress-strain states and slow strain autowaves in an unstable elastoplastic medium, and examples of simulations are presented for strain autowaves in ductile materials under tension and quasi-brittle materials and geomedia with a fault zone under compression.

The paper considers the evolution of views on the physical nature of slow deformation disturbances in geomediums. The accumulated contradictions and clear misconceptions are noted, the autosoliton concept of slow deformation dynamics in the active (loaded) nonlinear geomedium is presented. It is shown that the autosoliton concept of slow deformation dynamics is consistent and allows one to explain the deformation processes observed in the geomedium from a single perspective. An example of a pulsating autosoliton along a fault is given.

The paper considers an autosoliton model of slow deformation disturbances propogating in the elements of the Earth’s crust. An autosoliton model of the fault’s formation is also presented. The faults themselves are represented as static autosolitons. It is shown that running (moving) autosoliton perturbations are actively involved both in the formation of fault zones and in the formation of fracture foci by the means of an increase in the degree of inelastic strain and damage in the medium. The autosoliton concept developed by the authors for slow deformation processes in geomedia allows explaining from one point of view both the processes of faults formation, as stationary (pulsating) autosolitons, and the processes of fracture foci formation.

This article presents the numerical modeling of modern tectonic flows in the Siberian Craton. It is based on global geotectonic processes in the Asian continent as well as its geological structure. The margins of Siberian Craton are unstable geological structures where local active geotectonic processes such as collision, shear stretching and metamorphisms are observed. We selected the region of the Yenisei Ridge because of its geological and geophysical specifics. The type of state of stress and strain in this area was estimated on the base of calculations of global tectonic flows in Central Asia. To get more details on the type of state of stress and strain in the Yenisei Ridge, calculations were carried out for the geological cross sections of Batolit 1982 and Shpat. The results show the presence of regions of localized inelastic deformation in the overstep region of the Yenisei shear zone. Also, in both sections, the bands of localized inelastic strain propagate to the surface of the mountain group exactly in the regions of the location of the large Siberian rivers of Yenisei and Velmo.

A pilot sample of a TiNi-TiB2 metal-ceramic composite has been developed. The sample implements a mechanism of multi-level strengthening using nanosize particles with sizes from tens of nm to 250 nm. The size of the strengthening particles in the micron range does not exceed 5 µm, which ensures their high tensile strength. The authors have developed a computer model of such a metal-ceramic composite that takes into account multi-level strengthening of the TiNi-TiB2 system: the TiNi matrix is indirectly reinforced by nano-sized particles and there is a direct reinforcement by micron-sized TiB2 particles. The authors have performed numerical studies of the mechanisms of deformation and destruction of the metal-ceramic composite with different percentages of content of reinforcing TiB2 particles. It has been demonstrated that a significant contrast between the mechanical properties of the intermetallide TiNi matrix and the reinforcing particles, regardless of the content of reinforcing particles, always leads to the formation of local areas of extension in the metal-ceramic composite. This leads to the destruction of reinforcing particles via the extension mechanism. In the case of high content (57–60%) of micron-sized reinforcing particles, this process of the destruction of strong particles via the mechanism of extension is taking place significantly later at a greater macroscopic deformation of the samples and at greater levels of stress.

We perform the numerical simulation of slow deformation autowave perturbations of inelastic nature in an elastic-plastic medium. We show that these perturbations exhibit the properties of solitons during interactions. They penetrate each other or repel from one another as elastic particles. The properties of these deformation solitons are similar to the solitons obtained from the solutions of the Korteweg-de Vries and sine-Gordon equations. We demonstrate that slow deformation fronts actively participate in the formation of the fracture foci, being an effective mechanism for the transfer and redistribution of energy in a loaded medium.

The modelling of the generation and propagation of inelastic strain fronts of Lueders in metals and slow deformation waves in geomedia is carried out. It is supposed that the deformation waves have an identical physical nature. They are treated as auto-wave processes caused by the local loss of stability in loaded nonlinear media, its parametric disturbance and cooperative response under loading, i.e. resulting from self-organization in deformed media. The deformation waves display soliton-like behavior at mutual impact.

Numerical calculations of the formation and propagation of slow deformation waves in geological media are performed. The velocities of such a tectonic movements usually lie within the range of 1–100 km/year and these movements are treated as slow deformation waves. The deformation autowaves are shown to make a considerable contribution into the formation of fracture foci. When two such autowaves collide, they behave similar to solitons, reflecting from each other as elastic particles. The deformation autowaves form at the boundaries of structural elements, e.g., blocks of a geomedium during their fast movements. An autowave in a geomedium is developed due to a local loss of stability, and the velocity of its motion is found to be proportional to the velocity of crush movement (motion velocity of the grip during the formation of a Lüders front).

In this paper, a mathematical model of propagating slow waves of non-elastic deformation, whose velocities in magnitude are between the velocities of tectonic creep and sound velocities, is proposed. It is shown that the model describes both Lueders fronts and slow waves of deformation in geo-environments and in the faults. Our model is a related dynamic model of elasto-plastic deformation of loaded medium, where fast processes of dynamic medium response to loading develop together with the formation of slow deformational wave. These slow waves of deformation in the model are treated as auto-wave processes and they are a collective response to loading, i.e. they are the result of self-organization in the medium being deformed.

General theoretical ideas underlying the mathematical model of description of stress-strain state (SSS) evolution in rock mass with excavations are formulated. The developed ideas imply that rock mass is a typical multiscale nonlinear dynamic system. Numerical solutions based on these ideas demonstrate the characteristic features of dynamic systems evolution. Analysis of the average trend of the nature of SSS parameters’ fluctuations gives an indication of the proximity of the rock mass elements to catastrophic failure.

The results of 2D and 3D modelling of damage accumulation in rock mass elements are represented in the paper. The estimations of the initial (general) and set steps of roof caving are obtained for the lava conditions of Alardinskaya mine, OAS “YuzhKuzbassUgol”. The results of modelling give a good agreement with empirical estimations of roof caving steps for the flat-dipping coal seams.

An evolutionary approach proposed in [1, 2] combining the achievements of traditional macroscopic theory of solid mechanics and basic ideas of nonlinear dynamics is applied in a numerical simulation of present-day tectonic plates motion and seismic process in Central Asia. Relative values of strength parameters of rigid blocks with respect to the soft zones were characterized by the δ parameter that was varied in the numerical experiments within δ = 1.1–1.8 for different groups of the zonal-block divisibility. In general, the numerical simulations of tectonic block motion and accompanying seismic process in the model geomedium indicate that the numerical solutions of the solid mechanics equations characterize its deformation as a typical behavior of a nonlinear dynamic system under conditions of self-organized criticality.