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Currently, earthquake-resistant design of buildings based on the power calculation and presentation of effect of the earthquake static equivalent forces, which are calculated using elastic response spectra (linear-spectral method) that connects the law of motion of the soil with the absolute acceleration of the model in a nonlinear oscillator.

This approach does not directly take into account either the influence of the duration of strong motion or the plastic behavior of the structure. Frequency content and duration of ground vibrations directly affect the energy received by the building and causing damage to its elements. Unlike power or kinematic calculation of the seismic effect on the structure can be interpreted without considering separately the forces and displacements and to provide, as the product of both variables, i.e., the work or input energy (maximum energy that can be purchased building to the earthquake).

With the energy approach of seismic design, it is necessary to evaluate the input seismic energy in the structure and its distribution among various structural components.

The article provides substantiation of the energy approach in the design of earthquake-resistant buildings and structures instead of the currently used method based on the power calculation and presentation of effect of the earthquake static equivalent forces, which are calculated using spectra of the reaction.

Noted that interest in the use of energy concepts in earthquake-resistant design began with the works of Housner, which provided the seismic force in the form of the input seismic energy, using the range of speeds, and suggested that the damage in elastic-plastic system and elastic system causes one and the same input seismic energy.

The indices of the determination of the input energy of the earthquake, proposed by various authors, are given in this paper. It is shown that modern approaches to ensuring seismic stability of structures, based on the representation of the earthquake effect as a static equivalent force, do not adequately describe the behavior of the system during an earthquake.

In this paper, based on quantitative estimates of seismic risk analyzes developed in the NRU MSUCE Standard Organization (STO) “Seismic resistance structures. The main design provisions”. In the developed document a step forward with respect to the optimal design of earthquake-resistant structures.

The proposed concept of using the achievements of modern methods of calculation of buildings and structures on seismic effects, which are harmonized with the Eurocodes and are not contrary to the system of national regulations.

The paper studies the determination for one of the dynamic quality parameter (PDK) of railway vehicles — car body lateral acceleration — by using of computer simulation system for railway vehicles dynamic Simpack Rail. This provide the complex simulation environment with variable velocity depending on the train schedule. The rail vehicle model of typical 1520 mm gauge fright locomotive section used for simulation has been verified by means of the chair “Electric multiple unit cars and locomotives” in the Russian University of Transport (RUT (MIIT)). Due to this homologation the questions of model creating and verification in preprocessor are excluded in this paper. The paper gives the detail description of cartographic track modeling in situation plane, heights plane and superelevation plane based on the real operating data. The statistic parameters (moments) for the rail related track excitation and used cartographic track data of the specified track section in this simulation are given as a numeric and graphical results of reading the prepared data files. The measurement of the car body residual lateral acceleration occur under consideration of the earth gravity acceleration part like the accelerometer measurement in the real world. Finally the desired quality parameter determined by simulation is compared with the same one given by a test drive. The calculation method in both cases is based on the middle value of the absolute maximums picked up within the nonstationary realizations of this parameter. Compared results confirm that this quality factor all the first depends on the velocity and track geometry properties. The simulation of the track in this application uses the strong conformity original track data of the test ride track section. The accepted simplification in the rail vehicle model of fright electric locomotive section (body properties related to the center of gravity, small displacements between the bodies) by keeping the geometric and force law characteristics of the force elements and constraints constant allow in Simpack Rail the simulation with necessary validity of system behavior (reactions).

The paper presents the results of numerical simulation of the effect of a long spark discharge on the mixing dynamics of an injected gas jet with supersonic air flow. The calculations were performed using the CFD software package FlowVision. The fuel was supplied using an injector located on the channel wall, and the discharge was organized near the wall downstream of the injector. Simulation of electrical spark discharge was performed using a volumetric heat source. In order to describe the principal specifications of a plasma actuator to accelerate mixing in a supersonic flow (Mach number M = 2), the research involved varying the energy impact to the discharge in the range of 100–500 mJ per pulse, determining the influence of the shape and location of the discharge. A study of the fuel injection modes in a supersonic air flow has been carried out and an optimal gas jet outflow regime has been found to study the effect of a spark discharge. A method has been developed for analyzing the disturbance pattern of the fuel-oxidant interface caused by the operation of a pulsed spark discharge. A program was prepared in the LabView software environment for obtaining quantitative characteristics for further comparison with the results obtained in the experiment.

The simulation results allow us to conclude that the long spark discharge located along the flow downstream of the injector provides the maximum increase in the interface between the jet of fuel and the main flow. A typical repetition frequency of discharge pulses in a pulse-periodic mode should be more than 6 kHz with a discharge length of ~10 mm to ensure a continuous effect on the mixing at a flow velocity of 500 m/s.

The paper is devoted to convex-concave saddle point problems where the objective is a sum of a large number of functions. Such problems attract considerable attention of the mathematical community due to the variety of applications in machine learning, including adversarial learning, adversarial attacks and robust reinforcement learning, to name a few. The individual functions in the sum usually represent losses related to examples from a data set. Additionally, the formulation admits a possibly nonsmooth composite term. Such terms often reflect regularization in machine learning problems. We assume that the dimension of one of the variable groups is relatively small (about a hundred or less), and the other one is large. This case arises, for example, when one considers the dual formulation for a minimization problem with a moderate number of constraints. The proposed approach is based on using Vaidya’s cutting plane method to minimize with respect to the outer block of variables. This optimization algorithm is especially effective when the dimension of the problem is not very large. An inexact oracle for Vaidya’s method is calculated via an approximate solution of the inner maximization problem, which is solved by the accelerated variance reduced algorithm Katyusha. Thus, we leverage the structure of the problem to achieve fast convergence. Separate complexity bounds for gradients of different components with respect to different variables are obtained in the study. The proposed approach is imposing very mild assumptions about the objective. In particular, neither strong convexity nor smoothness is required with respect to the low-dimensional variable group. The number of steps of the proposed algorithm as well as the arithmetic complexity of each step explicitly depend on the dimensionality of the outer variable, hence the assumption that it is relatively small.

This paper presents the results of experimental validation of some structural issues concerning the practical use of methods to overcome catastrophic forgetting of neural networks. A comparison of current effective methods like EWC (Elastic Weight Consolidation) and WVA (Weight Velocity Attenuation) is made and their advantages and disadvantages are considered. It is shown that EWC is better for tasks where full retention of learned skills is required on all the tasks in the training queue, while WVA is more suitable for sequential tasks with very limited computational resources, or when reuse of representations and acceleration of learning from task to task is required rather than exact retention of the skills. The attenuation of the WVA method must be applied to the optimization step, i. e. to the increments of neural network weights, rather than to the loss function gradient itself, and this is true for any gradient optimization method except the simplest stochastic gradient descent (SGD). The choice of the optimal weights attenuation function between the hyperbolic function and the exponent is considered. It is shown that hyperbolic attenuation is preferable because, despite comparable quality at optimal values of the hyperparameter of the WVA method, it is more robust to hyperparameter deviations from the optimal value (this hyperparameter in the WVA method provides a balance between preservation of old skills and learning a new skill). Empirical observations are presented that support the hypothesis that the optimal value of this hyperparameter does not depend on the number of tasks in the sequential learning queue. And, consequently, this hyperparameter can be picked up on a small number of tasks and used on longer sequences.

In this paper, the structure of a shock wave in a binary gas mixture is studied on the basis of direct solution of the Boltzmann kinetic equation. The conservative projection method is used to evaluate the collision integral in the kinetic equation. The applied evaluation formulas and numerical methods are described in detail. The model of hard spheres is used as an interaction potential of molecules. Numerical simulation is performed using the developed simulation environment software, which makes it possible to study both steady and non-steady flows of gas mixtures in various flow regimes and for an arbitrary geometry of the problem. Modeling is performed on a cluster architecture. Due to the use of code parallelization technologies, a significant acceleration of computations is achieved. With a fixed accuracy controlled by the simulation parameters, the distributions of macroscopic characteristics of the mixture components through the shock wave front were obtained. Computations were conducted for various ratios of molecular masses and Mach numbers. The total accuracy of at least 1% for the local values of molecular density and temperature and 3% for the shock front width was achieved. The obtained results were compared with existing computation data. The results presented in this paper are of theoretical significance, and can serve as a test computation, since they are obtained using the exact Boltzmann equation.

In this paper, we present new parallel algorithms for finite element analysis implemented in the FEStudio software framework. We describe the programming model of finite element method, which supports parallelism on different stages of numerical simulations. Using this model, we develop parallel algorithms of numerical integration for dynamic problems and local stiffness matrices. For constructing and solving the systems of equations, we use the CUDA programming platform.

In the article is carried out the analysis of historical process with the use of methods of synergetics (science about the nonlinear developing systems in nature and the society), developed in the works of D. S. Chernavskii in connection with to economic and social systems. It is shown that social self-organizing depending on conditions leads to the formation of both the societies with the strong internal competition (Y-structures) and cooperative type societies (X-structures). Y-structures are characteristic for the countries of the West, X-structure are characteristic for the countries of the East. It is shown that in XIX and in XX centuries occurred accelerated shaping and strengthening of Y-structures. However, at present world system entered into the period of serious structural changes in the economic, political, ideological spheres: the domination of Y-structures concludes. Are examined the possible ways of further development of the world system, connected with change in the regimes of self-organizing and limitation of internal competition. This passage will be prolonged and complex. Under these conditions it will objectively grow the value of the civilizational experience of Russia, on basis of which was formed combined type social system. It is shown that ultimately inevitable the passage from the present do-mination of Y-structures to the absolutely new global system, whose stability will be based on the new ideology, the new spirituality (i.e., new “conditional information” according D. S. Chernavskii), which makes a turn from the principles of competition to the principles of collaboration.

We present a physico-mathematical statement of coupled geometrical and gas dynamics problem of intrachamber processes simulation and calculation of main internal ballistics characteristics of solid rocket motors in axisymmetric approximation. Method and numerical algorithm of solving the problem are described in this paper. We track the propellant burning surface using the level set method. This method allows us to implicitly represent the surface on a fixed Cartesian grid as zero-level of some function. Two-dimensional gas-dynamics equations describe a flow of combustion products in a solid rocket motor. Due to inconsistency of domain boundaries and nodes of computational grid, presence of ghost points lying outside the computational domain is taken into account. For setting the values of flow parameters in ghost points, we use the inverse Lax – Wendroff procedure. We discretize spatial derivatives of level set and gas-dynamics equations with standard WENO schemes of fifth and third-order respectively and time derivatives using total variation diminishing Runge –Kutta methods. We parallelize the presented numerical algorithm using CUDA technology and further optimize it with regard to peculiarities of graphics processors architecture.

Created software package is used for calculating internal ballistics characteristics of nozzleless solid rocket motor during main firing phase. On the base of obtained numerical results, we discuss efficiency of parallelization using CUDA technology and applying considered optimizations. It has been shown that implemented parallelization technique leads to a significant acceleration in comparison with central processes. Distributions of key parameters of combustion products flow in different periods of time have been presented in this paper. We make a comparison of obtained results between quasione-dimensional approach and developed numerical technique.

First-order optimization methods are workhorses in a wide range of modern applications in economics, physics, biology, machine learning, control, and other fields. Among other first-order methods accelerated and momentum ones obtain special attention because of their practical efficiency. The heavy-ball method (HB) is one of the first momentum methods. The method was proposed in 1964 and the first analysis was conducted for quadratic strongly convex functions. Since then a number of variations of HB have been proposed and analyzed. In particular, HB is known for its simplicity in implementation and its performance on nonconvex problems. However, as other momentum methods, it has nonmonotone behavior, and for optimal parameters, the method suffers from the so-called peak effect. To address this issue, in this paper, we consider an averaged version of the heavy-ball method (AHB). We show that for quadratic problems AHB has a smaller maximal deviation from the solution than HB. Moreover, for general convex and strongly convex functions, we prove non-accelerated rates of global convergence of AHB, its weighted version WAHB, and for AHB with restarts R-AHB. To the best of our knowledge, such guarantees for HB with averaging were not explicitly proven for strongly convex problems in the existing works. Finally, we conduct several numerical experiments on minimizing quadratic and nonquadratic functions to demonstrate the advantages of using averaging for HB. Moreover, we also tested one more modification of AHB called the tail-averaged heavy-ball method (TAHB). In the experiments, we observed that HB with a properly adjusted averaging scheme converges faster than HB without averaging and has smaller oscillations.