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The static three-level game-theoretic model of three-level control system of the ship’s water ballast is built. The methods of hierarchical control in view of requirements of keeping the system in the given state are used. A comparison of the results of study of the model in terms of $\Gamma_1$ and $\Gamma_2$ Germeyer’s games is conducted. Numerical calculations for some typical cases are given.

Excitation waves are a prototype of self-organized dynamic patterns in non-equilibrium systems. They develop their own intrinsic dynamics resulting in travelling waves of various forms and shapes. Prominent examples are rotating spirals and scroll waves. It is an interesting and challenging task to find ways to control their behavior by applying external signals, upon which these propagating waves react. We apply external electric fields to such waves in the excitable Belousov–Zhabotinsky (BZ) reaction. Remarkable effects include the change of wave speed, reversal of propagation direction, annihilation of counter-rotating spiral waves and reorientation of scroll wave filaments. These effects can be explained in numerical simulations, where the negatively charged inhibitor bromide plays an essential role. Electric field effects have also been investigated in biological excitable media such as the social amoebae Dictyostelium discoideum. Quite recently we have started to investigate electric field effect in the BZ reaction dissolved in an Aerosol OT water-in-oil microemulsion. A drift of complex patterns can be observed, and also the viscosity and electric conductivity change. We discuss the assumption that this system can act as a model for long range communication between neurons.

This work focuses on the application of a method of construction and conversion of three-dimensional computer models for optimization of geometric parameters of simulated devices. The method is used in design of complex technical devices for control system components of an exhaust gas recirculation vehicle – electric EGR valve with magnetic and electric motor. Three-dimensional geometric computer models were created in KOMPAS-3D environment and converted to Maxwell-2D. In Maxwell-2D environment transient electromagnetic processes for further optimization of parameters of therecirculation system devicewere calculated using a criterion of reducing power loss of the automobile engine.

Optimization of hull lines for the minimum resistance to movement is a problem of current interest in ship hydrodynamics. In practice, lines design is still to some extent an art. The usual approaches to decrease the ship resistance are based on the model experiment and/or CFD simulation, following the trial and error method. The paper presents a new method of in-detail hull form design based on the wave-based optimization approach. The method provides systematic variation of the hull geometrical form, which corresponds to alteration of longitudinal distribution of the hull volume, while its vertical volume distribution is fixed or highly controlled. It’s well known from the theoretical studies that the vertical distribution can't be optimized by condition of minimum wave resistance, thus it can be neglected for the optimization procedures. The method efficiency was investigated by application to the foreship of KCS, the well-known test object from the workshop Gothenburg-2000. The variations of the longitudinal distribution of the volume were set on the sectional area curve as finite volume increments and then transferred to the lines plan with the help of special frame transformation methods. The CFD towing simulations were carried out for the initial hull form and the six modified variants. According to the simulation results, examined modifications caused the resistance increments in the range 1.3–6.5 %. Optimization process was underpinned with the respective data analysis based on the new hypothesis, according to which, the resistance increments caused by separate longitudinal segments of hull form meet the principle of superposition. The achieved results, which are presented as the optimum distribution of volume present in the optimized designed hull form, which shows the interesting characteristics that its resistance has decrease by 8.9 % in respect to initial KCS hull form. Visualization of the wave patterns showed an attenuation of the transversal wave components, and the intensification of the diverging wave components.

We study the influence of fishery on a structured fish population under random changes of habitat conditions. The population parameters correspond to dominant pelagic fish species of Far-Eastern seas of the northwestern part of the Pacific Ocean (pollack, herring, sardine). Similar species inhabit various parts of the Word Ocean. The species body size distribution was chosen as a main population feature. This characteristic is easy to measure and adequately defines main specimen qualities such as age, maturity and other morphological and physiological peculiarities. Environmental fluctuations have a great influence on the individuals in early stages of development and have little influence on the vital activity of mature individuals. The fishery revenue was chosen as an optimality criterion. The main control characteristic is fishing effort. We have chosen quadratic dependence of fishing revenue on the fishing effort according to accepted economic ideas stating that the expenses grow with the production volume. The model study shows that the population structure ensures the increased population stability. The growth and drop out of the individuals’ due to natural mortality smoothens the oscillations of population density arising from the strong influence of the fluctuations of environment on young individuals. The smoothing part is played by diffusion component of the growth processes. The fishery in its turn smooths the fluctuations (including random fluctuations) of the environment and has a substantial impact upon the abundance of fry and the subsequent population dynamics. The optimal time-dependent fishing effort strategy was compared to stationary fishing effort strategy. It is shown that in the case of quickly changing habitat conditions and stochastic dynamics of population replenishment there exists a stationary fishing effort having approximately the same efficiency as an optimal time-dependent fishing effort. This means that a constant or weakly varying fishing effort can be very efficient strategy in terms of revenue.

We present results of a study aimed at identification of a controlled object’s channels based on postprocessing of measurements with development of a model of a multiple-input controlled object and subsequent active modelling experiment. The controlled object model is developed using approximation of its behavior by a neural network model using trends obtained during a passive experiment in the mode of normal operation. Recurrent neural network containing feedback elements allows to simulate behavior of dynamic objects; input and feedback time delays allow to simulate behavior of inertial objects with pure delay. The model was taught using examples of the object’s operation with a control system and is presented by a dynamic neural network and a model of a regulator with a known regulation function. The neural network model simulates the system’s behavior and is used to conduct active computing experiments. Neural network model allows to obtain the controlled object’s response to an exploratory stimulus, including a periodic one. The obtained complex frequency response is used to evaluate parameters of the object’s transfer system using the least squares method. We present an example of identification of a channel of the simulated control system. The simulated object has two input ports and one output port and varying transport delays in transfer channels. One of the input ports serves as a controlling stimulus, the second is a controlled perturbation. The controlled output value changes as a result of control stimulus produced by the regulator operating according to the proportional-integral regulation law based on deviation of the controlled value from the task. The obtained parameters of the object’s channels’ transfer functions are close to the parameters of the input simulated object. The obtained normalized error of the reaction for a single step-wise stimulus of the control system model developed based on identification of the simulated control system doesn’t exceed 0.08. The considered objects pertain to the class of technological processes with continuous production. Such objects are characteristic of chemical, metallurgic, mine-mill, pulp and paper, and other industries.

This article is devoted to the study of self-propulsion of bodies in a fluid by the action of internal mechanisms, without changing the external shape of the body. The paper presents an overview of theoretical papers that justify the possibility of this displacement in ideal and viscous liquids.

A special case of self-propulsion of a rigid body along the surface of a liquid is considered due to the motion of two internal masses along the circles. The paper presents a mathematical model of the motion of a solid body with moving internal masses in a three-dimensional formulation. This model takes into account the three-dimensional vibrations of the body during motion, which arise under the action of external forces-gravity force, Archimedes force and forces acting on the body, from the side of a viscous fluid.

The body is a homogeneous elliptical cylinder with a keel located along the larger diagonal. Inside the cylinder there are two material point masses moving along the circles. The centers of the circles lie on the smallest diagonal of the ellipse at an equal distance from the center of mass.

Equations of motion of the system (a body with two material points, placed in a fluid) are represented as Kirchhoff equations with the addition of external forces and moments acting on the body. The phenomenological model of viscous friction is quadratic in velocity used to describe the forces of resistance to motion in a fluid. The coefficients of resistance to movement were determined experimentally. The forces acting on the keel were determined by numerical modeling of the keel oscillations in a viscous liquid using the Navier – Stokes equations.

In this paper, an experimental verification of the proposed mathematical model was carried out. Several series of experiments on self-propulsion of a body in a liquid by means of rotation of internal masses with different speeds of rotation are presented. The dependence of the average propagation velocity, the amplitude of the transverse oscillations as a function of the rotational speed of internal masses is investigated. The obtained experimental data are compared with the results obtained within the framework of the proposed mathematical model.

Inverse geophysical problems are difficult to solve due to their mathematically incorrect formulation and large computational complexity. Geophysical exploration in frontier areas is even more complicated due to the lack of reliable geological information. In this case, inversion methods that allow interpretation of several types of geophysical data together are recognized to be of major importance. This paper is dedicated to one of such inversion methods, which is based on minimization of the determinant of the Gram matrix for a set of model vectors. Within the framework of this approach, we minimize a nonlinear functional, which consists of squared norms of data residual of different types, the sum of stabilizing functionals and a term that measures the structural similarity between different model vectors. We apply this approach to seismic and electromagnetic synthetic data set. Specifically, we study joint inversion of acoustic pressure response together with controlled-source electrical field imposing structural constraints on resulting electrical conductivity and P-wave velocity distributions.

We start off this note with the problem formulation and present the numerical method for inverse problem. We implemented the conjugate-gradient algorithm for non-linear optimization. The efficiency of our approach is demonstrated in numerical experiments, in which the true 3D electrical conductivity model was assumed to be known, but the velocity model was constructed during inversion of seismic data. The true velocity model was based on a simplified geology structure of a marine prospect. Synthetic seismic data was used as an input for our minimization algorithm. The resulting velocity model not only fit to the data but also has structural similarity with the given conductivity model. Our tests have shown that optimally chosen weight of the Gramian term may improve resolution of the final models considerably.

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.

The paper presents the physical and mathematical formulation of the problems of internal ballistics of an artillery shot for a charge consisting of a set of powder tubes and their stress-strain state. Combustion and movement of a bundle of powder tubes along the barrel channel is modeled by an equivalent tubular charge of all-round combustion. It is assumed that the equivalent tube moves along the axis of the bore. The speed of movement of an equivalent tubular charge and its current position are determined from Newton’s second law. When calculating the flow parameters, two-dimensional axisymmetric equations of gas dynamics were used, for the solution of which an axisymmetric orthogonalized difference grid is constructed, which adapts to the flow conditions. The control volume method is used to numerically solve the system of gas-dynamic equations. The gas parameters at the boundaries of the control volumes are determined using a self-similar solution to the Godunov’s problem of the decay of an arbitrary discontinuity. The stress-strain state is modeled for a separate burning powder tube located in the field of gas-dynamic parameters. The calculation of the gas-dynamic parameters of the shot is carried out without taking into account the deformed state of the powder elements. The behavior of powder elements during firing is considered under these conditions. The finite element method with the division of the calculation area into triangular elements is used to solve the problem of elasticity. In the process of powder tube burnout, the computational grid on each time layer of the dynamic problem is completely updated due to a change in the boundaries of the powder element due to combustion. The paper shows the time dependences of the parameters of the internal ballistics process and the stress-strain state of powder elements, as well as the distribution of the main parameters of the flow of combustion products at different points in time. It has been established that the tubular powder elements during the shot experience significant deformations, which must be taken into account when solving the basic problem of internal ballistics. The data obtained give an idea of the level of equivalent stresses acting at various points of the powder element. The results obtained indicate the relevance of the conjugate formulation of the problem of gas dynamics and the stress-strain state for charges consisting of tubular powders, since this allows a new approach to the design of tubular charges and opens up the possibility of determining the parameters on which the physics of the combustion process of gunpowder significantly depends, therefore, and the dynamics of the shot process.