Methods of computer formation of the equations of motion of multibody systems with a tree structure and algorithms for their reduction to the normal form of ordinary differential equations are considered. The equations of motion are written using Hamilton's formalism for an extended set of state variables of a mechanical system. The equations are presented in a compact visual form. Recursive formulas for determining all coefficients of equations are written out. Algorithms for reducing these equations to Hamilton equations in generalized coordinates and generalized momenta are presented. An algorithm for solving the obtained equations of motion for multibody systems using the LTDL-elimination is presented. Formulas are written that allow one to calculate the amount of arithmetic operations required to bring the equations of motion to normal form using the considered algorithms. On the basis of these formulas, a comparative analysis of the efficiency of algorithms for rigid bodies systems of various structures and with various types of connections between bodies is carried out. The results of the analysis are presented in the form of diagrams. The diagrams highlight areas in which the advantage of one or another method is manifested, depending on the type of mechanical system.

Keywords: multibody systems, equations of motion, dynamics, canonical momenta, mathematical modeling, computational efficiency

The problem of flexible vibrations of a rectangular orthotorque plate clamped along the contour is considered. The general solution of the problem, which satisfies the vibartion equation identically, is constructed on the basis of the superposition method in the form of two Fourier series. Clamped boundary conditions lead to a homogeneous infinite system of linear algebraic equations with respect to unknown coefficients in the general solution. The uniqueness of a bounded non-trivial solution of an infinite system for the natural frequency is proved, the asymptotics of the unknowns are found, and an effective solution algorithm is constructed. Examples of the numerical implementation of the developed algorithm for calculating the natural frequencies and natural modes of the plate vibrations are given.

Keywords: plate, vibrations, natural frequencies, planar forces, superposition method, infinite system of linear equations, asymptotics

The construction and substantiation of a finite element model of the capillary tube running-in process, which was obtained by drawing on a fixed mandrel, are considered. The rolling rolls are cylindrical and absolutely rigid. The condition for performing the work is a comparison of the resulting gap between the pipe and the mandrel and the facet formed during deformation. The solid-state model of the process is described by an adaptive grid. Under these conditions, an informative model was obtained, which was used in parametric analysis.

Keywords: drawing with a mandrel, capillary tube, extraction, rolling, model construction, compression selection, pipe size tolerance

The paper deals with the construction of an algorithm for nonparametric estimation of the transition probability distribution density for the Markov model of the dynamics of the number of university employees. The problem of reconstruction of transition probability distribution density on a retrospective sample of small volume is solved. The result of the solution is the transition probability matrix, the elements of which are random variables with distribution laws obtained from retrospective data. A distinctive feature of the algorithm is the simultaneous consideration of regional and functional constraints on the values of transition probabilities. The convergence of the algorithm has been experimentally confirmed.

Keywords: probability density, nonparametric estimation, Markov model, simulation modeling, university staff movement, publication activity

The article presents studies of a computer simulation statistical model between the characteristics of flows in terms of linear density and the proportion of components in a mixed flow. The results of evaluating the effect of the filling fraction of the component on the average and standard deviation of the fraction of the 1st component in the mixture are presented, the type of autocorrelation functions of the linear density of the mixed stream and the fraction of the 1st component in the mixed stream are determined, estimates of the spectral density of dispersion for the linear density of the mixed stream and the fraction of the 1st component in the mixed stream are shown.

Keywords: fiber mixing, linear density, component fraction, autocorrelation function, spectral density of dispersion, standard deviation

This article considers the problem of determining the temperature field near a heat-loaded source in the form of a dipole field. Solving this problem will make it possible to identify general patterns of distribution of the temperature field as one moves away from the source. This will make it possible to ensure the normal functioning of powerful electronic components by ensuring the required intensity of heat flux removal, mainly in close proximity to a heat-loaded source, that is, in the zone of maximum heat flux density.

Keywords: numerical methods, energy saving, heat engineering, thermal conditions of equipment, heat-loaded source, near zone, numerical modeling, temperature field, thermal processes, finite element method

This study is devoted to the development of a new mathematical model, a wedge-shaped sliding support with a non-standard elastically deformed support profile of the slider surface, taking into account nonlinear factors, under conditions of a two-layer lubricant flow, providing effective lubrication and reducing wear of the working surface. To develop this model, we will use mathematical modeling and data analysis methods to take into account all the necessary factors and parameters. To achieve this goal, well-known nonlinear equations are used: the motion of a viscous incompressible fluid for a "thin layer", the continuity equation and the Lame equation with appropriate boundary conditions, taking into account the elasticity and adaptability of the support surface of the slider, as well as equality of velocities at the interface of stratified layers, equality of pressure at the ends of the interval and equality of velocities on the surface of the guide. As a result, the main performance characteristics of the ras were identified

Keywords: nonlinear factors, elastically deformed, non-standard surface, flow of two-layer lubricant, dependence of viscosity characteristics of lubricating layers, ratio of density characteristics

The article considers the problem of cryptanalysis of an information security system based on a difficult-to-solve problem of Diophantine equations. A mathematical model of such a protection system is described in the article and a solution to the cryptanalysis problem using an artificial immune system adapted for solving Diophantine equations is proposed. The paper discusses the basic principles of building artificial immune systems and presents the results of experiments on evaluating the effectiveness of the proposed system of Diophantine equations of a degree not exceeding six. The results obtained demonstrate the possibility of using artificial immune systems to solve the problem of cryptanalysis of information security systems based on Diophantine equations.

Keywords: cryptanalysis, information security system, diophantine equations, artificial immune system, adaptive algorithm, efficiency assessment

The effect of impurities on the conductivity of the allotropic modification of phosphorene (ε-P) was studied. The quantum chemical research package Quantum Espresso was used for calculations. The study was conducted on the basis of simulation modeling. Three-dimensional structures are modeled using Quantum Espresso. The work adapted the model for two-dimensional ε-phosphorene by choosing a unit cell vector so large that interaction between the layers was possible. It has been shown that S has the smallest changes. Significant changes in conductivity can be achieved by placing F in various configurations relative to the crystal lattice, which can be actively used to create differetnt types of detectors.

Keywords: phosphorene, allotrope, semiconductor, impurity, adsorption, conductivity, density functional theory, modeling, Quantum Espresso, crystal structure

The article describes a technique for constructing a non-fuzzy model for selecting contour points on an image. The technique includes the following steps: the formation of linguistic variables “pixel brightness difference” and “a sign that a pixel belongs to a contour”, the formation of a knowledge base of a neuro-fuzzy model using a binary image, the formation of a training set using both grayscale and contour images, training a neuro-fuzzy model using genetic algorithm. A feature of the presented genetic algorithm is - checking the conditions for the correctness of the values of the parameters of the membership functions obtained during the generation of chromosomes. Described the structure of a neuro-fuzzy model for making a decision about whether a pixel belongs to a contour. Presented the result of applying a neuro-fuzzy model for constructing image contours.

Keywords: neuro-fuzzy model, contour image, contour extraction, contour pixel, linguistic variable, fuzzy set, membership function, genetic algorithm, Tsukamoto inference, neuro-fuzzy model learning

This article presents a research study dedicated to the application of the YOLOv8 neural network model for road sign detection. During the study, a model based on YOLOv8 was developed and trained, which successfully detects road signs in real-time. The article also presents the results of experiments in which the YOLOv8 model is compared to other widely used methods for sign detection. The obtained results have practical significance in the field of road traffic safety, offering an innovative approach to automatic road sign detection, which contributes to improving speed control, attentiveness, and reducing accidents on the roads.

Keywords: machine learning, road signs, convolutional neural networks, image recognition

The problem of developing an intelligent automated system for detecting defects in textile materials is considered. An analysis of machine learning and deep learning algorithms was carried out in relation to solving the problem of product quality control. The implementation of an artificial neural network implemented in a Raspberry Pi microcomputer and receiving a set of input data in the form of a large stream of images from a high-speed digital camera is considered. The stages of creating a model in Python using the TensorFlow and Keras libraries are described. The development process includes the preparation of initial data intended for training and testing the system, as well as testing the operation of the resulting neural network, which consists in recognizing images of defects on fabric according to classification criteria.

Keywords: machine learning, neural network, defect images, textile material, training, testing, accuracy

The article describes a technique of developing neural network models of controllers for controlling a technical object, approximating the relationship between the control action and the deviation of the state of the object from the setting action, its speed and acceleration. The application of a technique for controlling the temperature of a water bath water heater is considered. The technical object is described by a second-order differential equation and has a smooth monotonic behavior.

Keywords: technical object, water bath, water heater, neural regulator, control, object behavior, model, neural network, training set, perceptron

The work is devoted to the study of the effect of electrical pulses on the processes of cisplatin transport through the plasma membrane. Technical devices based on the application of this technology are used to increase cellular uptake of cytotoxic agents within certain cancer treatment strategies. This article presents the results of mathematical modeling performed using computer methods that allow us to study the influence of different pulse parameters (amplitude, duration, frequency) on the efficiency of cisplatin transport. Numerical experiments using various difference schemes and mathematical models that take into account the physical properties of the plasma membrane have been performed. The results obtained allow us to better understand the mechanisms of the impact of electrical impulses on the processes of cisplatin transport, which may be of practical importance for the development of new methods of drug delivery and cancer treatment.

Keywords: mathematical modeling, software package, electroporation, cisplastin transport, plasma membrane, computational experiment

The task of planning the sending of messages of known volumes from source points to destinations with known needs. At the same time, it is assumed that the costs of transmitting information on the one hand are proportional to the transmitted volumes and the cost of transmitting a unit of information over the selected communication channels, and on the other hand are associated with a fixed subscription fee for the use of channels that does not depend on the volume of transmitted information. An indicator of the quality of the plan with such a statement is the total cost of sending the entire planned volume of messages. A comparative characteristic of the effectiveness of methods for obtaining optimal plans using a linearized objective function and an exact solution by one of the combinatorial methods is carried out.

Keywords: message transmission, transport task, criterion of minimum total costs, computational complexity of the algorithm, linearization of the objective function

The article describes a way to optimize the trajectory optimization process by replacing the edges of the trajectory with spatial Bezier curves with a Pythagorean hodograph.

Keywords: Algorithms for generating trajectories, methods for constructing the formation of UAV groups, mathematical models of UAVs, multi-agent systems, Bezier curves, Pythagorean hodograph

This article explores how to optimize Quantum Espresso for efficient use of Nvidia's graphics processing unit (GPU) using CUDA technology. Quantum Espresso is a powerful tool for quantum mechanical simulation and calculation of material properties. However, the original version of the package was not designed for GPU use, so optimization is required to achieve the best performance.

Keywords: Quantum Espresso, GPU, CUDA, compute acceleration

The oil and gas engineering industry is undergoing changes that are associated with the introduction of innovative technologies, methods and tools to improve production processes and systems. All changes make it possible to achieve an increase in the average resource, durability and profit of the enterprise as a whole. Processing parts of the oil and gas complex and reducing all types of wear on the cutting part of the tool currently remains the most pressing topic. The continuous operation of a cutting tool is influenced by many factors. The relationship between cutting speed and tool life allows you to select the optimal speed. The work identifies the main directions of research on the selection of wear-resistant coatings for cutters to improve the accuracy of metalworking. The research was carried out using modern computer programs, which made it possible to draw certain conclusions, derive dependencies and determine the range of tasks for further research. Application of the main results will improve the processing efficiency and surface quality of parts in the oil and gas sector.

Keywords: durability, cutting mode, cutter, optimization, experiment, methodology, accuracy, processing, coatings, deformation

The procedure for filling positions of teaching staff of universities belonging to the teaching staff is regulated by federal laws and local regulations. At the same time, it becomes necessary to store and exchange a large number of documents between various participants of competitive events. The aim of the work was to automate the process of holding competitive events and use a common data warehouse, with the help of which it is possible to speed up paperwork, save time and consumables, ensure the safety of storing, transmitting and processing information. The article reflects the obtained results of automation of the competitive selection process at the St. Petersburg State University of Architecture and Civil Engineering.

Keywords: higher education institutions, competitive election, teaching staff, automation

This study is a pilot one. The purpose of the study is to identify the nature of the relationship between Poisson's ratio and cohesion, on the example of a soil mass. The main objective of the study is to identify the dependence of Poisson's ratio and cohesion coefficient to obtain the fracture limit of the material (in this study of soil massif) - plastic flows in the material. The study is conducted by methods of mathematical modeling. In order to achieve the objective, it is necessary to justify the possibility of performing this experiment by means of boundary value problem, and to perform the ranking of the number of numerical experiments by experiment planning method to obtain the extrema. Next, it is necessary to perform the numerical experiment itself to reveal the relationship between Poisson's ratio and cohesion. The obtained data will be used to compose the inverse problem when testing a new Russian software product in the field of geotechnical and geomechanical modeling.

Keywords: Poisson's ratio, cohesion, soil massif, numerical experiment, finite element method, mathematical modelling, plastic flow, deformation, stress

he article considers a plane problem of calculating the interaction of a culvert of different outlines with a soil embarckment, taking into account the constructive nonlinearity. Due to the impossibility of the soil to work in tension, the interaction of the pipe and soil is assumed to be uniulateral. In the problem, the outline of the pipe is changed, other parameters being equal. As the results of the calculation, the area of contact / separation and adhesion / slippage of the pipe with the soil is considered. Based on the results of calculations, recommendations are given for choosing the outline of culverts.

Keywords: constructive nonlinearity, frictional contact, unilateral constraints, linear complementarity problem, numerical models, finite element method

An original approach to describe airflow in the thin conic diffusor is suggested. It is based on approximate analytic solution of continuity equation. In addition simplified model of turbulence is combined. Reliability of derived formula is confirmed by comparison with finite-element solution for designed experimental setup. The elaboration is intended to direct computer simulation of multiphase flow.

Keywords: dust-air mixture, aspiration systems, turbulence, finite element modeling, separation diffuser, digital twin

A program for computer simulation of atomization of liquid fuels has been developed. A special calibrating experiment was carried out in a gravitational field. Verification of the computer model with experimental data is carried out, the correctness of simulation modeling is determined by the convergence of the results of static generalization. Tests of a model sample of the burner device were carried out, confirming the adequacy of computer simulation.

Keywords: burner, atomization of liquid fuels, mathematical modeling, fuel jet dispersion dynamics, nozzle

The article discusses the possibility of using the ANSYS WORKBENCH software package to calculate the uneven settlement of building foundations. The heterogeneity of the physical and mechanical properties of the soil, the difference in the thickness of the bearing layer and other factors lead to uneven development of settlement. This causes the appearance of cracks in the supporting structures, and in the worst case, the destruction of part of the building or the building as a whole. Methods for calculating settlements are very complex, but using the capabilities of modern computers and computer simulation programs makes it possible to obtain a simple and accurate solution to such problems. To evaluate the deformations of the foundation on heterogeneous soils the ANSYS software package was be used. The proposed method can be used to quantify the uneven settlement of the foundations of real buildings and structures.

Keywords: ANSYS WORKBENCH, foundation, uneven settlement, skew, computer modeling, deformation, finite element method

Pipeline fittings, which include butterfly valves, are not unimportant in pipeline systems. The main function of this design element is to prevent emergencies in pipeline systems. The principle of operation is based on closing of the shut-off device in case of change of direction of the transported medium flow. This ensures reliable flow control and prevents backflow of the medium in the pipeline. The rotary check valve provides reliability, tightness and safe operation of systems, as well as durability with regard to safety requirements. The article deals with the design and calculation of rotary check gates. The purpose of development of such a model range is to create a durable and reliable design, which will be able to ensure during the whole service life a safe operation in production with different parameters of the working environment. To confirm the reliability and serviceability parameters of the design, strength calculation of the butterfly valves has been carried out. As a result of numerical modelling of all designed check gates, the calculated parameters allow to give positive assessment to the gates and confirm compliance with technical requirements.

Keywords: rotary check gate, modelling, mathematical modelling, finite element method, calculation of reliability indices