The mathematical model of the bronchial tree developed by the authors includes alveolar sacs. Alveolar sacs begin to appear in the human bronchial tree starting from the 15th generation of bronchi. Their number increases geometrically as they move down the bronchial tree, reaching a maximum in the terminal bronchi. The total number of sacs is more than 500 million. Human respiratory physiology imposes a number of conditions on the mathematical model of alveolar respiration. These conditions are uniform ventilation of the alveoli and minimal work associated with breathing. Therefore, the model must satisfy the condition of equal pressure in all 500 million alveolar sacs. Based on these conditions, a model of human alveolar inhalation was constructed. The alveolar pressure during inhalation, as determined in the model, is lower than atmospheric pressure, which is consistent with physiological data. Based on this model, calculations were made of the deposition of anthropogenic particles (cement dust and soot) in the lungs, which allows the risks to the respiratory system to be assessed. It has been shown that a decrease in air flow velocity (a decrease in inhaled air flow) contributes to an increase in particle deposition in the upper parts of the lungs. An increase in inhaled air flow reduces particle deposition, but at the same time, particles are "driven" into the lower parts of the lungs. Particle density has a negligible effect on their deposition compared to particle size and air flow velocity.
The field of disturbances from a school of commercial fish moving at a constant depth is investigated. The fluid is considered to be ideal and uniformly stratified. A school of fish is modeled by a group of identical point mass sources. The sources move horizontally and rectilinearly at the same speed or along the same sinusoidal trajectories with a random phase shift. A 90-degree rotation of the flock is also simulated. It is found that the result of solving the problem differs significantly from the known asymptotics near the flock, as well as in the case of rapid changes in the speed of motion of the flock, while the motion of fish along sinusoidal trajectories has little effect on the character of disturbances compared to rectilinear motion. The effect of the change in the distance between the fishes on the velocity fields of the fluid is studied. A significant influence of the distance between fish in a flock on the disturbance pattern is found at distances of the order of several flock sizes, whereas in the far zone, the disturbance pattern of the fluid does not depend on the distance between the fish and is similar to the disturbance pattern from a point mass source.
Collaboration of robotic complex and a human operator sets a task of prevention of contacts and collides between robotic links and human body. To solve this task one needs to know not only their positions at every moment but also a prediction for a certain time interval. However, control programs and motion laws fulfilled by the programs may be known not for all the parts of a robotic complex. In this article the method of prediction of a robotic complex link position is developed that does not demand a priori information on the complex structure and links motion laws. The method is based on so-called canonization of matrixes constructed from the accumulated information on previous link positions. Canonization means evaluation of matrix zero and unit devisors. The method is applicable to robotic complexes with linear control systems. The set of functions in Matlab environment are developed to evaluate the prediction. The examples of simulation for some robotic structures are given.
Authors research the task of aluminum plate geometric parameters at excision of surface layer material on both sides of considering billet. This allows us to use the hypothesis of the identity of the areas of the regions of considering stresses. The authors propose a nonstandard approach to residual stresses identification for different variants of removing the surface layer with researching billet into account transformations in the residual stress diagram. They take into account the transformation of the residual stress diagram type at changing the thickness of the aluminum billet. The known theoretical provisions on the type of residual stress diagram and the standard integral mathematical apparatus are the basis of the proposed approach. This allows us to build a mathematical model of changing the type of residual stress diagram depending on the thickness of the surface layer removal of the research aluminum plate. The authors research the change in the geometry of the studied workpiece taking into account the correction of the parameters of the residual stress diagram. This makes it possible to use the hypothesis of the equality of the areas of compressive and tensile residual stresses. The obtained results clarify the known theoretical provisions on changing the residual stress diagram after mechanical processing of the studied workpieces made of aluminum alloys.
The peculiarity of mapping the memory of the central processing unit (CPU) to the memory of the graphics processing unit (GPU) is discussed in the case of its dynamic allocation using OpenACC directives. The problem is that the array is not placed contiguously in memory. Therefore, the program associates all bytes of the computer's RAM between the start and end elements of the dynamic array with bytes of the GPU's memory, regardless of whether all of these bytes are actually occupied by the array elements. This leads to an unjustified and unpredictable increase in the size of the GPU memory allocated to store the dynamic array. Our simulations show that the increase in memory size can reach two orders of magnitude. The source code for dynamic allocation of a contiguous block of memory for two-dimensional arrays in C is given. This approach can be easily generalized to the case of an arbitrary number of dimensions. Testing of the described method showed that the sizes of dynamic arrays in the memory of the central and graphic processors coincide.
The maximum traveling salesman problem (MAX TSP) is a mathematical optimization problem that requires the construction of a Hamiltonian cycle with the highest possible sum of edge weights. It finds applications in bioinformatics, coding, logistics, and numerous other fields. Despite the existence of theoretical bounds on the accuracy of approximation algorithms, their practical behavior remains insufficiently explored. In this study, we conduct an empirical analysis of the Cycle Merging Algorithm (CMA) for solving MAX TSP. The CMA is a greedy heuristic based on the sequential merging of cycles in a maximum-weight 2-factor. Our computational experiments, carried out on instances ranging from 100 to 3000 vertices, evaluate the accuracy of the CMA solutions relative to an upper bound determined by solving an assignment problem, as well as the algorithm's computational efficiency. A significant contribution of this work is the construction of a regression model that describes the dependency of the relative error estimate on the number of vertices for metric instances. The model demonstrates that the relative error decreases according to a power-law relationship, and the analysis confirms that the CMA consistently outperforms its guaranteed theoretical bound. The results indicate that the Cycle Merging Algorithm is a powerful heuristic for MAX TSP, providing high-quality solutions and computational efficiency in practice. Future research directions include optimizing the cycle merging strategy, developing hybrid algorithms, and implementing GPU-based version to enhance scalability.
The results of a comprehensive experimental-computational study of the dynamic behavior of B4C-CrB2 composite materials in the loading-velocity range up to 1650 m/s are presented. To describe the response of chromium diboride (CrB2), an approach based on an additive mixture model is proposed, which made it possible, by interpolating available experimental data, to construct the material's shock adiabat (Hugoniot) in the velocity range up to 2000 m/s. The model was validated by comparing the results of numerical simulations of high-velocity impact with experimental data. The criteria for agreement were the crater geometry and the morphology of the fracture surface.
The paper studies a mathematical model of a mass infectious disease, written as a system of nonlinear reaction-diffusion-advection equations. The spatiotemporal interaction of two population groups is considered: susceptible to infection and infected. Local interaction determining the mutual transition from one group to another and migration flows caused by diffusion and directed migration are taken into account. The modeling is carried out without taking into account the birth and mortality rates of the population. For spatial approximation of the problem, the finite difference method based on shifted grids was used. Computer experiments were carried out in the MATLAB system. The study established the existence of an analytical solution corresponding to the stationary distribution of both population groups. Using computational experiments, parametric dependencies were established that affect the formation of epidemiological structures and the ratio of the shares of the infected and healthy population.
A spatial model of an elastic blocky medium with thin interlayers is considered. Thin interlayers are presented as internal boundary conditions for the blocks. Using the solution for plane monochromatic waves in a medium with an elastic layer, it is shown that the proposed interlayer model is quite suitable for describing media with sufficiently thin and compliant layers. An algorithm based on the splitting method is developed for solving spatial problems in media with parallelepiped-shaped blocks. One-dimensional splitting problems are solved using a scheme with controllable artificial dissipation. A blocky half-space with a large elastic inclusion is considered. A pulse generated on the free surface is reflected from the inclusion and returns back to the surface. The parameters of the blocky medium affect the quality of the reflected signal. If the layers are thick and compliant, the waves are scattered, and the reflected signal cannot be detected.
To study the mechanism of acoustic wave scattering on a soundproof spheressystem, a numerical technique based on the orthogonal central compositional design method is developed, which allows varying several parameters of the system to determine the contribution of each of them to the calculated value. The method is implemented for a three-factor computational experiment with two variable physical (wave radius and complex admittance) and one geometric (minimum distance between sphere centers) parameters. For the obtained regression equation, the significance of the coefficients is checked by Student's t-criterion and the adequacy of the model by Fisher's Fcriterion for two simple types of configurations and three values of the number of spheres in them, as well as the search for optimal values of the objective function (normalized pressure at a fixed point in space). For each case considered, significant and insignificant factors are established and the parameters at which the objective functions achieve the greatest (least) value are determined. The analysis carried out allowed us to determine the parameters at which of increase and decrease pressure zone sare observed behind the system of spheres.
In the article we consider a second order parabolic equation and well-posedness questions in Sobolev spaces of inverse problems of recovering the heat flux on the boundary with the use of a collection of integrals of a solution with weights over the domain. The flux is representable in the form of a finite segments of the series with unknown coefficients depending on time. Under certain conditions on the data, it is demonstrated that there exists a unique solution to the problem which depends on the data continuously. A solution has all generalized derivatives occurring into the equation summable to some power. The proof relies on a priori estimates and the contraction mapping principle. The method is constructive and allows to provide numerical methods of solving the problem. The numerical algorithm is based on the finite element methods and the method of finite differences. The results of numerical experiments are quite satisfactory and the procedure of constructing a solution is stable under small perturbations.
The process of oil reservoir development in the elastic-water-drive mode is considered. It is assumed that the displacement of oil by the edge water occurs completely and a clear boundary between two liquids is formed in the reservoir, which moves according to a previously unknown law. Within the framework of a one-dimensional model of the elastic-water-drive development regime, the task is set to identify the main hydrodynamic parameters of the reservoir, i.e. the pressure at the interface between liquids, the pressure distribution in the reservoir and the position of the interface between liquids, only on the basis of information obtained from the gallery of production wells. The problem set belongs to the class of boundary inverse problems. By applying the methods of front straightening and difference approximation, the problem is reduced to solving a system of difference equations. A special representation is proposed to solve the system of difference equations, having previously written it down as a variational problem with local regularization. As a result, an explicit formula is obtained for determining the approximate value of the pressure at the interface of liquids and recurrent formulas for determining the distribution of pressure and the position of the interface of liquids in the reservoir at each time layer. Based on the proposed computational algorithm, numerical experiments were carried out for a model oil reservoir.
This article examines a swirling jet based on a two-fluid turbulence model. This task, despite its simplicity, is quite a difficult task for many turbulence models. Because anisotropic turbulence is observed in swirling flows. Therefore, many modern RANS models are not able to describe such flows even qualitatively. The two-fluid model used in this work has been developed recently. Pioneering work shows that the basis for constructing this model is the possibility of representing a turbulent flow as a heterogeneous mixture of two liquids. Approach was proposed by Spaulding. The idea of the approach is to represent turbulence as the interpenetrating motion of two fluids, with the pulsating nature of the turbulent flow being caused by the relative moverment of them. For each fluid, it's own equation of motion is written, which leads to a closed system of equations. These studies also show that the developed two-fluid model is able to adequately describe complex anisotropic turbulence. To numerically implement the equations of a turbulent axisymmetric swirling jet, a uniform staggered calculation grid and a control volume method were used, and velocity correction was carried out using a simple method. The numerical results obtained are compared with experimental data from the ERCOFTAC database. It is shown that the results of the two-fluid model, despite the use of a rather rough computational grid, are in satisfactory agreement with experimental data.
A system of tree ordinary differential equations is researched. This system describes the dynamics of the numerical characteristics of predators and prey inhabiting a certain patch and the trophic attractiveness of the patch. It is assumed that the predator population will leave the patch if the food attractiveness falls to zero and there not enough prey for the predator population. The problem of preserving the species composition of the biocommunity of the patch is solved by removing some part of the predator population and moving it to another patch. The time intervals and the corresponding removal intensities that provide the solution to the problem have been found. The solution that is optimal in terms of minimizing the implementation costs was selected by numerical modeling from among the solutions constructed.
The paper considers software performance optimization technologies. It examines algorithm characteristics (asymptotic complexity and computational complexity) and the performance of algorithms implemented as programs. Profiling technology is used to optimize program performance. The given description of modern computing architectures shows that a processor and RAM resources cannot be fully taken into account when analyzing using asymptotic and computational complexity. Several examples demonstrate the limited possibilities of optimization using asymptotic and computational complexity. For the given examples, it is shown that using information about the capabilities of the architecture on which the program is executed allows for performance optimization without using low-level commands. Computational experiments were conducted on x86-64 (Intel Core) and ARM (Apple M1) platforms. The paper proposes a methodology for optimizing the performance of developed programs.
The paper proposes an algorithm for spatial visualization of snow cover variability based on a nearly periodic analysis of linearized data obtained from preliminary polygonal transformation of satellite images of snow mass, and a mathematical model of an avalanche based on the smoothed particle hydrodynamics method. Data transformation involves forming a matrix of brightness values of discretization nodes obtained by applying an approximating grid to the spatial structure of the snow mass on a satellite image. A system of uniform longitudinal and transverse intervals of homogeneous behavior of linearized data obtained from the results of transformation of snow mass images is revealed. A set of uniform intervals of uniform behavior of linearized data determining the degree of snow cover variability is compiled. Based on the established intervals of uniform behavior of data obtained from preliminary polygonal transformation of satellite images, spatial qualitative and quantitative criteria for snow cover variability are proposed. Based on the proposed criteria, a condition for a snow avalanche descent is formulated. The proposed approach is applicable for the rapid assessment of avalanche danger based on the analysis of satellite images.
The object of study in this article is the "sharing robot (cobot)-human" system, the aim of the research is to ensure the absence of accidental contact between the cobot and the human, thereby guaranteeing the safety of their interaction within a shared workspace. A new approach is proposed for solving the pursuit & DZcy;evasion problem based on an acceleration control law with variable coefficients governing the relative motion of two selected material points. A rule for one-parameter tuning of the coefficients to ensure the stability of the target motion is introduced. The tuning parameter is the natural frequency of a link described by a second-order linear differential equation with variable coefficients. The control of this parameter is derived from the condition of decreasing the angle function between the velocity vectors of the considered points, which is reduced to the solution of an algebraic inequality. Simulation results of the developed control algorithm are presented for the translational degrees of freedom of the KUKA KR-30-3 robot. The robot drive was selected based on a three-loop DC motor drive with position feedback, tuned to a modulus optimum within the framework of the principle of subordinate loop regulation.
The paper considers the problem of stabilizing the solutions of the deterministic and stochastic Wenzell equations, which describe the dynamics of the filtering fluid in the hemisphere and at its boundary. First, the question of stability and instability of solutions of a deterministic system of Wenzell equations in terms of stable and unstable invariant spaces is examined. For solutions lying in an unstable invariant space, the stabilization problem is solved based on the principle of feedback. The results are then applied to the stochastic system of Wenzell equations. Here the Nelson-Glyclih derivative is considered as a derivative, and the solution is a stochastic process.
The paper presents the results of numerical simulation using the finite element method (FEM) in the FreeCAD environment, confirming the hypothesis about the occurrence of a stress singularity in an L-shaped bend of a pipeline. The study was conducted on two three-dimensional models: a smooth pipe connection with a break in the curvature of the axis and an angular connection with an infinitely large curvature at the junction. The developed FEM algorithm made it possible to simulate both types of connections in a single three-dimensional geometry. The critical radius of curvature was found, at which the stresses in the smooth connection model reach the level of stresses in the angular connection model. The numerical simulation results presented in the article demonstrate the influence of the connection geometry on the stress distribution and confirm the presence of a singularity in smooth connections with small radii of curvature. The work contributes to the development of stress analysis methods in complex pipeline systems.
Transmission of information over an unprotected radio channel can be carried out in two ways: either using a powerful source operating in a short time interval, or using low-power sources operating in a continuous mode. In both the first and second cases, the energy of the transmitted signal can be the same. One of the main problems of information transmission is related to the properties of the medium through which the electromagnetic signal propagates. In this regard, it is necessary to study the transfer function of the medium, which can be determined using noise-like signals. This approach is known in determining the impulse transfer function of various devices, considered as a "black box" model. However, in the case of radio communications, it is necessary to consider the electrodynamic problem of propagation of the electromagnetic field in the atmosphere, on the surface of the earth with complex terrain, in buildings and underground structures, etc. In this case, it is necessary to use Maxwell's equations, including both the dielectric constant and the electrical conductivity of the material medium. The most universal representation of information is considered-in the binary number system.
