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The article investigates the possibility of detecting traces of hazardous substances (explosives and narcotics) based on the detection of their vapors in the air. The relevance of the study stems from the need to counter terrorist threats and drug trafficking, where identifying even trace amounts of substances is critical. The focus is on mathematical modeling of the evaporation of a thin substance layer from a surface, based on molecular kinetic theory. A universal model is proposed, accounting for the physicochemical properties of substances, ambient temperature, adhesion to the surface, and the initial mass of the layer. Using the Hertz – Knudsen – Langmuir and Clausius – Clapeyron equations, analytical expressions are derived for the complete evaporation time, maximum vapor mass, and process dynamics. A dimensionless parameter, $\gamma$, is identified, determining the limiting conditions for evaporation. It is shown that substance adhesion (coefficient $\alpha$) affects the evaporation rate but not the final vapor mass. Calculations were performed for six model substances (TNT, RDX, PETN, amphetamine, cocaine, heroin) with a wide range of properties. At room temperature and a surface concentration of 100 ng/cm2, most substances evaporate completely, except for RDX, which remains on the surface at 84%. Evaporation times range from fractions of a second (amphetamine) to several hours (heroin). For low-volatility substances, the maximum mass capable of evaporating under given conditions is determined. The novelty of the work lies in the development of a universal model applicable to a broad class of hazardous substances and in identifying key parameters governing the evaporation process. The results enable the estimation of detection limits for trace substances using vapor-based methods and can be applied in the design of security systems.

The objective of this study is to determine the best formations for the joint movement of a group of small robots in an aquatic environment. Estimation of drag of the flow is a traditional and well-known area of research, but it is not always valid to extend the conclusions made for a single robot to a group of similar devices due to the physical effects that appear during joint movement, such as a wave shadow. For these reasons, it is necessary to study the hydrodynamic characteristics of certain robot formations as a stable structure. The hydrodynamic parameters of systems with two main types of propulsion were studied: locomotive (fishtails) and propellers. Formations similar in structure to schools of fish were mainly considered, and then their applicability for robots of different types was assessed. The relationship between the speed of movement of the group and the drag of each of its participants was also studied. Mathematical modeling of the flow around a group of robots was performed using the finite volume method using two software packages (FlowVision and OpenFoam). Robots with a screw propeller interfere with each other when packed into tight formations, and for the locomotive case, being in the disturbance zone, on the contrary, is preferable. Also, with poorly streamlined bodies, flows separating from the surface can turn into narrow turbulent jets that greatly interfere with the rear robots. It has been established that wake effect reduces energy costs only at low speeds of movement — about 5 cm/s; at high speeds, movement in columns becomes difficult for the rear robots. No large difference in frontal resistance was found between a single robot and a group for a fish-like tail. The studies made it possible to develop and substantiate recommendations for optimizing robot designs for group movement.

Currently, a significant development has been observed in the direction of distributed computing theory, where computational tasks are solved collectively by resource-constrained devices. In practice, this scenario is implemented when processing data in Internet of Things systems, with the aim of reducing system latency and network infrastructure load, as data is processed on edge network computing devices. However, the rapid growth and widespread adoption of IoT systems raise questions about the need to develop methods for reducing the resource intensity of computations. The resource constraints of computing devices pose the following issues regarding the distribution of computational resources: firstly, the necessity to account for the transit cost between different devices solving various tasks; secondly, the necessity to consider the resource cost associated directly with the process of distributing computational resources, which is particularly relevant for groups of autonomous devices such as drones or robots. An analysis of modern publications available in open access demonstrated the absence of proposed models or methods for distributing computational resources that would simultaneously take into account all these factors, making the creation of a new mathematical model for organizing distributed computing in IoT systems and its solution methods topical. This article proposes a novel mathematical model for distributing computational resources along with heuristic optimization methods, providing an integrated approach to implementing distributed computing in IoT systems. A scenario is considered where there exists a leader device within a group that makes decisions concerning the allocation of computational resources, including its own, for distributed task resolution involving information exchanges. It is also assumed that no prior knowledge exists regarding which device will assume the role of leader or the migration paths of computational tasks across devices. Experimental results have shown the effectiveness of using the proposed models and heuristics: achieving up to a 52% reduction in resource costs for solving computational problems while accounting for data transit costs, saving up to 73% of resources through supplementary criteria optimizing task distribution based on minimizing fragment migrations and distances, and decreasing the resource cost of resolving the computational resource distribution problem by up to 28 times with reductions in distribution quality up to 10%.

This paper proposes an architectural solution for organizing a convolutional neural network (CNN) oriented towards hardware implementation on edge devices under limited resources. To this goal, an approach to compressing spectrograms to a given size (28 × 28) is proposed using discretization, monoconversion, windowed Fourier transform, and two-dimensional interpolation. A balanced convolution procedure is developed based on compact convolutional filters, the size of which provides the balance between computational complexity and accuracy required for edge devices. An algorithm that enables convolution operations and calculation of the error function gradient in the convolutional layer in a single cycle ensuring increased performance in both inference and training modes of the CNN is proposed. The tradeoff between network trainability and its resistance to overfitting is optimized by applying the Dropout regularization method with a dropout coefficient of 0.5 for the fully connected layer.

The effectiveness of the proposed solution was demonstrated using the example of recognizing audio spectrograms of car and airplane engine sounds. The CNN was trained on a balanced dataset consisting of 7160 audio recordings. The trained network demonstrated high recognition accuracy (95%), low loss values (< 0.2), and balanced precision/recall/F-metric, demonstrating the effectiveness of the developed CNN model.

A new flow modeling method on unstructured grid was proposed. As a basis system this method used quasi-hydro-dynamic equations. The finite volume method vas used for solving these equations. The Delaunay triangulation was used for constructing mesh. This proposed method was tested in modeling of incompressible flow through a channel with complex profile. The acquired results showed that the proposed method could be used in flow modeling in unstructured grid.

An approach to evaluation of a parametric portrait of integral equations of the theory of liquids in the RISM approximation was proposed. To obtain all associated solutions the continuation method was used. The equations reduced to a two-centered molecule model for symmetry reasons were deduced for molecular liquids. For molecular liquids, some equations were obtained which could be reduced, for symmetry reasons, to a two-center molecular model. To avoid critical points we changed the dependence of RISM-equations on reverse compressibility. The suggested method was used to perform numerical computations of methane reverse compressibility isotherms with three closures. No bifurcation of solutions was observed in the case of the partially linearized hypernetted chain closure. For other closures bifurcations of solutions were obtained and the model behavior nontypical for simple liquids was observed. In the case of Percus-Yevick closure nonphysical solutions were obtained at low temperature and density. Additional solution branch with a kink in the bifurcation point was obtained in the case of hypernetted chain closure at temperature above the critical point.

Numerical methods of obtaining collective and one-particle states were used for the quantum description of two-nuclear systems behavior at the initial stage of near-barrier heavy nuclei fusion. The collective exited states in such systems represent concordant oscillations of surfaces of spherical nuclei. The one-particle states of the external neutrons are similar to the states of valence electrons of diatomic molecules.

A mathematical model for the evolution of microbial populations during prolonged cultivation in a chemostat has been constructed. This model generalizes the sequence of the well-known mathematical models of the evolution, in which such factors of the genetic variability were taken into account as chromosomal mutations, mutations in plasmid genes, the horizontal gene transfer, the plasmid loss due to cellular division and others. Liapunov’s function for the generic model of evolution is constructed. The existence proof of bounded, positive invariant and globally attracting set in the state space of the generic mathematical model for the evolution is presented because of the application of La-Salle’s theorem. The analytic description of this set is given. Numerical methods for estimate of the number of limit sets, its location and following investigation in the mathematical models for evolution are discussed.

The method of modelling of a compact bone tissue microstructure is presented. The modelling sample is considered as set of the structural elements containing reinforcing element – osteon and a matrix. The form of structural elements is defined by distances to next osteons and directions of next osteons arrangement. Calculation of the stress and strain state of the modelling sample is carried out at tension in program complex ANSYS. Results of calculation have shown, that haversian canals are stress concentrators.

The paper presents a new dense material modeling method based on spherepolyhedra packing algorithm, describes mathematical model of spherepolyhedra and discuss the results of computation experiments on different spherepolyhedra packs. The results of experiments show convergence of proposed method. Experiments include investigations of spherepolyhedra packs with different shapes, polydisperse and oriented structures. Presented method would be applied to virtual design of dense materials composed of non-spherical particles.