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We present a novel model for the dynamical trap of the stimulus – response type that mimics human control over dynamic systems when the bounded capacity of human cognition is a crucial factor. Our focus lies on scenarios where the subject modulates a control variable in response to a certain stimulus. In this context, the bounded capacity of human cognition manifests in the uncertainty of stimulus perception and the subsequent actions of the subject. The model suggests that when the stimulus intensity falls below the (blurred) threshold of stimulus perception, the subject suspends the control and maintains the control variable near zero with accuracy determined by the control uncertainty. As the stimulus intensity grows above the perception uncertainty and becomes accessible to human cognition, the subject activates control. Consequently, the system dynamics can be conceptualized as an alternating sequence of passive and active modes of control with probabilistic transitions between them. Moreover, these transitions are expected to display hysteresis due to decision-making inertia.

Generally, the passive and active modes of human control are governed by different mechanisms, posing challenges in developing efficient algorithms for their description and numerical simulation. The proposed model overcomes this problem by introducing the dynamical trap of the stimulus-response type, which has a complex structure. The dynamical trap region includes two subregions: the stagnation region and the hysteresis region. The model is based on the formalism of stochastic differential equations, capturing both probabilistic transitions between control suspension and activation as well as the internal dynamics of these modes within a unified framework. It reproduces the expected properties in control suspension and activation, probabilistic transitions between them, and hysteresis near the perception threshold. Additionally, in a limiting case, the model demonstrates the capability of mimicking a similar subject’s behavior when (1) the active mode represents an open-loop implementation of locally planned actions and (2) the control activation occurs only when the stimulus intensity grows substantially and the risk of the subject losing the control over the system dynamics becomes essential.

The study of the structural characteristics of composites and nanostructures is of fundamental importance in materials science. Theoretical and numerical modeling and simulation of the mechanical properties of nanostructures is the main tool that allows for complex studies that are difficult to conduct only experimentally. One example of nanostructures considered in this work are carbon nanotubes (CNTs), which have good thermal and electrical properties, as well as low density and high Young’s modulus, making them the most suitable reinforcement element for composites, for potential applications in aerospace, automotive, metallurgical and biomedical industries. In this review, we reviewed the modeling methods, mechanical properties, and applications of CNT-reinforced metal matrix composites. Some modeling methods applicable in the study of composites with polymer and metal matrices are also considered. Methods such as the gradient descent method, the Monte Carlo method, methods of molecular statics and molecular dynamics are considered. Molecular dynamics simulations have been shown to be excellent for creating various composite material systems and studying the properties of metal matrix composites reinforced with carbon nanomaterials under various conditions. This paper briefly presents the most commonly used potentials that describe the interactions of composite modeling systems. The correct choice of interaction potentials between parts of composites directly affects the description of the phenomenon being studied. The dependence of the mechanical properties of composites on the volume fraction of the diameter, orientation, and number of CNTs is detailed and discussed. It has been shown that the volume fraction of carbon nanotubes has a significant effect on the tensile strength and Young’s modulus. The CNT diameter has a greater impact on the tensile strength than on the elastic modulus. An example of works is also given in which the effect of CNT length on the mechanical properties of composites is studied. In conclusion, we offer perspectives on the direction of development of molecular dynamics modeling in relation to metal matrix composites reinforced with carbon nanomaterials.

In today’s technology-driven world, lite devices like Internet of Things (IoT) devices and microcontrollers (MCUs) are becoming increasingly common. These devices are more energyefficient and affordable, often with reduced features compared to the standard versions such as very limited memory and processing power for typical machine learning models. However, modern machine learning models can have millions of parameters, resulting in a large memory footprint. This complexity not only makes it difficult to deploy these large models on resource constrained devices but also increases the risk of latency and inefficiency in processing, which is crucial in some cases where real-time responses are required such as autonomous driving and medical diagnostics. In recent years, neural networks have seen significant advancements in model optimization techniques that help deployment and inference on these small devices. This narrative review offers a thorough examination of the progression and latest developments in neural network optimization, focusing on key areas such as quantization, pruning, knowledge distillation, and neural architecture search. It examines how these algorithmic solutions have progressed and how new approaches have improved upon the existing techniques making neural networks more efficient. This review is designed for machine learning researchers, practitioners, and engineers who may be unfamiliar with these methods but wish to explore the available techniques. It highlights ongoing research in optimizing networks for achieving better performance, lowering energy consumption, and enabling faster training times, all of which play an important role in the continued scalability of neural networks. Additionally, it identifies gaps in current research and provides a foundation for future studies, aiming to enhance the applicability and effectiveness of existing optimization strategies.

The efficiency of mobile robotic systems (MRS) that monitor the traffic situation, urban infrastructure, consequences of emergency situations, etc., directly depends on the quality of vision systems, which are the most important part of MRS. In turn, the accuracy of image processing in vision systems depends to a great extent on the accuracy of spatial orientation of the video camera placed on the MRS. However, when video cameras are placed on the MRS, the level of errors of their spatial orientation increases sharply, caused by wind and seismic vibrations, movement of the MRS over rough terrain, etc. In this connection, the paper considers a general solution to the problem of stochastic estimation of spatial orientation parameters of video cameras in conditions of both random mast vibrations and arbitrary character of MRS movement. Since the methods of solving this problem on the basis of satellite measurements at high intensity of natural and artificial radio interference (the methods of formation of which are constantly being improved) are not able to provide the required accuracy of the solution, the proposed approach is based on the use of autonomous means of measurement — inertial and non-inertial. But when using them, the problem of building and stochastic estimation of the general model of video camera motion arises, the complexity of which is determined by arbitrary motion of the video camera, random mast oscillations, measurement disturbances, etc. The problem of stochastic estimation of the general model of video camera motion arises. Due to the unsolved nature of this problem, the paper considers the synthesis of both the video camera motion model in the most general case and the stochastic estimation of its state parameters. The developed algorithm for joint estimation of the spatial orientation parameters of the video camera placed on the mast of the MRS is invariant to the nature of motion of the mast, the video camera, and the MRS itself, providing stability and the required accuracy of estimation under the most general assumptions about the nature of interference of the sensitive elements of the autonomous measuring complex used. The results of the numerical experiment allow us to conclude that the proposed approach can be practically applied to solve the problem of the current spatial orientation of MRS and video cameras placed on them using inexpensive autonomous measuring devices.

The adequate complexity three-dimensional finite element model of biomechanical system with space, shell and beam-type elements was built. The model includes the Ilizarov fixator and tibial bone’s simulator with the regenerating tissue at the fracture location. The proposed model allows us to specify the orthotropic elastic properties of tibial bone model in cortical and trabecular zones. It is also possible to change the basic geometrical and mechanical characteristics of biomechanical system, change the finite element mash density and define the different external loads, such as pressure on the bone and compression or distraction between the repositioned rings of Ilizarov device.

By using special APDL ANSYS program macros the mode of deformation was calculated in the fracture zone for various static loads on the simulator bone, for compression or distraction between the repositioned rings and for various mechanical properties during different stages of the bone regenerate formation (gelatinous, cartilaginous, trabecular and cortical bone remodeling). The obtained results allow us to estimate the permissible values of the external pressure on the bone and of the displacements of the Ilizarov fixator rings for different stages of the bone regeneration, based on the admittance criterion for the maximum of the stresses in the callus. The presented data can be used in a clinical condition for planning, realization and monitoring of the power modes for transosseous osteosynthesis with the external Ilizarov fixator.

In the present paper, we discuss the possibility of a simplified three-dimensional unsteady simulation of plasma-assisted combustion of gaseous fuel in a supersonic airflow. Simulation was performed by using FlowVision CFD software. Analysis of experimental geometry show that it has essentially 3D nature that conditioned by the discrete fuel injection into the flow as well as by the presence of the localized plasma filaments. Study proposes a variant of modeling geometry simplification based on symmetry of the aerodynamic duct and periodicity of the spatial inhomogeneities. Testing of modified FlowVision $k–\varepsilon$ turbulence model named «KEFV» was performed for supersonic flow conditions. Based on that detailed grid without wall functions was used the field of heat and near fuel injection area and surfaces remote from the key area was modeled with using of wall functions, that allowed us to significantly reduce the number of cells of the computational grid. Two steps significantly simplified a complex problem of the hydrocarbon fuel ignition by means of plasma generation. First, plasma formations were simulated by volumetric heat sources and secondly, fuel combustion is reduced to one brutto reaction. Calibration and parametric optimization of the fuel injection into the supersonic flow for IADT-50 JIHT RAS wind tunnel is made by means of simulation using FlowVision CFD software. Study demonstrates a rather good agreement between the experimental schlieren photo of the flow with fuel injection and synthetical one. Modeling of the flow with fuel injection and plasma generation for the facility T131 TSAGI combustion chamber geometry demonstrates a combustion mode for the set of experimental parameters. Study emphasizes the importance of the computational mesh adaptation and spatial resolution increasing for the volumetric heat sources that model electric discharge area. A reasonable qualitative agreement between experimental pressure distribution and modeling one confirms the possibility of limited application of such simplified modeling for the combustion in high-speed flow.

In this paper we present Rayleigh formulas obtained from Kirchhoff integral formulas, which can later be used to obtain migration images. The relevance of the studies conducted in the work is due to the widespread use of migration in the interests of seismic oil and gas seismic exploration. A special feature of the work is the use of an elastic approximation to describe the dynamic behaviour of a geological environment, in contrast to the widespread acoustic approximation. The proposed approach will significantly improve the quality of seismic exploration in complex cases, such as permafrost and shelf zones of the southern and northern seas. The complexity of applying a system of equations describing the state of a linear-elastic medium to obtain Rayleigh formulas and algorithms based on them is a significant increase in the number of computations, the mathematical and analytical complexity of the resulting algorithms in comparison with the case of an acoustic medium. Therefore in industrial seismic surveys migration algorithms for the case of elastic waves are not currently used, which creates certain difficulties, since the acoustic approximation describes only longitudinal seismic waves in geological environments. This article presents the final analytical expressions that can be used to develop software systems using the description of elastic seismic waves: longitudinal and transverse, thereby covering the entire range of seismic waves: longitudinal reflected PP-waves, longitudinal reflected SP-waves, transverse reflected PS-waves and transverse reflected SS-waves. Also, the results of comparison of numerical solutions obtained on the basis of Rayleigh formulas with numerical solutions obtained by the grid-characteristic method are presented. The value of this comparison is due to the fact that the method based on Rayleigh integrals is based on analytical expressions, while the grid-characteristic method is a method of numerical integration of solutions based on a calculated grid. In the comparison, different types of sources were considered: a point source model widely used in marine and terrestrial seismic surveying and a flat wave model, which is also sometimes used in field studies.

The review and systematization of current papers on the mathematical modeling of population dynamics allow us to conclude the key interests of authors are two or three main research lines related to the description and analysis of the dynamics of both local structured populations and systems of interacting homogeneous populations as ecological community in physical space. The paper reviews and systematizes scientific studies and results obtained within the framework of dynamics of structured and interacting populations to date. The paper describes the scientific idea progress in the direction of complicating models from the classical Malthus model to the modern models with various factors affecting population dynamics in the issues dealing with modeling the local population size dynamics. In particular, they consider the dynamic effects that arise as a result of taking into account the environmental capacity, density-dependent regulation, the Allee effect, complexity of an age and a stage structures. Particular attention is paid to the multistability of population dynamics. In addition, studies analyzing harvest effect on structured population dynamics and an appearance of the hydra effect are presented. The studies dealing with an appearance and development of spatial dissipative structures in both spatially separated populations and communities with migrations are discussed. Here, special attention is also paid to the frequency and phase multistability of population dynamics, as well as to an appearance of spatial clusters. During the systematization and review of articles on modeling the interacting population dynamics, the focus is on the “prey–predator” community. The key idea and approaches used in current mathematical biology to model a “prey–predator” system with community structure and harvesting are presented. The problems of an appearance and stability of the mosaic structure in communities distributed spatially and coupled by migration are also briefly discussed.

The development of structured molecular systems based on a nucleic acid framework takes into account the ability of single-stranded DNA to form a stable double-stranded structure due to stacking interactions and hydrogen bonds of complementary pairs of nucleotides. To increase the stability of the DNA double helix and to expand the temperature range in the hybridization protocols, it was proposed to use more stable metal-mediated complexes of nucleotide pairs as an alternative to Watson-Crick hydrogen bonds. One of the most frequently considered options is the use of silver ions to stabilize a pair of cytosines from opposite DNA strands. Silver ions specifically bind to N3 cytosines along the helix axis to form, as is believed, a strong N3–Ag⁺–N3 bond, relative to which, two rotational isomers, the cis- and trans-configurations of C–Ag⁺–C can be formed. In present work, a theoretical study and a comparative analysis of the free energy profile of the dissociation of two С–Ag⁺–C isomers were carried out using the combined method of molecular mechanics and quantum chemistry (QM/MM). As a result, it was shown that the cis-configuration is more favorable in energy than the trans- for a single pair of cytosines, and the geometry of the global minimum at free energy profile for both isomers differs from the equilibrium geometries obtained previously by quantum chemistry methods. Apparently, the silver ion stabilization model of the DNA duplex should take into account not only the direct binding of silver ions to cytosines, but also the presence of related factors, such as stacking interaction in extended DNA, interplanar hydrogen bonds, and metallophilic interaction of neighboring silver ions.

In real problems of exploration seismology we deal with a heterogeneity of the nature of elastic waves interaction with the surface of a fracture by the propagation through it. The fracture is a complex heterogeneous structure. In some locations the surfaces of fractures are placed some distance apart and are separated by filling fluid or emptiness, in some places we can observe the gluing of surfaces, when under the action of pressure forces the fracture surfaces are closely adjoined to each other. In addition, fractures can be classified by the nature of saturation: fluid or gas. Obviously, for such a large variety in the structure of fractures, one cannot use only one model that satisfies all cases.

This article is concerned with description of developed mathematical fracture models which can be used for numerical solution of exploration seismology problems using the grid-characteristic method on unstructured triangular (in 2D-case) and tetrahedral (in 3D-case) meshes. The basis of the developed models is the concept of an infinitely thin fracture, whose aperture does not influence the wave processes in the fracture area. These fractures are represented by bound areas and contact boundaries with different conditions on contact and boundary surfaces. Such an approach significantly reduces the consumption of computer resources since there is no need to define the mesh inside the fracture. On the other side, it allows the fractures to be given discretely in the integration domain, therefore, one can observe qualitatively new effects, such as formation of diffractive waves and multiphase wave front due to multiple reflections between the surfaces of neighbor fractures, which cannot be observed by using effective fracture models actively used in computational seismology.

The computational modeling of seismic waves propagation through layers of mesofractures was produced using developed fracture models. The results were compared with the results of physical modeling in problems in the same statements.