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In this paper we describe an algorithm of numerical solving of an inverse problem on a hyperbolic heat equation with additional second time derivative with a small parameter. The problem in this case is finding an initial distribution with given final distribution. This algorithm allows finding a solution to the problem for any admissible given precision. Algorithm allows evading difficulties analogous to the case of heat equation with inverted time. Furthermore, it allows finding an optimal grid size by learning on a relatively big grid size and small amount of iterations of a gradient method and later extrapolates to the required grid size using Richardson’s method. This algorithm allows finding an adequate estimate of Lipschitz constant for the gradient of the target functional. Finally, this algorithm may easily be applied to the problems with similar structure, for example in solving equations for plasma, social processes and various biological problems. The theoretical novelty of the paper consists in the developing of an optimal procedure of finding of the required grid size using Richardson extrapolations for optimization problems with inexact gradient in ill-posed problems.

Scheduling computational workflows represented by directed acyclic graphs (DAGs) is crucial in many areas of computer science, such as cloud/edge tasks with distributed workloads and data mining. The complexity of online DAG scheduling is compounded by the large number of computational nodes, data transfer delays, heterogeneity (by type and processing power) of executors, precedence constraints imposed by DAG, and the nonuniform arrival of tasks. This paper introduces the Multi-Agent Local Voting Protocol (MLVP), a novel approach focused on dynamic load balancing for DAG scheduling in heterogeneous computing environments, where executors are represented as agents. The MLVP employs a local voting protocol to achieve effective load distribution by formulating the problem as a differentiated consensus achievement. The algorithm calculates an aggregated DAG metric for each executor-node pair based on node dependencies, node availability, and executor performance. The balance of these metrics as a weighted sum is optimized using a genetic algorithm to assign tasks probabilistically, achieving efficient workload distribution via information sharing and reaching consensus among the executors across the system and thus improving makespan. The effectiveness of the MLVP is demonstrated through comparisons with the state-of-the-art DAG scheduling algorithm and popular heuristics such as DONF, FIFO, Min- Min, and Max-Min. Numerical simulations show that MLVP achieves makepsan improvements of up to 70% on specific graph topologies and an average makespan reduction of 23.99% over DONF (state-of-the-art DAG scheduling heuristic) across randomly generated diverse set of DAGs. Notably, the algorithm’s scalability is evidenced by enhanced performance with increasing numbers of executors and graph nodes.

Mathematical simulation of unsteady natural convection and thermal surface radiation within a rotating square enclosure was performed. The considered domain of interest had two isothermal opposite walls subjected to constant low and high temperatures, while other walls are adiabatic. The walls were diffuse and gray. The considered cavity rotated with constant angular velocity relative to the axis that was perpendicular to the cavity and crossed the cavity in the center. Mathematical model, formulated in dimensionless transformed variables “stream function – vorticity” using the Boussinesq approximation and diathermic approach for the medium, was performed numerically using the finite difference method. The vorticity dispersion equation and energy equation were solved using locally one-dimensional Samarskii scheme. The diffusive terms were approximated by central differences, while the convective terms were approximated using monotonic Samarskii scheme. The difference equations were solved by the Thomas algorithm. The approximated Poisson equation for the stream function was solved by successive over-relaxation method. Optimal value of the relaxation parameter was found on the basis of computational experiments. Radiative heat transfer was analyzed using the net-radiation method in Poljak approach. The developed computational code was tested using the grid independence analysis and experimental and numerical results for the model problem.

Numerical analysis of unsteady natural convection and thermal surface radiation within the rotating enclosure was performed for the following parameters: Ra = 10³–10⁶, Ta = 0–10⁵, Pr = 0.7, ε = 0–0.9. All distributions were obtained for the twentieth complete revolution when one can find the periodic behavior of flow and heat transfer. As a result we revealed that at low angular velocity the convective flow can intensify but the following growth of angular velocity leads to suppression of the convective flow. The radiative Nusselt number changes weakly with the Taylor number.

The paper proposes and investigates a mathematical model of a distributed computing system of parallel interacting processes competing for the use of a limited number of copies of a structured software resource. In cases of unlimited and limited parallelism by the number of processors of a multiprocessor system, the problems of determining operational and exact values of the execution time of heterogeneous and identically distributed competing processes in a synchronous mode are solved, which ensures a linear order of execution of blocks of a structured software resource within each of the processes without delays. The obtained results can be used in a comparative analysis of mathematical relationships for calculating the implementation time of a set of parallel distributed interacting competing processes, a mathematical study of the efficiency and optimality of the organization of distributed computing, solving problems of constructing an optimal layout of blocks of an identically distributed system, finding the optimal number of processors that provide the directive execution time of given volumes of computations. The proposed models and methods open up new prospects for solving problems of optimal distribution of limited computing resources, synchronization of a set of interacting competing processes, minimization of system costs when executing parallel distributed processes.

Currently, earthquake-resistant design of buildings based on the power calculation and presentation of effect of the earthquake static equivalent forces, which are calculated using elastic response spectra (linear-spectral method) that connects the law of motion of the soil with the absolute acceleration of the model in a nonlinear oscillator.

This approach does not directly take into account either the influence of the duration of strong motion or the plastic behavior of the structure. Frequency content and duration of ground vibrations directly affect the energy received by the building and causing damage to its elements. Unlike power or kinematic calculation of the seismic effect on the structure can be interpreted without considering separately the forces and displacements and to provide, as the product of both variables, i.e., the work or input energy (maximum energy that can be purchased building to the earthquake).

With the energy approach of seismic design, it is necessary to evaluate the input seismic energy in the structure and its distribution among various structural components.

The article provides substantiation of the energy approach in the design of earthquake-resistant buildings and structures instead of the currently used method based on the power calculation and presentation of effect of the earthquake static equivalent forces, which are calculated using spectra of the reaction.

Noted that interest in the use of energy concepts in earthquake-resistant design began with the works of Housner, which provided the seismic force in the form of the input seismic energy, using the range of speeds, and suggested that the damage in elastic-plastic system and elastic system causes one and the same input seismic energy.

The indices of the determination of the input energy of the earthquake, proposed by various authors, are given in this paper. It is shown that modern approaches to ensuring seismic stability of structures, based on the representation of the earthquake effect as a static equivalent force, do not adequately describe the behavior of the system during an earthquake.

In this paper, based on quantitative estimates of seismic risk analyzes developed in the NRU MSUCE Standard Organization (STO) “Seismic resistance structures. The main design provisions”. In the developed document a step forward with respect to the optimal design of earthquake-resistant structures.

The proposed concept of using the achievements of modern methods of calculation of buildings and structures on seismic effects, which are harmonized with the Eurocodes and are not contrary to the system of national regulations.

In this paper, a time-dependent natural convective heat transfer in a closed square cavity filled with non- Newtonian fluid was considered in the presence of an isothermal energy source located on the lower wall of the region under consideration. The vertical boundaries were kept at constant low temperature, while the horizontal walls were completely insulated. The behavior of a non-Newtonian fluid was described by the Ostwald de Ville power law. The process under study was described by transient partial differential equations using dimensionless non-primitive variables “stream function – vorticity – temperature”. This method allows excluding the pressure field from the number of unknown parameters, while the non-dimensionalization allows generalizing the obtained results to a variety of physical formulations. The considered mathematical model with the corresponding boundary conditions was solved on the basis of the finite difference method. The algebraic equation for the stream function was solved by the method of successive lower relaxation. Discrete analogs of the vorticity equation and energy equation were solved by the Thomas algorithm. The developed numerical algorithm was tested in detail on a class of model problems and good agreement with other authors was achieved. Also during the study, the mesh sensitivity analysis was performed that allows choosing the optimal mesh.

As a result of numerical simulation of unsteady natural convection of a non-Newtonian power-law fluid in a closed square cavity with a local isothermal energy source, the influence of governing parameters was analyzed including the impact of the Rayleigh number in the range 104–106, power-law index $n = 0.6–1.4$, and also the position of the heating element on the flow structure and heat transfer performance inside the cavity. The analysis was carried out on the basis of the obtained distributions of streamlines and isotherms in the cavity, as well as on the basis of the dependences of the average Nusselt number. As a result, it was established that pseudoplastic fluids $(n < 1)$ intensify heat removal from the heater surface. The increase in the Rayleigh number and the central location of the heating element also correspond to the effective cooling of the heat source.

Modern methods of complex planning the execution of task packages in multistage systems are characterized by the presence of restrictions on the dimension of the problem being solved, the impossibility of guaranteed obtaining effective solutions for various values of its input parameters, as well as the impossibility of registration the conditions for the formation of sets from the result and the restriction on the interval duration of time of the system operating. The decomposition of the generalized function of the system into a set of hierarchically interconnected subfunctions is implemented to solve the problem of scheduling the execution of task packages with generating sets of results and the restriction on the interval duration of time for the functioning of the system. The use of decomposition made it possible to employ the hierarchical approach for planning the execution of task packages in multistage systems, which provides the determination of decisions by the composition of task groups at the first level of the hierarchy decisions by the composition of task packages groups executed during time intervals of limited duration at the second level and schedules for executing packages at the third level the hierarchy. In order to evaluate decisions on the composition of packages, the results of their execution, obtained during the specified time intervals, are distributed among the packages. The apparatus of the theory of hierarchical games is used to determine complex solutions. A model of a hierarchical game for making decisions by the compositions of packages, groups of packages and schedules of executing packages is built, which is a system of hierarchically interconnected criteria for optimizing decisions. The model registers the condition for the formation of sets from the results of the execution of task packages and restriction on duration of time intervals of its operating. The problem of determining the compositions of task packages and groups of task packages is NP-hard; therefore, its solution requires the use of approximate optimization methods. In order to optimize groups of task packages, the construction of a method for formulating initial solutions by their compositions has been implemented, which are further optimized. Moreover, a algorithm for distributing the results of executing task packages obtained during time intervals of limited duration by sets is formulated. The method of local solutions optimization by composition of packages groups, in accordance with which packages are excluded from groups, the results of which are not included in sets, and packages, that aren’t included in any group, is proposed. The software implementation of the considered method of complex optimization of the compositions of task packages, groups of task packages, and schedules for executing task packages from groups (including the implementation of the method for optimizing the compositions of groups of task packages) has been performed. With its use, studies of the features of the considered planning task are carried out. Conclusion are formulated concerning the dependence of the efficiency of scheduling the execution of task packages in multistage system under the introduced conditions from the input parameters of the problem. The use of the method of local optimization of the compositions of groups of task packages allows to increase the number of formed sets from the results of task execution in packages from groups by 60% in comparison with fixed groups (which do not imply optimization).

The article focuses on the problem of mechanisms’ co-design for robotic systems to perform adaptive physical interaction with an unstructured environment, including physical human robot interaction. The co-design means simultaneous optimization of mechanics and control system, ensuring optimal behavior and performance of the system. Mechanics optimization refers to the search for optimal structure, geometric parameters, mass distribution among the links and their compliance; control refers to the search for motion trajectories for mechanism’s joints. The paper presents a generalized method of structural-parametric synthesis of underactuated mechanisms with closed kinematics for robotic systems for various purposes, e. g., it was previously used for the co-design of fingers’ mechanisms for anthropomorphic gripper and legs’ mechanisms for galloping robots. The method implements the concept of morphological computation of control laws due to the features of mechanical design, minimizing the control effort from the algorithmic component of the control system, which reduces the requirements for the level of technical equipment and reduces energy consumption. In this paper, the proposed method is used to optimize the structure and geometric parameters of the passive mechanism of the back support module of an industrial exosuit. Human movements are diverse and non-deterministic when compared with the movements of autonomous robots, which complicates the design of wearable robotic devices. To reduce injuries, fatigue and increase the productivity of workers, the synthesized industrial exosuit should not only compensate for loads, but also not interfere with the natural human motions. To test the developed exosuit, kinematic datasets from motion capture of an entire human body during industrial operations were used. The proposed method of structural-parametric synthesis was used to improve the ergonomics of a wearable robotic device. Verification of the synthesized mechanism was carried out using simulation: the passive module of the back is attached to two geometric primitives that move the chest and pelvis of the exosuit operator in accordance with the motion capture data. The ergonomics of the back module is quantified by the distance between the joints connecting the upper and bottom parts of the exosuit; minimizing deviation from the average value corresponds to a lesser limitation of the operator’s movement, i. e. greater ergonomics. The article provides a detailed description of the method of structural-parametric synthesis, an example of synthesis of an exosuit module and the results of simulation.

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.