Nonstationary Problem Research Articles

USING OPERATOR INEQUALITIES IN STABILITY RESEARCH OF DIFFERENCE SCHEMES FOR NONLINEAR BOUNDARY PROBLEMS WITH NONLINEARITY OF UNLIMITED GROWTH

The article develops the theory of stability of linear operator schemes for operator inequalities and nonlinear nonstationary initial-boundary value problems of mathematical physics with nonlinearities of unlimited growth. Based on sufficient conditions for the stability of A.A. Samarsky’s two-layer and three-layer difference schemes, the corresponding a priori estimates for operator inequalities are obtained under the condition of the criticality of the difference schemes under consideration, i.e. when the difference solution and its first time derivative are non-negative at all nodes of the grid region. The results obtained are applied to the analysis of the stability of difference schemes that approximate the Fisher and Klein-Gordon equation with a nonlinear right-hand side.

On the kinetic physical and mathematical metal creep theory controlled by thermally activated dislocation sliding

The rationale for the prospects of using the physical and mathematical theory of metal creep in creep computations is carried out by a comparative analysis of the classical phenomenological and physical and mathematical metal creep theories. On the example of the description by both theories specific results of non-stationary creep experiments and analysis of the theories equations it is shown that implementing the physical kinetic equation for the actual structural parameter of the material, namely the scalar density of immobile dislocations, makes the physical and mathematical theory universal for solving non-stationary metal creep problems with multiaxial loading, when change, including abruptly, temperature, forces and loading rates.

Non-axisymmetric coupled non-stationary problem of thermoelectroelasticity for a long piezoceramic cylinder

A new closed solution to the non-axisymmetric coupled non-stationary problem of thermoelectroelasticity was constructed for a long piezoceramic cylinder for the case of satisfaction of the first and the third kind boundary conditions. Cylindrical surfaces were made as electrodes and connected to a measurement device with large input resistance. Limitation of a temperature change “load” rate made it possible to include equations of statics, electrostatics and thermal conductivity in the initial formula. The finite biorthogonal transforms are applying to explore a non-selfadjoint system of differential equations and to develop a closed solution. The obtained relations made it possible to determine the temperature and electric fields, and the stress-strain state in the piezoceramic cylinder, as well as the potential difference between cylindrical surfaces (electrodes) under non-stationary non-axisymmetric temperature impact.

Analysis of the thermomechanical behavior of a three-layer rectangular plate of the ceramic-metal-ceramic structure due to non-stationary convective heating

A rectangular isotropic layered plate is considered, which is convectively heated by the external environment. The thermal stress state of the plate is determined in two stages. At the first stage, the nonstationary temperature field is determined from the ratios of the non-stationary thermal conductivity problem. At the second stage, using the five-modal mathematical model of the shear theory of thermoelasticity, the parameters of the stress-strain state are determined.

Development of the wave motion induced by near-bottom periodic disturbances in a two-layer shear current

The behavior of wave motion arising in an ideal incompressible homogeneous fluid under switching-on periodic bottom disturbances is studied in the linear approximation for the two-dimensional non-stationary problem. In the undisturbed state, the velocities of two-layer fluid flow are linear functions of the vertical coordinate in each of the layers with different gradients and coincide on the boundary of the layers. The upper boundary of fluid can be either free or bounded by the rigid cover. The dispersion dependences and the group velocities of the appearing wave modes are determined. The vertical displacements of the free surface and the interface between the layers are calculated. A comparison with the solution for a single-layer fluid is carried out.

Progressive Supervision via Label Decomposition: An long-term and large-scale wireless traffic forecasting method

Long-term and Large-scale Wireless Traffic Forecasting (LL-WTF) is pivotal for strategic network management and comprehensive planning on a macro scale. However, LL-WTF poses greater challenges than short-term ones due to the pronounced non-stationarity of extended wireless traffic and the vast number of nodes distributed at the city scale. To cope with this, we propose a Progressive Supervision method based on Label Decomposition (PSLD). Specifically, we first introduce a Random Subgraph Sampling (RSS) algorithm designed to sample a tractable subset from large-scale traffic data, thereby enabling efficient network training. Then, PSLD employs label decomposition to obtain multiple easy-to-learn components, which are learned progressively at shallow layers and combined at deep layers to effectively cope with the non-stationary problem raised by LL-WTF tasks. Finally, we compare the proposed method with various state-of-the-art (SOTA) methods on three large-scale WT datasets. Extensive experimental results demonstrate that the proposed PSLD significantly outperforms existing methods, with an average 2%, 4%, and 11% performance improvement on three WT datasets, respectively. In addition, we built an open source library for WT forecasting (WTFlib) to facilitate related research, which contains numerous SOTA methods and provides a strong benchmark. Experiments can be reproduced through https://github.com/Anoise/WTFlib.

Cauchy Type Nonlinear Inverse Problem in a Two-Layer Cylindrical Area

Various types of protective coatings, such as ceramics, are used to increase the efficiency of metal parts that are exposed to high heat loads. Maintaining mechanical properties and acceptable thermal stresses requires temperature control for components such as turbine blades, gun barrels or combustion chambers. This paper presents a new method for controlling thermal parameters by solving a non-stationary Cauchy problem for the heat conduction equation. The solution is presented in a cylindrical two-layer area considering the variation of the thermophysical parameters of the metal and ceramic. The non-linear equation was solved by successive approximation method using differential quotients for the space and time variable. In order to regularize the ill-conditioned inverse problem, a quasi-regularization method was applied by performing an energy balance for the ceramic. Numerical calculations were carried out for different thicknesses of the ceramic layer. The temperature, heat flux density and heat transfer coefficient for the protective layer were calculated. For the same values of the heat transfer coefficient for 0.1 and 0.3 mm thick protective layers, the difference in permissible gas temperature differs by 10.5 °C.

Numerical modeling of three-dimensional non-stationary problems of radiation magnetohydrodynamics

This work presents a mathematical model for solving three-dimensional radiation problems of magnetohydrodynamics. An implicit fully conservative difference scheme is used to solve the system of differential equations. Two methods are used to solve the system of difference equations: the method of separate and the method of combined solution of equations, which are split by physical processes. A software implementation of the developed numerical algorithms is carried out, and calculations are performed modeling the compression of plasma by a magnetic field. The time dynamics of the parameters of matter and the magnetic field are studied. During the calculation process, at its various stages, both numerical methods used in the program are involved. The results obtained correspond to the physics of the process. В данной работе представлена математическая модель для решения трехмерных радиационных задач магнитной гидродинамики. Для решения системы дифференциальных уравнений применена неявная полностью консервативная разностная схема. Используется два метода решения системы разностных уравнений: метод раздельного и метод комбинированного решения уравнений, которые расщеплены по физическим процессам. Произведена программная реализация разработанных численных алгоритмов, выполнены расчеты, моделирующие сжатие плазмы магнитным полем. Изучалась динамика по времени параметров вещества и магнитного поля. В процессе расчета на его различных стадиях были задействованы оба используемых в программе численных метода. Полученные результаты соответствуют физике процесса.

Mathematical modeling of nonstationary problems of methane's laser thermochemistry in the presence of catalytic nanoparticles

Mathematical modeling of nonstationary problems of methane's laser thermochemistry in the presence of catalytic nanoparticles

Аналіз розподілу температури у двошаровій композитній циліндричній оболонці зумовленої конвективним теплообміном на її зовнішній поверхні

A non-stationary thermal conductivity problem for a two-layer cylindrical shell is formulated. The materials of the constituent layers of the shell are assumed to be homogeneous and isotropic. This shell is convectively heated by the external environment. The system of linear two-dimensional equations for the integral temperature characteristics summed over the component layers of the shell was used as the initial system of equations of the problem under consideration. When obtaining this system, the hypothesis of a linear distribution of temperature along the thickness of the entire shell was applied. On the basis of the developed two-dimensional mathematical model of thermal conductivity for layered cylindrical shells, a general solution to the thermal conductivity problem for a two-layered cylindrical shell was obtained. A temperature distribution was found for such a shell, which is locally convectively heated by the external environment in a rectangular region on the outer surface. For the numerical analysis, a metal-ceramic cylindrical shell was considered, the inner layer of which is made of tungsten, and the outer layer is made of ceramics. Under such a structure and conditions of heat exchange with the external environment for the considered shell, the effect of its geometric parameters and thermophysical characteristics of the materials of its component layers on the temperature field on the outer surface of the shell was investigated. The revealed new qualitative and quantitative regularities can be used to estimate temperature fields in composite elements of layered structures and in structures with one-sided coatings. The dependences of temperature distributions on geometric parameters and thermophysical characteristics obtained in this work are the basis of the theoretical basis for the analysis of temperature regimes of metal-ceramic cylindrical shells. In particular, metal-ceramic dental crowns to predict their temperature regimes are modeled by the two-layer metal-ceramic cylindrical shells described above, which are locally convectively heated by the external environment

MODELING THE ENTRY OF AIR CONTAMINANTS INTO A ROOM

A mathematical model of air contaminant (products of human activity) inflow into the isolated air space has been developed. On the basis of the formula modified by us the simulation of human respiration with carbon dioxide, water vapor and heat emission is implemented. The model also takes into account the heat input from the human body through clothing. Applying numerical modelling ANSYS CFD (Computational Fluid Dynamics) on the basis of continuity equations and Reynolds-Averaged Navier-Stokes equations "RANS" (Reynolds-Averaged Navier-Stokes) the following results on air medium state change in the isolated space were obtained: - the human respiratory cycle is modelled at simultaneous heat transfer from the body surface through clothes into the studied air space; - the exponential equation of the trend line of concentration to observation time was obtained; - monitoring and rendering (visualization) of changes in concentration, temperature and relative humidity in the space under study by time along the room height was performed. These results and regularities served as initial data for solving a number of model non-stationary problems on aerodynamics and heat and mass transfer in the room. The inverse problem of general exchange ventilation was to be solved. Changes in the state of the air environment initially contaminated with carbon dioxide, heat and water vapors were studied when people were in the studied space and the supply and exhaust ventilation was operating. Of the four air change schemes planned for the study, the results for one schemes are presented in this publication. The dynamics of assimilation of excess heat, humidity and carbon dioxide made it possible to assess the efficiency of ventilation systems and to predict improvements in their energy efficiency when air parameters are brought up to standard values.

Signal Separation Operator Based on Wavelet Transform for Non-Stationary Signal Decomposition.

This paper develops a new frame for non-stationary signal separation, which is a combination of wavelet transform, clustering strategy and local maximum approximation. We provide a rigorous mathematical theoretical analysis and prove that the proposed algorithm can estimate instantaneous frequencies and sub-signal modes from a blind source signal. The error bounds for instantaneous frequency estimation and sub-signal recovery are provided. Numerical experiments on synthetic and real data demonstrate the effectiveness and efficiency of the proposed algorithm. Our method based on wavelet transform can be extended to other time-frequency transforms, which provides a new perspective of time-frequency analysis tools in solving the non-stationary signal separation problem.

Modified RNN for Solving Comprehensive Sylvester Equation With TDOA Application.

The augmented Sylvester equation, as a comprehensive equation, is of great significance and its special cases (e.g., Lyapunov equation, Sylvester equation, Stein equation) are frequently encountered in various fields. It is worth pointing out that the current research on simultaneously eliminating the lagging error and handling noises in the nonstationary complex-valued field is rather rare. Therefore, this article focuses on solving a nonstationary complex-valued augmented Sylvester equation (NCASE) in real time and proposes two modified recurrent neural network (RNN) models. The first proposed modified RNN model possesses gradient search and velocity compensation, termed as RNN-GV model. The superiority of the proposed RNN-GV model to traditional algorithms including the complex-valued gradient-based RNN (GRNN) model lies in completely eliminating the lagging error when employed in the nonstationary problem. The second model named complex-valued integration enhanced RNN-GV with the nonlinear acceleration (IERNN-GVN) model is proposed to adapt to a noisy environment and accelerate the convergence process. Besides, the convergence and robustness of these two proposed models are proved via theoretical analysis. Simulative results on an illustrative example and an application to the moving source localization coincide with the theoretical analysis and illustrate the excellent performance of the proposed models.

The Study of Coordinate-Wise Decomposition Descent Method for Non-Stationary Optimization Problems

The Study of Coordinate-Wise Decomposition Descent Method for Non-Stationary Optimization Problems

Decentralized Counterfactual Value with Threat Detection for Multi-Agent Reinforcement Learning in mixed cooperative and competitive environments

This paper proposes a fully decentralized approach to address the challenge of general mixed cooperation and competition within the domain of Multi-Agent Reinforcement Learning (MARL). Conventional MARL approaches do not achieve full decentralization as they necessitate either the communication of implicit information or the retention of a centralized critic, rendering them impractical in mixed cooperative and competitive environments. To address these challenges, this paper proposes a Decentralized Counterfactual Value (DCV) to model the behaviors of other agents and mitigate the non-stationary problem, accompanied by a Threat Detection (TD) mechanism to discern latent competitive or cooperative relationships. In addition, DCVTD is incorporated into both value-based and policy-based RL paradigms with theoretical convergence guarantee. Finally, empirical validation across four representative environments demonstrates the superior performance of DCVTD in terms of collective returns, computational efficiency, and agent scalability over other fully decentralized approaches, centralized training with decentralized execution approaches, and alternative approaches involving agent modeling or reward shaping in comprehensive experiments.

Mathematical Modeling of Nonstationary Problems Related to Laser Thermochemistry of Methane in the Presence of Catalytic Nanoparticles

Mathematical Modeling of Nonstationary Problems Related to Laser Thermochemistry of Methane in the Presence of Catalytic Nanoparticles

Experience in using ceramics (Si3N4) as a material for rolling bearings of high-speed machines

To analyse the influence of the material of the rolling elements (steel and ceramics) of a high-speed ball bearing on the stresses in the contact zone of the rolling elements and rings and on friction losses in the contact zone.The study considers the outer ring of an angular contact ball bearing, which is loaded with additional centrifugal force. A nonstationary nonlinear volumetric interaction problem between the ball and the raceway was solved to determine the contact angle using the “DYNA” application package. The values of contact stresses for ceramic and steel rolling elements of a hybrid ball bearing are determined, as well as the value of deformations of balls and raceways based on Hertz's theory. The specific friction power deals with the differential slipping of the rolling elements relative to the raceway was estimated.Analysis of the behaviour of the bearings at different rotation speeds showed that at rotational speeds of more than 7000 rad/s, bearings with ceramic rolling elements of the considered standard size have advantages in contact strength. In addition, it was found out that at high rotational speeds, the friction power of the ceramic rolling elements is almost two times less than the friction power of the steel rolling elements.The research results relate to rolling ball bearings operating at a speed parameter dn of up to 4∙106 mm∙rpm and the analysis of friction losses is limited to losses from differential slip, which suggests further research of other components of losses.The study can justify the choice of bearing type (steel or ceramic rolling elements) depending on the operating speed and the lubrication and cooling system, which depends on the level of heat generation in the bearing.The work obtained original results of contact stresses and friction loss components for a certain type of bearing in a wide range of rotation speeds.

Computational decomposition and composition technique for approximate solution of nonstationary problems

Stable computational algorithms for the approximate solution of the Cauchy problem for nonstationary problems are based on implicit time approximations. Computational costs for boundary value problems for systems of coupled multidimensional equations can be reduced by additive decomposition of the problem operator(s) and composition of the approximate solution using particular explicit–implicit time approximations. Such a technique is currently applied in conditions where the decomposition step is uncomplicated. A general approach is proposed to construct decomposition–composition algorithms for evolution equations in finite-dimensional Hilbert spaces. It is based on two main variants of the decomposition of the unit operator in the corresponding spaces at the decomposition stage and the application of additive operator-difference schemes at the composition stage. The general results are illustrated on the boundary value problem for a second-order parabolic equation by constructing standard splitting schemes on spatial variables and region-additive schemes (domain decomposition schemes).

Исследование процессов передачи тепла в системе «трубопровод – датчик давления»

The one-dimensional non-stationary problem of temperature determination in the mechanical system «pipeline‒ pressure sensor» is studied. The solution of the problem is constructed using the method of separation of variables. Temperature distributions in the working medium in the pipeline and in the material of the sensor sensing element are obtained

Multi-agent reinforcement learning clustering algorithm based on silhouette coefficient

As an important branch of emerging artificial intelligence algorithms, multi-agent reinforcement learning (MARL) has shown strong performance in collaborative environments. It can utilize multiple agents to find the optimal set of strategies for solving sequential decision problem through trial-and-error. One of the main challenges facing multi-agent system is the non-stationarity problem, which brings poor convergence and seriously affects its performance. Clustering is a commonly used unsupervised analytical method in machine learning, which aims to group samples with similar internal properties into the same cluster. In this paper, we propose a MARL clustering algorithm based on silhouette coefficient (SC-MARLC), and use the trial-and-error strategy to find the best cluster groups. In SC-MARLC, we establish a mapping relationship between multi-agent and samples, construct a novel clustering model based on MARL, and design a good clustering subset structure based on the sample silhouette coefficient. The designed structure is helpful for multi-agent system to solve the non-stationary problem. Finally, we compare the performance of SC-MARLC with 11 existing clustering algorithms on fifteen public datasets. The results show that the new clustering algorithm performs best on ten datasets.