Convergence Of Method Research Articles

Large deviation principle for a 2D liquid crystal model with multiplicative noise

In this paper, we consider a stochastic 2D liquid crystal system with a small multiplicative noise of Gaussian type, which models the dynamic of nematic liquid crystals under the influence of stochastic external forces. We derive a large deviation principle for the model. The proof relies on the weak convergence method that was introduced in [A. Budhiraja, P. Dupuis and V. Maroulas, Variational representations for continuous time processes, Ann. Inst. Henri Poincaré Probab. Stat. 47(3) (2011) 725–747] and based on a variational representation on infinite-dimensional Brownian motion.

Phase transition of parabolic Ginzburg–Landau equation with potentials of high‐dimensional wells

AbstractIn this work, we study the co‐dimensional one interface limit and geometric motions of parabolic Ginzburg–Landau systems with potentials of high‐dimensional wells. The main result generalizes the one by Lin et al. (Comm. Pure Appl. Math. 65 (2012), no. 6, 833–888) to a dynamical case. In particular combining modulated energy methods and weak convergence methods, we derive the limiting harmonic heat flows in the inner and outer bulk regions segregated by the sharp interface, and a non‐standard boundary condition for them. These results are valid provided that the initial datum of the system is well‐prepared under natural energy assumptions.

Improved approximation-free control for the leader-follower tracking of the multi-agent systems with disturbance and unknown nonlinearity.

Approximation-free control effectively addresses uncertainty and disturbances without relying on approximation techniques such as fuzzy logic systems (FLS) and neural networks (NNs). However, singularity problems-where signals exceed preset boundaries under dynamic operating conditions-remain a challenge. This paper proposes an improved approximation-free control (I-AFC) method for the multi-agent system, which introduces a novel singularity compensator, providing a low-complexity design with exceptional adaptability while reducing the risk of singularity issues under changing working conditions (random initial values, system parameter variations, and changes in topology graph and followers' dynamics). Furthermore, theoretical analysis guides parameter selection by demonstrating the method's favorable convergence rate and appropriate control gain. Simulation results validate the approach.

Design of Power Economic Dispatch Method Integrating Differential Evolution and PSO

As energy demand continues to grow and environmental problems become increasingly serious, optimizing the economic dispatch of the power system is crucial to ensuring the sustainability and economic benefits of energy supply. To ensure the safe operation of the power system, reduce power generation costs as much as possible, and develop a method that can adapt to the needs of different power systems, the experiment combines the differential evolution algorithm with the power economic dispatch problem and proposes a method based on improved differential evolution. Electric power economic dispatch method with particle swarm optimization algorithm. The experiment first introduces a moderate interference strategy to appropriately adjust the position of the particles; then combines the local mutation strategy to enhance the searchability of the differential evolution algorithm in the solution space and achieve good economic dispatch. The results show that when running on the F11 test set and F21 test set, when the system iterates to the 26th and 32nd times respectively, the loss function of the method constructed in the experiment begins to have a minimum value and remains stable thereafter. In addition, on the F11 test set, when the number of iterations is 150, this method has a minimum time of 0.153s. While running the loop for the first time on System 1, the total cost of this approach was only $1.01× 104. Through the actual operation of power generation equipment, under the operation of this method, the power system can ensure optimal operating power of each power generation equipment unit based on ensuring optimal cost. It can be seen from the above results that this method provides power system operators and decision-makers with a new tool to help them maximize cost-effectiveness while ensuring system stability and meeting power demand. In addition, the method's superior convergence and stability can effectively improve the solution's accuracy and speed and has strong practicality and promotion value.

Research on the Innovation of College English Teaching Mode from the Perspective of VR/AR Technology

In order to improve the innovation effect of English teaching mode, this paper applies Augmented Reality (AR) and Virtual Reality (VR) technology to the innovation of college English teaching mode to promote the improvement of English teaching quality. Moreover, this paper accelerates ray tracing through Compute Unified Device Architecture (CUDA)’s parallel operations, hierarchical bounding box space structure, and a series of optimization methods for Monte Carlo estimation sampling convergence. Furthermore, this paper computes global illumination by collecting lighting information in textures through voxel cone tracking. In addition, this paper proposes attenuation based on normal weights, which can reduce the normal consistency problem of voxel direct lighting calculations. Through the experimental research, it can be seen that the college English teaching model based on VR/AR technology proposed in this paper can effectively improve the effect of English teaching

Averaging principle for two-time-scale stochastic functional differential equations with past-dependent switching

<p>This paper aimed to establish the averaging principle for the two-timescale stochastic functional differential equations with past-dependent switching. Initially, the existence and uniqueness of solutions, as well as moment estimates, were obtained by using classical interlacing techniques. Furthermore, the interaction between the fast and slow processes was derived based on the properties of the Poisson random measure. Subsequently, employing the coupling method and the integration by parts formula for the generator, the exponential ergodicity of the frozen Markov chain and the Lipschitz continuity of its invariant measures were proved. In addition to the challenges posed by the dependence on history, the Lipschitz condition under uniform norms that the generator satisfies also introduced computational and proof difficulties. Therefore, more refined estimates were provided for the segment process. Based on these results, together with weak convergence and martingale methods, the averaging principle for the original system was established. Finally, two examples were provided to illustrate the differences between the results presented here and the classical results.</p>

Accelerated Convergence Method for Flow Field Based on DMD-POD Combined Reduced-Order Optimization Model

Accelerated Convergence Method for Flow Field Based on DMD-POD Combined Reduced-Order Optimization Model

THERMALLY STRATIFIED FLOW OF POWELL EYRING HYBRID NANOFLUID WITH JOULE HEATING OVER A POROUS STRETCHING CYLINDER

These days, scientists are eager to investigate the management of illnesses brought on by a lack of magnesium. Hypomagnesaemia is an extra trigger for a number of illnesses like nausea, vomiting, drowsiness, and appetite loss, due to blood magnesium deficiency. Magnesium nanoparticles are injected into the blood (base fluid) to meet the shortage. Furthermore, magnetic nanomaterials have received significant attention for their potential use in medicine; iron oxide nanoparticles, in particular, have shown to be highly effective because of their basic chemical makeup, which makes them biocompatible and biodegradable. Considering the aforementioned uses, this study focuses on the hybrid nanofluid under the suspension of Mg-Fe3O4 nanoparticles through Powell-Eyring (Blood) fluid model originated by a permeable cylinder. The heat transport parameters are revealed by incorporating Joule heating, thermal radiation and viscous dissipation. The hybrid nanofluid is subjected to mixed convection effects and magnetic field. By suitable transformations, dimensionless governing equations are derived as a system. Using comparing graphs, the physical behaviour of the temperature and velocity fields are explained. Graphs that match relevant characteristics are used to reveal skin friction and heat transmission. The model’s solution is obtained by applying the well-known Keller-Box method of convergence. The flow accelerates as the buoyancy convection parameter increases. Additionally, it is noted that as the magnetic parameter and Eckert number increase, the temperature rises.

An efficient computational framework for data assimilation of fractional-order dynamical system with sparse observations

We introduce an efficient computational framework for data assimilation of fractional dynamical systems, extending traditional data assimilation techniques to fractional models. This framework offers effective computational methods that eliminate the need for complex adjoint model derivations and algorithm redesign. We establish the fundamental problem formulation, develop both the AtD and DtA approaches, and derive adjoint forms and numerical schemes for each method. Additionally, we create a unified fractional-order variational data assimilation framework applicable to both linear and nonlinear models, incorporating both explicit and implicit discrete methods. Specific discretization schemes and gradient formulas are derived for three distinct types of fractional-order models. The method's reliability and convergence are verified, and the effect of observation sparsity and quality is examined through numerical examples.

Asymptotic analysis of a coupled ODE‐PDE system arising from heterogeneous diffusion‐reaction kinetics

AbstractThis contribution is concerned with the well‐posedness and homogenization of an ordinary differential equation (ODE) of Arrhenius‐type coupled with a doubly nonlinear parabolic partial differential equation (PDE) with rapidly oscillating coefficients and taking into account disparate diffusion‐reaction time scales, including regularly as well as singularly perturbed problems. The ODE‐PDE system is spatially dependent and is subjected to Robin‐type boundary conditions. Such problems are used to model a variety of processes and phenomena such as combustion and exothermal chemical reactions. We will have a special look at the questions of the existence, uniqueness, boundedness, and the asymptotic limit of the microscale problem by applying the two‐scale convergence and unfolding method. A numerical example illustrates both the expected behavior of the approximated solutions as well as the capability of the proposed upscaled models.

Research on a Multidimensional Dynamic Environmental Assessment: Based on the PSR Analysis Framework and Bootstrap-DEA Model, in the Yellow River Basin, China

An environmental assessment is a complex and interrelated entity. A multidimensional and dynamic environmental assessment can directly reflect the effectiveness and capacity of the ecological governance system. Assessing the factors influencing the resource–environment coupling efficiency in the Yellow River Basin is crucial for advancing environmental management and regulation, enhancing public participation and transparency, as well as fostering international exchange and cooperation. This study uses the PSR analysis framework and the Bootstrap-DEA model to measure the resource–environment coupling efficiency. It employs spatial autocorrelation, kernel density estimation, Dagum Gini coefficient analysis, σ-convergence, and spatial beta convergence methods to explore the multi-level spatial pattern and convergence trend of the resource–environment coupling efficiency. The findings indicate that overall resource–environment coupling efficiency exhibits minimal temporal variation characterized by a hierarchy of upstream > downstream > middle reaches, alongside a spatial differentiation trend marked by small agglomeration coupled with significant dispersion. Additionally, regional disparities reveal a distribution pattern of downstream > middle reaches > upstream. Notably, while there are no σ-convergence characteristics, evidence supporting spatial β-convergence suggests that these efficiencies will converge toward a steady-state level over time.

Large deviation for slow-fast McKean–Vlasov stochastic differential equations driven by fractional Brownian motions and Brownian motions

In this paper, we consider slow-fast McKean–Vlasov stochastic differential equations driven by fractional Brownian motions with Hurst parameter [Formula: see text] and Brownian motions. We give a definition of the large deviation principle (LDP) on the product space related to fractional Brownian motion and Brownian motion, which is different from the traditional definition for LDP. Under some proper assumptions on coefficients, LDP is investigated for this type of equations by using the weak convergence method.

3D complex dispersion curves and attenuation characteristics based on Drude-Lorentz oscillators for Lamb wave in various metal-piezoelectric composites

Given that many micro-nano piezoelectric acoustic devices operate at very high frequencies, the dissipation caused by metal electrodes significantly affects their performance (e.g., quality factor), but these dissipation characteristics cannot be explained by conductivity at high frequencies. This study uses the Drude-Lorentz oscillator model, incorporating the frequency-dependent dielectric properties of metals, which in physics refer to electron oscillations at high frequencies, to investigate the three-dimensional (3D) complex dispersion curves and attenuation characteristics of Lamb waves in metal-piezoelectric composites. Five commonly used electrode metals (Pt, Al, Ag, Au, Cu) are analyzed to reveal the widespread attenuation characteristics. The Multidimensional Moduli Ratio Convergence Method (MMRCM) is employed, which utilizes the convergence and divergence of the moduli ratio to accurately locate zeros of complex dispersion equations. Meanwhile, multidimensional scanning is adopted to ensure comprehensive identification of minima moduli points. Two primary attenuation characteristics are identified: (1) attenuation trends related to the real part of the wavenumber for different branches, and (2) significant jumps in attenuation due to mode shape conversions in metals with veering regions. Furthermore, a size-dependent attenuation characteristic is observed, showing a quadratic increase in attenuation as the composite structure’s total thickness decreases. These findings provide crucial insights for optimizing the design and performance of micro-nano devices where precise control over wave attenuation and dispersion is essential.

A two-point Newton-like method of optimal fourth order convergence for systems of nonlinear equations

A two-step Newton-like method is proposed to efficiently solve the systems of nonlinear equations. Extending Newton scheme to a next step as weighted-Newton iteration, the proposed iteration scheme shows optimal fourth order of convergence. The primary objective in formulating the method is to keep the computational efficiency as high as possible. In this context, the efficiency analysis is thoroughly examined using a systematic approach, wherein the efficiency index of the new method is compared with those of existing methods of comparable complexity. Numerical experimentation is performed to investigate the computational efficacy of the developed method. Results indicate higher efficiency and numerical precision in comparison to the existing counterparts.

Consensus Seeking in Large-Scale Multiagent Systems With Hierarchical Switching-Backbone Topology.

Recent developments in multiagent consensus problems have heightened the role of network topology when the agent number increases largely. The existing works assume that the convergence evolution typically proceeds over a peer-to-peer architecture where agents are treated equally and communicate directly with perceived one-hop neighbors, thus resulting in slower convergence speed. In this article, we first extract the backbone network topology to provide a hierarchical organization over the original multiagent system (MAS). Second, we introduce a geometric convergence method based on the constraint set (CS) under periodically extracted switching-backbone topologies. Finally, we derive a fully decentralized framework named hierarchical switching-backbone MAS (HSBMAS) that is designed to conduct agents converge to a common stable equilibrium. Provable connectivity and convergence guarantees of the framework are provided when the initial topology is connected. Extensive simulation results on different-type and varying-density topologies have shown the superiority of the proposed framework.

An efficient Q-learning integrated multi-objective hyper-heuristic approach for hybrid flow shop scheduling problems with lot streaming

Efficient scheduling in flow shop environments with lot streaming remains a critical challenge in various industrial settings, necessitating innovative approaches to optimize production processes. This study investigates a hybrid flow shop scheduling problem dominant in real-world printed circuit board assembly shops. A novel multi-objective hyper-heuristic combining Q-learning, i.e., two-stage improved spider monkey optimization (TS-ISMO), is tailored to address the complexities of the flow shop scheduling problems. The proposed method aims to simultaneously optimize conflicting objectives such as minimizing makespan, total energy consumption, and total tardiness time while incorporating lot streaming considerations. For multi-objective hyper-heuristic techniques, the algorithm dynamically selects and adapts a diverse set of low-level heuristics to explore the solution space comprehensively and strike a balance among competing objectives. The proposed TS-ISMO algorithm incorporates several significant features aimed at enhancing its performance. These features encompass hybrid heuristics for solution initialization, a contribution value method for comprehensive convergence and diversity assessment, diverse evolutionary state judgments to promote the algorithm’s balance between exploration and exploitation capabilities, and a Q-learning strategy for self-adaptive parameter tuning. The integration of Q-learning facilitates intelligent parameter control, enabling the algorithm to autonomously adjust its behavior based on past experiences and evolution dynamics. This adaptive mechanism enhances convergence speed and solution quality by effectively guiding the search process toward promising regions of the solution space. Extensive computational experiments are conducted on benchmark instances of hybrid flow shop scheduling problems with lot streaming to evaluate the performance of the proposed algorithm. Comparative analyses against state-of-the-art approaches demonstrate its superior solution quality and computational efficiency.

Factor structure and validation of the electronic form of the Oxford Happiness Questionnaire in patients with COVID-19

Background and Objectives: Background and Aim: Validity Scale Validation can help identify coronavirus disease patients; therefore, the aim of this study was to evaluate the validation of the electronic form of the Oxford Happiness Questionnaire in patients with COVID-19. Methods: This study is instrumental psychometrics that the statistical population includes all patients in 19 cases in Tehran. The number of samples was determined based on psychometric criteria to be 100 for the predictive validity section and 251 for the convergence validity section. Samples were selected by cluster sampling. Research data were collected electronically through two questionnaires of happiness (Oxford) and happiness of positive psychological characteristics by sending the questionnaire link to the participants' mobile phones. To evaluate the validity of the scale, content validity, convergence, and factor analysis methods were used. The reliability of the scale was assessed by internal consistency methods and class reliability. Results: The results of exploratory factor analysis showed that the researcher-made questionnaire consists of three factors and has good validity and reliability. The second-order confirmatory factor analysis also confirmed the three-factor model. This questionnaire was administered along with the short form of the Oxford Happiness Scale, which had 13 items of good reliability and validity. Conclusion: The Oxford Happiness Scale in COVID-19 patients can be used to assess happiness in COVID-19 patients.

Homogenization of a Thermoelastic Bristly Structure Immersed in a Thermofluid

The article considers the mathematical model describing the joint motion of a viscous compressible heat-conducting fluid and a thermoelastic plate with a fine two-level thermoelastic bristly microstructure attached to it. The bristly microstructure consists of a great amount of taller and shorter bristles, which are periodically located on the surface of the plate, and the model under consideration incorporates a small parameter, which is the ratio of the characteristic lengths of the microstructure and the entire plate. Using classical methods in the theory of partial differential equations, we prove that the initial-boundary value problem for the considered model is well-posed. After this, we fulfill the homogenization procedure, i.e., we pass to the limit as the small parameter tends to zero, and, as a result, we derive the effective macroscopic model in which the dynamics of the interaction of the ‘liquid–bristly structure’ is described by equations of two homogeneous thermoviscoelastic layers with memory effects. The homogenization procedure is rigorously justified by means of the Allaire–Briane three-scale convergence method. The developed effective macroscopic model can potentially find application in further mathematical modeling in biotechnology and bionics taking account of heat transfer.

A Study of Algorithms for the p th Root of Matrix

Some results for Pth root of square matrix are revived. It shows that matrix sign function and Wiener- Hopf factorization plays important role in Pth root of matrix. Some new algorithms for computing P th root numerically can design by these results. We can analyze Stability properties of iterative methods for convergence.

European institutional quality and carbon emissions: Convergence club analysis

If the quality of institutions in the European Union (EU) converged, harmonized policies could achieve climate neutrality. This paper examines institutional convergence within the EU using log-t regression, allowing for the possibility of multiple equilibria. It also analyzes how overall institutional quality affects carbon dioxide (CO2) emissions in three identified convergence clubs over thirty years. Driscoll-Kraay and Prais-Winsten standard errors estimators are used, accounting for economic growth, renewable energy, industrialization, urbanization, innovation, and exogenous shocks. The results show that institutional quality affects CO2 emissions differently across clubs, emphasizing customized policy approaches. Addressing endogeneity, a two-stage least squares fixed effects estimator reveals that institutional quality has a negative, but statistically insignificant, effect on CO2 emissions in both the highest and lowest institutional quality clubs, while significantly increasing emissions in the mid-tier club. Economic growth increases CO2 emissions, whereas renewable energy consumption reduces them across all convergence clubs and methods. Other factors vary across clubs.