Stability Analysis Research Articles

Stability analysis of MHD Jeffery–Hamel flow using artificial neural network

The current research explores the useful impact of artificial neural networks (ANN) back-propagation along Levenberg-Marquardt Method (ANN-BLMM), for findng the influence of dimensionless numbers on the flow distribution pertaining magnetohydrodynamics (MHD) Jeffery–Hamel fluid amid two plates which are enclined at angles 2α. We have employed a numerical approach, ANN-BLMM to assess various aspects of our data, including testing, training, validation, Mean Square Errors (MSE), performance, and fitting. The methodology being used has been tested and validated through comparison with other results obtain numerically, showing extreme level of accuracy. Moreover, we have confirmed our findings through error histograms and regression tests. We used OHAM for the data set. Furthermore, we have also explored the influence of Reynolds number (R) on both flow and pressure distribution, visually representing our findings through graphical analysis. We have discussed about the nature and variations of velocity profiles within MHD Jefery–Hamel flow (MHDJHF), taking into account various values of Ha and Re in both convergent and divergent channels. It was discovered that a significant stabilizing influence of an increase in the magnetic field intensity was observed for both diverging and converging channel geometries and as the Hartman numbers rise, so does the fluid velocity. The absolute error is reduced to 10–2 to 10–6.

Small-Signal Stability Analysis of DC Ship Hybrid Power System With Energy Storage Device Based on Hybrid H-Matrix Model

Small-Signal Stability Analysis of DC Ship Hybrid Power System With Energy Storage Device Based on Hybrid H-Matrix Model

Stability Analysis of a T-S Prey-Predator Model with Disease in both Species using Fuzzy Impulsive Control

Stability Analysis of a T-S Prey-Predator Model with Disease in both Species using Fuzzy Impulsive Control

Stability Analysis for Joule Heating on the Fluid Flows over an Exponentially Shrinking Sheet

Stability Analysis for Joule Heating on the Fluid Flows over an Exponentially Shrinking Sheet

Physicochemical and stability analysis of mung bean protein hydrolysates with lipid peroxidation inhibition

This study investigated mung bean protein hydrolysates (MBPH) produced using neutral protease, examining their physicochemical properties, stability, and lipid peroxidation inhibition capabilities. The research revealed that MBPH molecular weight ranged from 17 to 26 kDa and perform various functions, including catalytic, nutrient storage, and binding. Stability assessments showed that MBPH are stable at 45 °C and pH of 7.5 but are light-sensitive and unstable in solution or when combined with sugars. Additionally, increased concentrations of digestive enzymes reduce MBPH stability. Antioxidant tests in vitro and in Caenorhabditis elegans confirmed MBPH's ability to neutralizing radicals, enhance antioxidant enzyme activities, and reduce lipid peroxidation, thereby protecting against oxidative damage. Furthermore, in vivo experiments showed that MBPH extend the lifespan of worms and reduced their body lipid content, indicating potential benefits in mitigating cholesterol-related damage. This research demonstrates the potential of MBPH in inhibiting lipid peroxidation.

Stability Analysis of a Discrete-Time Limit Cycle Model Predictive Controller

Stability Analysis of a Discrete-Time Limit Cycle Model Predictive Controller

Postural and Spinal Stability Analysis for Different Floor Sitting Styles

In contrast to Western countries, traditional floor-seating cultures are prevalent in Korea, Japan, the Middle East, and Africa, where sitting on the floor in static positions such as squatting, kneeling, or sitting cross-legged is common. Most studies on sitting posture have predominantly focused on chair sitting in Western cultures, resulting in a cultural bias. This study aimed to investigate the effects of different cushion types (floor and traditional cushions of 3-cm, 5-cm, and 8-cm thickness) and seating postures (cross-legged, mother’s leg, and kneeling) on measures of postural stability, trunk muscle activity, rotational spinal stability, and subjective postural stability in an Asian population. Forty right-hand and right-foot-dominant volunteers who did not experience activity-limiting back pain in the past 12 months were recruited. Multivariate analyses of variance (MANOVA) and ANOVA with a repeated-measures design were employed to assess the within-subject effects of the cushion type and seating posture. An alpha value of 0.05 was set for statistical significance. The results of this study suggest that preventing lordosis posture, seating on the floor, and maintaining a kneeling posture may reduce the loss of balance and trunk muscle fatigue. These results emphasize the need for additional ergonomic studies that focus on the seating traditions of Asian cultures.

A comprehensive mathematical analysis of fractal–fractional order nonlinear re-infection model

In recent times, various real word problems including infectious diseases, engineering problems, and chemical processes, etc are modelled by using differential equations with fractals and fractional orders. The mentioned area provides a powerful tool to investigate the aforesaid problems from different perspectives like analysis, numerical investigation, and qualitative theory. Similarly, one of the global issue is devoted to re-infection of viral diseases like COVID-19. The said behaviour has produced very saviour impact on human life worldwide. Also, this is very critical for health system of a country as well as for its economics situation. To study the aforesaid phenomenon of re-infection, a hybrid type fractal–fractional three compartments model is formulated. The basic results related to boundedness, positivity, equilibrium points, basic reproductive number, and sensitivity analysis of the basic threshold are included in the theoretical aspect. Additionally, the Volterra–Lyapunov approach is used to establish both local and global stability analysis under fractals and fractional derivative. Furthermore, utilizing techniques from numerical functional analysis and fixed point theory, the existence and Hyers–Ulam stability of the solutions are also examined. A numerical algorithm based on Lagrange’s interpolation polynomials is extended to simulate the results of various compartments. Graphical interpretations corresponding to different fractals–fractional order values are presented. For verification of our numerical results, a comparison is provided between the real and simulated data. Here it should be kept in mind that the differential operator of fractals–fractional order is considered with Mittag-Leffler kernel. The mentioned operator is more general among the available fractals fractional differential operators in literature.

Physical and mechanical characterization of solid waste collected from rural areas of China: Experimental study

To support the landfill design and waste management in rural areas of China, solid waste covering eight provisional regions was collected and tested in the laboratory to characterize its physical properties (composition, moisture content, specific gravity, dry unit weight) and mechanical properties (compressibility and shear strength). The results show that, compared with solid wastes from urban areas (MSW), solid waste from rural areas (RSW) comprised a much lower content of soil-like, gravel, and inert waste and a significantly higher content of combustible waste, thereby yielding a much lower specific gravity and dry unit weight. Similar to MSW, the compression index of RSW correlated well with its physical properties. However, its strength properties displayed divergence. Notably, the friction angle φ' of RSW remained relatively consistent, ranging from 28.4° to 30.9°. This narrow range is attributed to RSW's higher combustible-to-inert (CI) ratio compared to MSW. The cohesion intercept c' of RSW ranged from 13.5 to 24.9 kPa, showing a positive correlation with the fiber content without considering contribution from paper waste. This finding combined with data from the literature further revealed that the trend of increasing cohesion intercept with increasing fiber content became weakened over time. Relationships between φ' and c' versus C/I for RSW observed in this study will serve as an extension to the existing finding reported for MSW in the literature, i.e., for predominately combustible waste with C/I exceeding 10, constant values of strength parameters (i.e., moderate values φ' = 30°, c' = 20 kPa) are recommended. The results of this study are useful for the capacity design and slope stability analysis of landfills as well as waste recycle and reuse, ensuring a sustainable development of environment in China.

A class of nonlinear ship stability analysis: Stochastic dynamics with time-delayed control in crosswind and wave conditions

The impact of ocean waves and crosswinds on ships has long been a focal point of research for many scholars. This paper proposes a stochastic ship rolling model influenced by crosswinds, ocean waves, and time delays. The safe operating region for ship navigation is presented through the phase space of the system. A quantitative discussion of the system is conducted using the stochastic Melnikov function, and the stochastic P-D bifurcation of the system is discussed using topological data analysis techniques. The research indicates that incorporating time delay feedback can effectively enhance the system’s stability.

Brinkman–Bénard convection in a box with temperature modulation

A bounded porous box saturated with Newtonian fluid and subjected to a sinusoidal temperature gradient has various practical applications, such as solar energy storage, groundwater remediation, food processing, and chemical reactors. We address the generalization of the classical Rayleigh–Bénard convection problem in a horizontal fluid layer in an infinitely large domain heated from below to a finite three-dimensional box. We also look into a more intricate form of the modulated Rayleigh–Bénard problem in which the temperature at the bottom boundary varies sinusoidally. The Rayleigh number quantifies the non-sinusoidal part of the temperature gradient, while the amplitude and frequency of modulation describe the sinusoidal one. The critical Rayleigh number is determined using linear and nonlinear stability analyses; for the latter, the energy method is used. There is a possibility of subcritical instabilities, as evidenced by the energy stability estimates being lower than the linear ones. Furthermore, eigenvalues are obtained as a function of aspect ratios, modulation amplitude, and frequency for varying Darcy numbers. Modulation amplitude more significantly triggers a change in flow patterns at the onset of convection compared to the effect of other parameters. Considering water-saturated porous media made up of different materials, we report the critical temperature difference between lower and upper surfaces required for the onset of convection. In addition, a comparison between such a temperature difference obtained from linear theory and the energy method is also provided in the same manner. It is observed that subharmonic instability occurs for all considered porous media packed densely or sparsely.

General synthetic iterative scheme for rarefied gas mixture flows

The numerical simulation of rarefied gas mixtures with disparate mass and concentration is a huge research challenge. Based on our recent kinetic modelling for monatomic gas mixture flows, this problem is tackled by the general synthetic iterative scheme (GSIS), where the mesoscopic kinetic and macroscopic synthetic equations are alternately solved by the finite-volume discrete velocity method. Three important features of GSIS are highlighted. First, the synthetic equations are precisely derived from the kinetic equation, naturally reducing to the Navier-Stokes equations in the continuum flow regime; in other flow regimes, the kinetic equation provides high-order closure of the constitutive relations to capture the rarefaction effects. Second, these synthetic equations, which can be solved quickly, help to adjust the kinetic system to relax rapidly toward the steady state. Furthermore, in such a two-way coupling, the constraint on the spatial cell size is relieved. Third, the linear Fourier stability analysis demonstrates that the error decay rate in GSIS is smaller than 0.5 for various combinations of mass, concentration and viscosity ratios, such that the error can be reduced by three orders of magnitude after 10 iterations. The efficiency and accuracy of GSIS are demonstrated through several challenging cases covering a wide range of mass ratio, species concentration, and flow speed.

Artificial neural network prediction of wellbore stability in offshore shallow formations

Wellbore instability is one of the most critical challenges during drilling, which may result in complex problems such as stuck pipe, high torque and mud loss, impeding the drilling progress and increasing the cost of drilling operations. Offshore shallow formations are characterized by weak consolidation and low strength, causing serious wellbore collapse frequently. The traditional physics-based wellbore instability models attempt to predict the risk of failure of the wellbore for given drilling fluid densities and provide optimal fluid density for safe drilling. However, these models generally involve quite a few empirical coefficients, determination of which heavily rely on the field experiences of the engineers, and thus the results may vary greatly from person to person. In this study, an artificial neural network (ANN) model has been established for wellbore stability prediction, aiming to reduce the subjectivity while mapping the drilling performance of neighboring wells into the predicted results. Eleven factors that may affect wellbore stability have been identified from the prevailing physics-based model and used as the input of the ANN model, while the wellbore enlargement rate (WER) is used as the output to quantify the wellbore stability performance. The model has been trained using data from 5 wells drilled in the offshore shallow formations of the Bohai Bay Basin in east China and then used to predict the WER of another well in the same region. The results show that the mean absolute percentage error is 6.113%, and at most well depths the predicted wellbore diameter deviate from the measured values not more than 5%. Comparison of the ANN model and some other machine learning models, including random forest model, decision trees model, linear regression model, was conducted, which demonstrated the best performance of the ANN model in terms of the predicted wellbore diameter profile. Finally, the potential application of the ANN model in optimizing mud weight has been illustrated through the predicted wellbore diameter profiles for different mud weights. It is worth noting that the method presented in this paper is of physics and data-driven nature and provides a new research insight for wellbore stability analysis.

Convergence of reputations under indirect reciprocity

Previous research has shown how indirect reciprocity can promote cooperation through evolutionary game theoretic models. Most work in this field assumes a separation of time-scales: individuals’ reputations equilibrate at a fast time scale for given frequencies of strategies while the strategies change slowly according to the replicator dynamics. Much of the previous research has focused on the behaviour and stability of equilibria for the replicator dynamics. Here we focus on the underlying reputational dynamics that occur on a fast time scale. We describe reputational dynamics as systems of differential equations and conduct stability analyses on their equilibria. We prove that reputations converge to a unique equilibrium under a solitary observer model for each of the five standard norms and whether assessments are public or private. These results confirm a crucial but previously understudied assumption underlying the theory of indirect reciprocity for the most studied set of norms.

The in situ stress prediction of a fractured shale reservoir based on amplitude variation with angle and azimuth inversion: A case study from Southwest China

In situ stress estimation of a shale reservoir is critical for the design of shale hydraulic fracturing and wellbore stability analysis. Fractured shales have orthogonal anisotropy (OA) because of the presence of vertical fractures and lamination. However, the existing in situ stress estimation method mainly focuses on transversely isotropic media. To accommodate orthogonally anisotropic media, an in situ stress estimation method is developed by using amplitude variation with angle and azimuth inversion and linear-slip theory. First, an orthogonal anisotropic medium is introduced to characterize the fractured shale by using a linear-slip model, and then we formulate a reflection coefficient approximation for OA media to perform the seismic inversion. Next, a fracture weakness inversion strategy that incorporates the vertically transverse isotropic background is developed to obtain the stiffness matrix of the media. Finally, the in situ stresses of the OA medium are formulated by using a stress-strain relationship. Inversion tests and a real data application indicate that our method is effective.

Engineering Geological Investigation of Gololcha Dam for Evaluation of Leakage and Abutment Slope Stability, Eastern Ethiopia

The Ethiopian economy is primarily dependent on agriculture, making the construction of water harvesting facilities, such as dams, crucial for improving the productivity of this sector. The ongoing construction of the Gololcha dam on the Kurkura River located in Eastern Ethiopia aims to enhance irrigation schemes in the region. However, the dam site's complex geological and structural conditions pose challenges related to leakage and slope instability. Hence, this study focuses on addressing the abutment slope stability and leakage condition of this dam. This study employed kinematic analysis and the Limit Equilibrium Method (LEM) to assess slope stability. Additionally, engineering geological mapping, discontinuity surveys, seismic refraction tomography (SRT), and in-situ permeability testing were used to evaluate the leakage condition of the dam site. Notably, the permeability and SRT survey results identified potential leakage zones to the depth of 35, 30, and 35 m at the left, right, and central foundations of the dam, respectively. The kinematic method revealed one planar and two wedge modes of failure in the slope section covered by slightly weathered and fractured basalt rock at the right abutment. Further stability analysis of these two modes of failures via LEM analysis indicated slope instability under saturated conditions, emphasizing the role of pore water pressure. Furthermore, LEM modeling was directly utilized using the Slide 6.0 software to analyze the slope stability condition of the left abutment of the dam. This modeling also uncovered instability under saturated conditions. Based on the study findings, this study recommended curtain grouting to address potential leakage, as well as slope flattening and removing unstable rock wedges and loose material to stabilize unstable slope sections.

Transient Stability Analysis of Grid-Forming Converters During Presynchronization Process in Islanded Mode

Transient Stability Analysis of Grid-Forming Converters During Presynchronization Process in Islanded Mode

Isolation, purification, characterization and stability analysis of melanin pigment from Mesona chinensis

In this study, the isolation and purification of melanin pigment from Mesona chinensis (MCM) were conducted, and the structural characterization and stability evaluation of MCM were performed. The results indicate that MCM is consistent with the spectral features of catechins and polyphenols, identified the stretching vibrations of functional groups such as OH, CH, CO, and CO. It is inferred that the structure of MCM is consistent with that of theophylline and it is mainly composed of phenolic acids, terpenoids, and organic acids. Stability evaluations indicate that MCM exhibits stability under white light, ultraviolet (UV) light, neutral, and alkaline environments, and it shows low sensitivity to reducing agents.

Intelligent frequency control of AC microgrids with communication delay: An online tuning method subject to stabilizing parameters

Smart control techniques have been implemented to address fluctuating power levels within isolated microgrids, mitigating the risk of unstable frequencies and the potential degradation of power supply quality. However, a challenge lies in the fact that employing these computationally complex methods without stability preservation might not suffice to handle the rapid changes of this highly dynamic environment in real-world scenarios over communication delays. This study introduces a flexible real-time approach for the frequency control problem using an artificial neural network (ANN) constrained to stabilized regions. Our solution integrates stabilizing PID controllers, computed through small-signal analysis and tuned via an automated search for optimal ANN weights and reinforcement learning (RL)-based selected constraints. First, we design stabilizing PID controllers by applying the stability boundary locus method and the Mikhailov criterion, specifically addressing communication delays. Next, we refine the controller parameters online through an automated process that identifies optimal coefficient combinations, leveraging a constrained ANN to manage frequency deviations within a restricted parameter range. Our approach is further enhanced by employing the RL technique, which trains the tuning system using an interpolated stability boundary curve to ensure both stability and performance. This one-of-a-kind combination of ANN, RL, and advanced PID tuning methods is a big step forward in how we handle frequency control problems in isolated AC microgrids. The experiments show that our solution outperforms traditional methods due to its reduced parameter search space. In particular, the proposed method reduces transient and steady-state frequency deviations more than semi- and unconstrained methods. The improved metrics and stability analysis show that the method improves system performance and stability under changing conditions.

Combining approach of collocation and finite difference methods for fractional parabolic PDEs

This research aims to estimate the solutions of fractional-order partial differential equations of spacial fractional and both time-space fractional order. For this, we use finite differences for time derivatives and the well-known collocation method for space derivatives with lower-order Bernstein polynomials as basis functions. We explain the mathematical formulations in detail. Convergence and stability analysis of the space–time fractional diffusion equation with the source term is reported subsequently. Three numerical examples are considered for demonstrating the accuracy and reliability of the proposed method.