Stability Analysis Research Articles

Landslide hazard vulnerability assessment using surface wave method coupled with slope stability analysis: a case study

Landslide hazard vulnerability assessment using surface wave method coupled with slope stability analysis: a case study

Periodic Solutions of Strongly Nonlinear Oscillators Using He’s Frequency Formulation

In this paper, we address several scientific and technological challenges with a novel non-perturbative approach (NPA), simplifying processing time compared to traditional methods. The proposed approach transforms nonlinear ordinary differential equations into linear ones, akin to simple harmonic motion, producing a new frequency. This method yields highly accurate outcomes, surpassing well-known approximate methodologies, as validated through numerical comparisons in mathematical software. The congruence between numerical solution tests and theoretical predictions further supports our findings. While classical perturbation methods rely on Taylor expansions to simplify restoring forces, NPA also enables stability analysis. Thus, for analyzing approximations of highly nonlinear oscillators in mathematical software, NPA serves as a more reliable tool.

Fractional Dynamics of Cassava Mosaic Disease Model with Recovery Rate Using New Proposed Numerical Scheme

Food security is a basic human right that guarantees humans an adequate amount of nutritious food. However, plant viruses and agricultural pests cause real damage to food sources, leading to negative impacts on meeting the human right of obtaining a sufficient amount of food. Understanding infectious disease dynamics can help us to design appropriate control and prevention strategies. Although cassava is among the most produced and consumed crops and greatly contributes to food security, cassava mosaic disease causes a decrease in photosynthesis and reduces cassava yield, resulting in a lack of crops. This paper developed a fractional model for cassava mosaic disease (CMD) dynamics based on the Caputo–Fabrizio (CF) fractional derivative to decrease cassava plant infection. We used fixed-point theory to study the existence of a unique solution in the form of the CMD model. A stability analysis of the model was conducted by using fixed-point theory and the Picard technique. A new numerical scheme was proposed for solving the nonlinear system of a fractional model in the sense of the CF-derivative and applied to obtain numerical simulations for a fractional model of the dynamics of CMD. The obtained results are described using figures that show the dynamics and behaviors of the compartments of CMD, and it is concluded that decreasing the population of whitefly vectors can prevent cassava plants from becoming infected better than increasing the recovery rate of the infected cassava plants.

Based on graph theory, design of distributed control system for multi-quadcopter UAVs

This paper addresses the formation control system for multi-quadcopter UAVs, proposing a control strategy based on finite-time stability theory. It designs position controllers with a dual power structure and attitude controllers combined with non-singular terminal sliding mode to achieve fast convergence and high-precision tracking. Through Lyapunov stability analysis, the paper proves the finite-time convergence of the control strategy. Simulation experiments validate the method's excellent performance in formation establishment, maintenance, and complex trajectory tracking, demonstrating rapid convergence, high precision, and strong disturbance rejection capabilities. This research provides theoretical and technical support for cooperative control of multi-quadcopters.

Analysis of a Resistive-Capacitive Shunted Josephson Junction with Topologically Nontrivial Barrier Coupledto a RLC Resonator

This paper presents the resistive-capacitive shunted Josephson junction (RCSJJ) with a topologically nontrivial barrier (TNB) coupled to a linear RLC resonator. The rate equations describing RCSJJ with TNB coupled to the linear RLC resonator are established via Kirchhoff’s current and voltage laws. The model exhibits four, two, or no equilibrium points depending on the external direct current (DC) source and the fractional parameter. The stability analysis of the equilibrium points with credit to the Routh-Hurwitz stability criterion reveals that the stability of equilibrium points depends on the DC source and the fractional parameter. Current-voltage characteristic reveals the presence of a birhythmicity zone which is sensitive to the fractional parameter m. As the fractional parameter increases, the coexistence of the resonant state is destroyed, which is followed simultaneously by the appearance of a new resonance state. Depending on initial conditions, birhythmic behaviour is characterized by the existence of a limit cycle. The projection of the phase space in the specific plane and the time evolution of charge is predicted in which the amplitude of attractors reported is sensitive to the parameter m. Lastly, with a defined fractional parameter, the amplitude of the branch locked to the resonator is greater than the unlocked branch.

Stability analysis of porous FG sandwich plates under thermomechanical loads via integral HySDT

Stability analysis of porous FG sandwich plates under thermomechanical loads via integral HySDT

Stability and instability nature of solitons in an optical fiber with four wave mixing effect

Abstract The investigation into modulational instability (MI) within the Kundu-Eckhaus (KE) equation, governing optical solitons, involves a thorough examination of the effects of self-phase modulation, cross-phase modulation, and intermodal dispersion. Special attention is given to understanding the influence of the four-wave mixing effect. The KE equation, which models birefringent fiber and includes terms related to intermodal dispersion, cross-phase modulation, and self-phase modulation, serves as the fundamental framework for this analytical study. Employing conventional linear stability analysis, the gain within the KE equation is determined. To shed light on the role of four-wave mixing in various scenarios, the gain spectrum is utilized as a tool to analyze the behavior of the KE equation under different conditions. This methodology seeks to provide insightful information about the intricate interactions that impact the modulational instability of solitonic pulses in an optical systems. After that, we have investigated the soliton solution by implementing the Jacobian elliptical function approach. Finally, our focus here is on linear stability analysis, which employs eigenvalue spectra to study solitons' stability via direct numerical simulation.

Stability Analysis of the Secondary Motion of a Textured Piston

Piston–cylinder pairs are very common in industrial mechanisms. While a piston is primarily designed for axial reciprocating motion, the occurrence of secondary motions—lateral and rotational—due to the small clearance between the piston and the cylinder may lead to frictional contact, energy loss, wear and an increase in unwanted leakage. This study focuses on mitigating the secondary motion of a ringless piston. The influence of a Rayleigh step bearing and partial surface texturing with numerous micro-dimples on the dynamic stability of the secondary motion is studied. A linear model was used to obtain the trajectory of the secondary motion and Floquet theory was applied to analyze the stability and draw stability maps. The influence of various texturing and step parameters, including the dimple area density and aspect ratio for partial texturing, as well as the length and depth of treatment for both partial texturing and step profiles, on the stability of the secondary motion was examined. The normalization method is presented, enabling the expansion of the results for various operating conditions and geometries. Conclusions and guidelines regarding the optimal parameters, in terms of a wider stability range and higher decay rate, are formulated.

Stability analysis of explicit exponential Rosenbrock methods for stiff differential equations with constant delay

Delay differential equations have been used to model numerous phenomena in nature. We extend the previous work of one of the authors to analyze the stability properties of the explicit exponential Rosenbrock methods for stiff differential equations with constant delay. We first derive sufficient conditions so that the exponential Rosenbrock methods satisfy the desired stability property. We accomplish this without relying on some extreme constraints, which are usually necessary in stability analysis. Then, with the aid of the integral form of the method coefficients, we provide a simple stability criterion that can be easily verified. We also present a theorem on the order barrier for the proposed methods, stating that there is no method of order five or higher that satisfies the simple criterion. Numerical tests are carried out to validate the theoretical results.

A compartmental modal for type2 diabetes on the effect of plasma glucose -insulin regulatory system by Jacobes model

A compartmental model for diabetes is developed. The model describes the dynamics of the spread of Type 2 diabetes. A theoretical analysis in the non-adherence to drugs is investigated. A system of differential equations is analyzed by stability analysis; the non-trivial critical point obtained is locally asymptotically firm under the given conditions. In consideration of Mathematical model for glucose tolerance test (GTT) is considered, actual glucose data values are fixed using MATLAB least squares curve fitting technique. Two methods are used to numerically work out the distributions of steady states of diabetic sub-populations. The Gauss-Seidel method is more accurate than the Jacobi method. The result show that more than 50% of clinical diagnosis attempt needs to be applied to have more diagnosed population than undiagnosed. The GTT model shows that if severe diet and medication is followed diabetes can be controlled.

Stability and Hopf-bifurcation analysis of diffusive Leslie–Gower prey–predator model with the Allee effect and carry-over effects

Identification of the various dynamical kinetics relating to prey–predator interconnection is the main goal of theoretical ecologists. In addition to direct killing (the lethal effect) in prey–predator interactions, a number of studies have suggested that there are some indirect effects (non-lethal), such as fear of predation. This non-lethal effect slows down the growth rate of prey and this phenomenon can be carried over to upcoming seasons or generations. The Allee effect also has an impact not only on prey populations but also on predator populations. Considering these, we first propose a modified Leslie–Gower predator–prey model that takes into account the fear-induced carry-over effect (COE), the predator’s Allee effect, and intraspecific competition among predators. The ecologically viable equilibrium points and corresponding local and global stability criteria are derived for the model. Moreover, we establish the conditions for the occurrence of Hopf-bifurcation around coexistence equilibrium and compute the first Lyapunov coefficient to verify the stability of the limit cycle. Secondly, we extend the proposed model to include the spatial variable by considering the spatial movements of the species. For the spatial model with zero flux boundary conditions, the criteria for Turing instability and Hopf-bifurcation are derived. Numerical simulations aim to verify the theoretical results. Our study suggests that the parameters related to fear-induced COE, the predator’s Allee effect, and intraspecific competition have a greater impact on system dynamics.

Enhancing the Mechanical Strength and Thermal Stability of Polylactic Acid (PLA) with the Addition of Epoxidized Waste Cooking Oil (EWCO)

Polylactic Acid (PLA) comes from renewable resources, has a reasonable biodegradability rate, and is used in biomedical, food packaging, textiles, and agricultural applications. PLA offers high mechanical strength and the ability to compost, similar to polyethylene terephthalate (PET) and nylon. However, the brittleness of PLA has always limited its usage. Therefore, bio-based plasticizers in the biopolymer matrices can increase flexibility (elasticity), durability, and workability. This study aims to determine the optimal blending ratio for the PLA blended with epoxidized waste cooking oil (EWCO) to enhance the mechanical and thermal properties of PLA/EWCO. The mechanical strength test consists of the hardness test (N/mm<sup>2</sup>), flexural strength (MPa), and impact energy (kJ/m<sup></sup>) adopted to evaluate the plasticizing characteristics. The thermal stability analysis involves glass transition temperature (T<sub>g</sub>) (°C), cold-crystallization temperature (T<sub>cc</sub>) (°C) and melting temperature (T<sub>m</sub>) (°C). The blending ratio is 97.5PLA/2.5EWCO, 95PLA/5EWCO, 92.5PLA/7.5EWCO and 90PLA/10EWCO. As a result, 97.5:2.5 of PLA/EWCO reduces intermolecular interactions by stimulating more free volume in biopolymer chains’ mobility and enhancing the flexibility and elasticity of the PLA blends. Ultimately, the brittleness of PLA decreased with increasing EWCO bio-based plasticizer.

Aggregate data‐driven dynamic modeling of active distribution networks with DERs for voltage stability studies

AbstractElectric distribution networks increasingly host distributed energy resources based on power electronic converter (PEC) toward active distribution networks (ADN). Despite advances in computational capabilities, electromagnetic transient models are limited in scalability because of their reliance on exact data about the distribution system and each of its components. Similarly, the use of the DER_A model, which is intended to examine the combined dynamic behavior of many DERs, is limited by the difficulty in parameterization. There is a need for improved dynamic models of DERs for use in large power system simulations for stability analysis. This paper proposes an aggregate model‐free, data‐driven approach for deriving a dynamic partitioned model (DPM) of ADNs. Detailed residential distribution feeders were first developed, including PEC‐based DERs and composite load models (CMLDs), from which the aggregated DPM was derived. The performance was evaluated through various case studies and validated against the detailed ADN model and state‐of‐the‐art DER_A model with CMLD. The data‐driven DPM achieved a of over 90%, accurately representing the aggregated dynamic behavior of ADNs. Furthermore, the DPM significantly accelerated the simulation process with a computational speedup of 68 times compared to the detailed ADN and a 3.5 times speedup compared to the DER_A CMLD model.

Modeling reactive film flows down a heated fiber

We study the dynamics of an ultra-thin reactive liquid film flowing down a heated vertical fiber under the influence of gravity. A key focus is on the impact of the van der Waals attraction, which is proportional to h−3, where h denotes the film thickness. Linear stability analysis of the film flow reveals that the van der Waals attractions and the Marangoni effect enhance the instability. Furthermore, instability is reduced by exothermic chemical reactions, while it is strengthened in the case of endothermic chemical reactions. Moreover, the weakly nonlinear stability of the film flow is studied. The results indicate the possibility of both subcritical and supercritical stability in the system. Lastly, direct numerical simulations of the evolution equation are conducted for various flow parameters. These results enhance our understanding of the intricate interplay of chemical reactions, thermal effects, and intermolecular forces influencing the liquid film dynamics in complex systems.

Dynamical analysis of hearing loss due to mumps virus with Caputo fractional derivative

Mumps is the most common disease for children, which causes hearing loss in all auditory systems. WHO initiated compulsory vaccination for children who are at age of 12 months to 12 years, since 1967. Children must take two doses of vaccination for mumps. The dynamics of the system describing the mumps transmission is studied in this work. The main aim is to elucidate the nonlinear behavior of the system which can provide insights into the long-term effects of Mumps infection on auditory function. As the fractional-order derivative preserves the impact of system memory, we employ the Caputo fractional derivative as the dynamical system describing modeling to simulate hearing loss in children brought on by the mumps virus. The boundedness existence of the solution and stability analysis of the dynamical system are derived in the framework. The result is derived using a well-known numerical method to capture the corresponding consequences and predict the future consequence of the dynamical system associated with parameters. To testify to the importance of the generalizing classical model with a fractional operator, we plot 2D graphs. This study helps to researcher beginners to understand the essential and fundamental tools while investigating real-world problems.

Long-Term Stability Analysis and Structural Safety Assessment of Tunnel Surrounding Rock in Carbonaceous Slate Formation

Long-Term Stability Analysis and Structural Safety Assessment of Tunnel Surrounding Rock in Carbonaceous Slate Formation

Influence of 3D subsurface flow on slope stability for unsaturated soils

The occurrence of rainfall-induced slope failures has become more frequent due to the effect of climate change. Hence, various studies have been conducted to analyse the effect of rainfall infiltration on slope stability. Physically-based hydrological models have been commonly used with slope stability models such as the infinite slope model to develop slope susceptibility maps. However, a combination of three-dimensional (3D) water balance model with 3D limit equilibrium method (LEM) has not been commonly used. Hence, in this study, a water balance model, GEOtop was used to investigate the influence of subsurface flow in unsaturated soil under extreme rainfall conditions on regional slope stability in 3D directions. The results from the GEOtop model were used as inputs for 3D LEM slope stability analysis performed using the Scoops3D software to obtain the factor of safety (FOS) map for the region. Four slopes within the region were then selected to be modelled in the two-dimensional (2D) seepage and slope stability analyses, SEEP/W and SLOPE/W. Results from the detailed study showed that the pore-water pressures (PWPs) from the 3D water balance analyses were found to be higher than the 2D seepage analyses. Under similar PWP conditions, the FOS from the 2D slope stability analysis was observed to be lower than the 3D analysis for two out of the four slopes. However, the combined 3D water balance and slope stability analyses produced lower FOS compared to the 2D seepage and slope stability analyses due to the higher PWPs in the 3D water balance analyses. Therefore, this study highlights the importance of considering the 3D subsurface flow in unsaturated soil given that it has a significant influence on the FOS of slopes.

Preparation and mechanism research on hydrophobic coupling modification of HTV silicone rubber

Neat high-temperature vulcanized silicone rubber (HTV SR) showed bad hydrophobicity due to the existence of a large number of inorganic reinforcing fillers on its surface, which affected its security application in outdoor insulation systems. In this work, hydrophobic silane chains were grafted onto the surface of inorganic particles on the skin layer of HTV SR by a one-step coupling modification to improve its hydrophobicity. The effects of coupling agent types and coupling reaction conditions on the hydrophobicity of HTV SR were investigated. It was determined that the perfluorooctane trichlorosilicon with a large number of low surface energy fluorine atoms was the preferred coupling agent. The contact angle of HTV SR was increased by 15.70% when the optimal coupling reaction conditions were determined to be a reaction temperature of 60°C, a reaction time of 4 h, and an amount of coupling agent of 0.5%. The study found that both etching reaction and grafting reaction occurred during the whole coupling modification process, which led to the disappearance or decrease of a lot of holes on the HTV SR surface. After the fluorination coupling reaction, the surface of HTV SR became smooth and dense that led to the decrease of water absorption. The result of Fourier-transform infrared spectroscopy analysis showed the formation of C-F bond in HTV SR after fluorination modification, and the energetic dispersive spectroscopy analysis showed that the fluorine content on the surface of the fluorinated HTV SR increased significantly. Moreover, the stability analysis showed that the fluorinated HTV SR still had a good thermal stability and mechanical property stability.

Improved fixed-time stability analysis and applications to synchronization of discontinuous complex-valued fuzzy cellular neural networks

This article mainly centers on proposing new fixed-time (FXT) stability lemmas of discontinuous systems, in which novel optimization approaches are utilized and more relaxed conditions are required. The conventional discussions about Vt>1 and 0<Vt⩽1 are no longer required. For the purpose of verifying the new lemmas, complex-valued fuzzy cellular neural networks (CVFCNNs) with discontinuous activation functions are studied with a nontraditional non-separation method, which could reduce the conservatism of the obtained results greatly. Besides, FXT synchronization is discussed simultaneously. When contrasted with the results of other similar prominent pioneering works nowadays, the accuracy of settling times (STs) is quite enhanced. At last, numerical simulations are conducted to demonstrate the validity and superiority of our established theoretical results.

Slope Stability Analysis Some Selected Sites at Bajalia Anticline in Missan Governorate, Eastern Iraq

In this study, rock stability has been assessed to pinpoint the critical factors affecting slope instability. The discontinuity data collected during the field surveys was evaluated using stereograph projection. Bai Hassan, Mukdadiya, and Injana Formations that were exposed in the research region show slope collapses, ranging in severity from most to least in terms of secondary toppling and rock fall. The characteristics of the rock discontinuities determine the kind and extent of hazards. According to this study, warning signs and fencing should be used to prevent people from walking along the edges of the slopes in the Bajalia anticline and the areas around to alert them of potential failure threats.