Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 20

Stability Analysis Related Abstracts

20 Flow and Heat Transfer over a Shrinking Sheet: A Stability Analysis

Authors: Anuar Ishak


The characteristics of fluid flow and heat transfer over a permeable shrinking sheet is studied. The governing partial differential equations are transformed into a set of ordinary differential equations, which are then solved numerically using MATLAB routine boundary value problem solver bvp4c. Numerical results show that dual solutions are possible for a certain range of the suction parameter. A stability analysis is performed to determine which solution is linearly stable and physically realizable.

Keywords: Heat Transfer, Stability Analysis, dual solutions, shrinking sheet

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19 Landfill Design for Reclamation of Şırnak Coal Mine Dumps: Shalefill Stability and Risk Assessment

Authors: Yıldırım I. Tosun, Halim Cevizci, Hakan Ceylan


By GEO5 FEM program with four rockfill slope modeling and stability analysis was performed for S1, S2, S3 and S4 slopes where landslides of the shalefills were limited. Effective angle of internal friction (φ'°) 17°-22.5°, the effective cohesion (c') from 0.5 to 1.8 kPa, saturated unit weight 1.78-2.43 g/cm3, natural unit weight 1.9-2.35 g/cm3, dry unit weight 1.97-2.40 g/cm3, the permeability coefficient of 1x10-4 - 6.5x10-4 cm/s. In cross-sections of the slope, GEO 5 FEM program possible critical surface tension was examined. Rockfill dump design was made to prevent sliding slopes. Bulk material designated geotechnical properties using also GEO5 programs FEM and stability program via a safety factor determined and calculated according to the values S3 and S4 No. slopes are stable S1 and S2 No. slopes were close to stable state that has been found to be risk. GEO5 programs with limestone rock fill dump through FEM program was found to exhibit stability.

Keywords: Slope Stability, Stability Analysis, rockfills, sock stability

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18 Dual Solutions in Mixed Convection Boundary Layer Flow: A Stability Analysis

Authors: Anuar Ishak


The mixed convection stagnation point flow toward a vertical plate is investigated. The external flow impinges normal to the heated plate and the surface temperature is assumed to vary linearly with the distance from the stagnation point. The governing partial differential equations are transformed into a set of ordinary differential equations, which are then solved numerically using MATLAB routine boundary value problem solver bvp4c. Numerical results show that dual solutions are possible for a certain range of the mixed convection parameter. A stability analysis is performed to determine which solution is linearly stable and physically realizable.

Keywords: Heat Transfer, Stability Analysis, mixed convection, dual solutions

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17 Stability Analysis of Three-Dimensional Flow and Heat Transfer over a Permeable Shrinking Surface in a Cu-Water Nanofluid

Authors: Roslinda Nazar, Amin Noor, Khamisah Jafar, Ioan Pop


In this paper, the steady laminar three-dimensional boundary layer flow and heat transfer of a copper (Cu)-water nanofluid in the vicinity of a permeable shrinking flat surface in an otherwise quiescent fluid is studied. The nanofluid mathematical model in which the effect of the nanoparticle volume fraction is taken into account is considered. The governing nonlinear partial differential equations are transformed into a system of nonlinear ordinary differential equations using a similarity transformation which is then solved numerically using the function bvp4c from Matlab. Dual solutions (upper and lower branch solutions) are found for the similarity boundary layer equations for a certain range of the suction parameter. A stability analysis has been performed to show which branch solutions are stable and physically realizable. The numerical results for the skin friction coefficient and the local Nusselt number as well as the velocity and temperature profiles are obtained, presented and discussed in detail for a range of various governing parameters.

Keywords: Heat Transfer, Nanofluid, Stability Analysis, shrinking surface, three-dimensional flow

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16 Stability Analysis of Three-Lobe Journal Bearing Lubricated with a Micropolar Fluids

Authors: Boualem Chetti


The dynamic characteristics of a three-lobe journal bearing lubricated with micropolar fluids are determined by the linear stability theory. Lubricating oil containing additives and contaminants is modeled as micropolar fluid. The modified Reynolds equation is obtained using the micropolar lubrication theory and the finite difference technique has been used to solve it. The dynamic characteristics in terms of stiffness, damping coefficients, the critical mass and whirl ratio are determined for various values of size of material characteristic length and the coupling number. The computed results show compared with Newtonian fluids, that micropolar fluid exhibits better stability.

Keywords: Stability Analysis, dynamic characteristics, three-lobe bearings, micropolar fluid

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15 Stability Analysis of Stagnation-Point Flow past a Shrinking Sheet in a Nanofluid

Authors: Amin Noor, Roslinda Nazar, Norihan Md. Arifin


In this paper, a numerical and theoretical study has been performed for the stagnation-point boundary layer flow and heat transfer towards a shrinking sheet in a nanofluid. The mathematical nanofluid model in which the effect of the nanoparticle volume fraction is taken into account is considered. The governing nonlinear partial differential equations are transformed into a system of nonlinear ordinary differential equations using a similarity transformation which is then solved numerically using the function bvp4c from Matlab. Numerical results are obtained for the skin friction coefficient, the local Nusselt number as well as the velocity and temperature profiles for some values of the governing parameters, namely the nanoparticle volume fraction Φ, the shrinking parameter λ and the Prandtl number Pr. Three different types of nanoparticles are considered, namely Cu, Al2O3 and TiO2. It is found that solutions do not exist for larger shrinking rates and dual (upper and lower branch) solutions exist when λ < -1.0. A stability analysis has been performed to show which branch solutions are stable and physically realizable. It is also found that the upper branch solutions are stable while the lower branch solutions are unstable.

Keywords: Heat Transfer, Nanofluid, Stability Analysis, shrinking sheet, stagnation-point flow

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14 Stagnation-Point Flow towards a Stretching/Shrinking Sheet in a Nanofluid: A Stability Analysis

Authors: Anuar Ishak


The characteristics of stagnation point flow of a nanofluid towards a stretching/shrinking sheet are investigated. The governing partial differential equations are transformed into a set of ordinary differential equations, which are then solved numerically using MATLAB routine boundary value problem solver bvp4c. The numerical results show that dual (upper and lower branch) solutions exist for the shrinking case, while for the stretching case, the solution is unique. A stability analysis is performed to determine the stability of the dual solutions. It is found that the skin friction decreases when the sheet is stretched, but increases when the suction effect is increased. It is also found that increasing the thermophoresis parameter reduces the heat transfer rate at the surface, while increasing the Brownian motion parameter increases the mass transfer rate at the surface.

Keywords: Heat Transfer, Nanofluid, Stability Analysis, forced convection, dual solutions

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13 Stability Analysis of Rabies Model with Vaccination Effect and Culling in Dogs

Authors: Eti Dwi Wiraningsih, Folashade Agusto, Lina Aryati, Syamsuddin Toaha, Suzanne Lenhart, Widodo, Willy Govaerts


This paper considers a deterministic model for the transmission dynamics of rabies virus in the wild dogs-domestic dogs-human zoonotic cycle. The effect of vaccination and culling in dogs is considered on the model, then the stability was analysed to get basic reproduction number. We use the next generation matrix method and Routh-Hurwitz test to analyze the stability of the Disease-Free Equilibrium and Endemic Equilibrium of this model.

Keywords: Stability Analysis, rabies model, vaccination effect, culling in dogs

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12 Convergence Analysis of Reactive Power Based Schemes Used in Sensorless Control of Induction Motors

Authors: N. Ben Si Ali, N. Benalia, N. Zerzouri


Many electronic drivers for the induction motor control are based on sensorless technologies. Speed and torque control is usually attained by application of a speed or position sensor which requires the additional mounting space, reduce the reliability and increase the cost. This paper seeks to analyze dynamical performances and sensitivity to motor parameter changes of reactive power based technique used in sensorless control of induction motors. Validity of theoretical results is verified by simulation.

Keywords: Stability Analysis, Sensorless Control, adaptive observers, model reference adaptive system, RP-based estimator

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11 Further Analysis of Global Robust Stability of Neural Networks with Multiple Time Delays

Authors: Sabri Arik


In this paper, we study the global asymptotic robust stability of delayed neural networks with norm-bounded uncertainties. By employing the Lyapunov stability theory and Homeomorphic mapping theorem, we derive some new types of sufficient conditions ensuring the existence, uniqueness and global asymptotic stability of the equilibrium point for the class of neural networks with discrete time delays under parameter uncertainties and with respect to continuous and slopebounded activation functions. An important aspect of our results is their low computational complexity as the reported results can be verified by checking some properties symmetric matrices associated with the uncertainty sets of network parameters. The obtained results are shown to be generalization of some of the previously published corresponding results. Some comparative numerical examples are also constructed to compare our results with some closely related existing literature results.

Keywords: Neural Networks, Stability Analysis, delayed systems, lyapunov functionals

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10 Reconfigurable Consensus Achievement of Multi Agent Systems Subject to Actuator Faults in a Leaderless Architecture

Authors: F. Amirarfaei, K. Khorasani


In this paper, reconfigurable consensus achievement of a team of agents with marginally stable linear dynamics and single input channel has been considered. The control algorithm is based on a first order linear protocol. After occurrence of a LOE fault in one of the actuators, using the imperfect information of the effectiveness of the actuators from fault detection and identification module, the control gain is redesigned in a way to still reach consensus. The idea is based on the modeling of change in effectiveness as change of Laplacian matrix. Then as special cases of this class of systems, a team of single integrators as well as double integrators are considered and their behavior subject to a LOE fault is considered. The well-known relative measurements consensus protocol is applied to a leaderless team of single integrator as well as double integrator systems, and Gersgorin disk theorem is employed to determine whether fault occurrence has an effect on system stability and team consensus achievement or not. The analyses show that loss of effectiveness fault in actuator(s) of integrator systems affects neither system stability nor consensus achievement.

Keywords: Stability Analysis, multi-agent system, actuator fault, consensus achievement

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9 The Stability Study of Large-Scale Grid-Tied Photovoltaic System Containing Different Types of Inverter

Authors: Chen Zheng, Lin Zhou, Bao Xie, Xiao Du, Nianbin Shao


Power generated by large-scale photovoltaic plants (LSPVPs) is usually transmitted to the grid through several transformers and long distance overhead lines. Impedance of transformers and transmission lines results in complex interactions between the plant and the grid and among different inverters. In accordance with the topological structure of LSPV in reality, an equivalent model containing different inverters was built and then interactions between the plant and the grid and among different inverters were studied. Based on the vector composition principle of voltage at the point of common coupling (PCC), the mathematic function of PCC voltage in regard to the total power and grid impedance was deduced, from which the uttermost total power to guarantee the system stable is obtained. Taking the influence of different inverters numbers and the length of transmission lines to the system stability into account, the stability criterion of LSPV containing different inverters was derived. The result of simulation validated the theory analysis in the paper.

Keywords: Stability Analysis, LSPVPs, grid impedance, different types of inverter, PCC voltage

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8 Cessna Citation X Business Aircraft Stability Analysis Using Linear Fractional Representation LFRs Model

Authors: Yamina Boughari, Ruxandra Mihaela Botez, Florian Theel, Georges Ghazi


Clearance of flight control laws of a civil aircraft is a long and expensive process in the Aerospace industry. Thousands of flight combinations in terms of speeds, altitudes, gross weights, centers of gravity and angles of attack have to be investigated, and proved to be safe. Nonetheless, in this method, a worst flight condition can be easily missed, and its missing would lead to a critical situation. Definitively, it would be impossible to analyze a model because of the infinite number of cases contained within its flight envelope, that might require more time, and therefore more design cost. Therefore, in industry, the technique of the flight envelope mesh is commonly used. For each point of the flight envelope, the simulation of the associated model ensures the satisfaction or not of specifications. In order to perform fast, comprehensive and effective analysis, other varying parameters models were developed by incorporating variations, or uncertainties in the nominal models, known as Linear Fractional Representation LFR models; these LFR models were able to describe the aircraft dynamics by taking into account uncertainties over the flight envelope. In this paper, the LFRs models are developed using the speeds and altitudes as varying parameters; The LFR models were built using several flying conditions expressed in terms of speeds and altitudes. The use of such a method has gained a great interest by the aeronautical companies that have seen a promising future in the modeling, and particularly in the design and certification of control laws. In this research paper, we will focus on the Cessna Citation X open loop stability analysis. The data are provided by a Research Aircraft Flight Simulator of Level D, that corresponds to the highest level flight dynamics certification; this simulator was developed by CAE Inc. and its development was based on the requirements of research at the LARCASE laboratory. The acquisition of these data was used to develop a linear model of the airplane in its longitudinal and lateral motions, and was further used to create the LFR’s models for 12 XCG /weights conditions, and thus the whole flight envelope using a friendly Graphical User Interface developed during this study. Then, the LFR’s models are analyzed using Interval Analysis method based upon Lyapunov function, and also the ‘stability and robustness analysis’ toolbox. The results were presented under the form of graphs, thus they have offered good readability, and were easily exploitable. The weakness of this method stays in a relatively long calculation, equal to about four hours for the entire flight envelope.

Keywords: Stability Analysis, Robustness Analysis, flight control clearance, LFR

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7 Quintic Spline Method for Variable Coefficient Fourth-Order Parabolic Partial Differential Equations

Authors: Reza Mohammadi, Mahdieh Sahebi


We develop a method based on polynomial quintic spline for numerical solution of fourth-order non-homogeneous parabolic partial differential equation with variable coefficient. By using polynomial quintic spline in off-step points in space and finite difference in time directions, we obtained two three level implicit methods. Stability analysis of the presented method has been carried out. We solve four test problems numerically to validate the proposed derived method. Numerical comparison with other existence methods shows the superiority of our presented scheme.

Keywords: Stability Analysis, fourth-order parabolic equation, variable coefficient, polynomial quintic spline, off-step points

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6 Stability Analysis of Tumor-Immune Fractional Order Model

Authors: Sadia Arshad, Yifa Tang, Dumitru Baleanu


A fractional order mathematical model is proposed that incorporate CD8+ cells, natural killer cells, cytokines and tumor cells. The tumor cells growth in the absence of an immune response is modeled by logistic law as it was the simplest form for which predictions also agreed with the experimental data. Natural Killer Cells are our first line of defense. NK cells directly kill tumor cells through several mechanisms, including the release of cytoplasmic granules containing perforin and granzyme, expression of tumor necrosis factor (TNF) family members. The effect of the NK cells on the tumor cell population is expressed with the product term. Rational form is used to describe interaction between CD8+ cells and tumor cells. A number of cytokines are produced by NKs, including tumor necrosis factor TNF, IFN, and interleukin (IL-10). Source term for cytokines is modeled by Michaelis-Menten form to indicate the saturated effects of the immune response. Stability of the equilibrium points is discussed for biologically significant values of bifurcation parameters. We studied the treatment of fractional order system by investigating analytical conditions of tumor eradication. Numerical simulations are presented to illustrate the analytical results.

Keywords: Numerical Simulations, Fractional Calculus, Stability Analysis, cancer model

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5 Numerical Analysis of Rapid Drawdown in Dams Based on Brazilian Standards

Authors: Renato Santos Paulinelli Raposo, Vinicius Resende Domingues, Manoel Porfirio Cordao Neto


Rapid drawdown is one of the cases referred to ground stability study in dam projects. Due to the complexity generated by the combination of loads and the difficulty in determining the parameters, analyses of rapid drawdown are usually performed considering the immediate reduction of water level upstream. The proposal of a simulation, considering the gradual reduction in water level upstream, requires knowledge of parameters about consolidation and those related to unsaturated soil. In this context, the purpose of this study is to understand the methodology of collection and analysis of parameters to simulate a rapid drawdown in dams. Using a numerical tool, the study is complemented with a hypothetical case study that can assist the practical use of data compiled. The referenced dam presents homogeneous section composed of clay soil, a height of 70 meters, a width of 12 meters, and upstream slope with inclination 1V:3H.

Keywords: Stability Analysis, dam, GeoStudio, rapid drawdown

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4 Modeling and Optimal Control of Pneumonia Disease with Cost Effective Strategies

Authors: Getachew Tilahun, Oluwole Makinde, David Malonza


We propose and analyze a non-linear mathematical model for the transmission dynamics of pneumonia disease in a population of varying size. The deterministic compartmental model is studied using stability theory of differential equations. The effective reproduction number is obtained and also the local and global asymptotically stability conditions for the disease free and as well as for the endemic equilibria are established. The model exhibit a backward bifurcation and the sensitivity indices of the basic reproduction number to the key parameters are determined. Using Pontryagin’s maximum principle, the optimal control problem is formulated with three control strategies; namely disease prevention through education, treatment and screening. The cost effectiveness analysis of the adopted control strategies revealed that the combination of prevention and treatment is the most cost effective intervention strategies to combat the pneumonia pandemic. Numerical simulation is performed and pertinent results are displayed graphically.

Keywords: Optimal Control, Numerical Simulation, Stability Analysis, cost effectiveness analysis, pneumonia dynamics

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3 Fixed Point Iteration of a Damped and Unforced Duffing's Equation

Authors: Paschal A. Ochang, Emmanuel C. Oji


The Duffing’s Equation is a second order system that is very important because they are fundamental to the behaviour of higher order systems and they have applications in almost all fields of science and engineering. In the biological area, it is useful in plant stem dependence and natural frequency and model of the Brain Crash Analysis (BCA). In Engineering, it is useful in the study of Damping indoor construction and Traffic lights and to the meteorologist it is used in the prediction of weather conditions. However, most Problems in real life that occur are non-linear in nature and may not have analytical solutions except approximations or simulations, so trying to find an exact explicit solution may in general be complicated and sometimes impossible. Therefore we aim to find out if it is possible to obtain one analytical fixed point to the non-linear ordinary equation using fixed point analytical method. We started by exposing the scope of the Duffing’s equation and other related works on it. With a major focus on the fixed point and fixed point iterative scheme, we tried different iterative schemes on the Duffing’s Equation. We were able to identify that one can only see the fixed points to a Damped Duffing’s Equation and not to the Undamped Duffing’s Equation. This is because the cubic nonlinearity term is the determining factor to the Duffing’s Equation. We finally came to the results where we identified the stability of an equation that is damped, forced and second order in nature. Generally, in this research, we approximate the solution of Duffing’s Equation by converting it to a system of First and Second Order Ordinary Differential Equation and using Fixed Point Iterative approach. This approach shows that for different versions of Duffing’s Equations (damped), we find fixed points, therefore the order of computations and running time of applied software in all fields using the Duffing’s equation will be reduced.

Keywords: Damping, Stability Analysis, Duffing's equation, fixed point analysis, second order differential

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2 Topping Failure Analysis of Anti-Dip Bedding Rock Slopes Subjected to Crest Loads

Authors: Chaoyi Sun, Congxin Chen, Yun Zheng, Kaizong Xia, Wei Zhang


Crest loads are often encountered in hydropower, highway, open-pit and other engineering rock slopes. Toppling failure is one of the most common deformation failure types of anti-dip bedding rock slopes. Analysis on such failure of anti-dip bedding rock slopes subjected to crest loads has an important influence on engineering practice. Based on the step-by-step analysis approach proposed by Goodman and Bray, a geo-mechanical model was developed, and the related analysis approach was proposed for the toppling failure of anti-dip bedding rock slopes subjected to crest loads. Using the transfer coefficient method, a formulation was derived for calculating the residual thrust of slope toe and the support force required to meet the requirements of the slope stability under crest loads, which provided a scientific reference to design and support for such slopes. Through slope examples, the influence of crest loads on the residual thrust and sliding ratio coefficient was investigated for cases of different block widths and slope cut angles. The results show that there exists a critical block width for such slope. The influence of crest loads on the residual thrust is non-negligible when the block thickness is smaller than the critical value. Moreover, the influence of crest loads on the slope stability increases with the slope cut angle and the sliding ratio coefficient of anti-dip bedding rock slopes increases with the crest loads. Finally, the theoretical solutions and numerical simulations using Universal Distinct Element Code (UDEC) were compared, in which the consistent results show the applicability of both approaches.

Keywords: Stability Analysis, anti-dip bedding rock slope, crest loads, toppling failure

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1 Diffusion Dynamics of Leech-Heart Inter-Neuron Model

Authors: Arnab Mondal, Sanjeev Kumar Sharma, Ranjit Kumar Upadhyay


We study the spatiotemporal dynamics of a neuronal cable. The processes of one- dimensional (1D) and 2D diffusion are considered for a single variable, which is the membrane voltage, i.e., membrane voltage diffusively interacts for spatiotemporal pattern formalism. The recovery and other variables interact through the membrane voltage. A 3D Leech-Heart (LH) model is introduced to investigate the nonlinear responses of an excitable neuronal cable. The deterministic LH model shows different types of firing properties. We explore the parameter space of the uncoupled LH model and based on the bifurcation diagram, considering v_k2_ashift as a bifurcation parameter, we analyze the 1D diffusion dynamics in three regimes: bursting, regular spiking, and a quiescent state. Depending on parameters, it is shown that the diffusive system may generate regular and irregular bursting or spiking behavior. Further, it is explored a 2D diffusion acting on the membrane voltage, where different types of patterns can be observed. The results show that the LH neurons with different firing characteristics depending on the control parameters participate in a collective behavior of an information processing system that depends on the overall network.

Keywords: Pattern Formation, Stability Analysis, bifurcation, spatio-temporal dynamics

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