Search results for: numerical stability

Authors: Abhishek Kumar, Nilam

Abstract:

As we know that, time delay exists almost in every biological phenomenon. Therefore, in the present study, we propose a susceptible–infected–recovered (SIR) epidemic model along with time delay, modulated incidence rate of infection, and Holling Type II nonlinear treatment rate. The present model aims to provide a strategy to control the spread of epidemics. In the mathematical study of the model, it has been shown that the model has two equilibriums which are named as disease-free equilibrium (DFE) and endemic equilibrium (EE). Further, stability analysis of the model is discussed. To prove the stability of the model at DFE, we derived basic reproduction number, denoted by (R₀). With the help of basic reproduction number (R₀), we showed that the model is locally asymptotically stable at DFE when the basic reproduction number (R₀) less than unity and unstable when the basic reproduction number (R₀) is greater than unity. Furthermore, stability analysis of the model at endemic equilibrium has also been discussed. Finally, numerical simulations have been done using MATLAB 2012b to exemplify the theoretical results.

Keywords: time delayed SIR epidemic model, modulated incidence rate, Holling type II nonlinear treatment rate, stability

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Authors: Fares Senouci, Bachir Imine

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This document provides numerical and experimental optimization of the aerodynamic performance of a drone equipped with three types of horizontal stabilizer. To build this optimal configuration, an experimental and numerical study was conducted on three parameters: the geometry of the stabilizer (horizontal form or reverse V form), the position of the horizontal stabilizer (up or down), and the landing gear position (closed or open). The results show that up-stabilizer position with respect to the horizontal plane of the fuselage provides better aerodynamic performance, and that the landing gear increases the lift in the zone of stability, that is to say where the flow is not separated.

Keywords: aerodynamics, drag, lift, turbulence model, wind tunnel

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Authors: T. H. Young, S. J. Huang, Y. S. Chiu

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This paper investigates the parametric stability of an axially moving web subjected to nonuniform in-plane edge excitations on two opposite, simply-supported edges. The web is modeled as a viscoelastic plate whose constitutive relation obeys the Kelvin-Voigt model, and the in-plane edge excitations are expressed as the sum of a static tension and a periodical perturbation. Due to the in-plane edge excitations, the moving plate may bring about parametric instability under certain situations. First, the in-plane stresses of the plate due to the nonuniform edge excitations are determined by solving the in-plane forced vibration problem. Then, the dependence on the spatial coordinates in the equation of transverse motion is eliminated by the generalized Galerkin method, which results in a set of discretized system equations in time. Finally, the method of multiple scales is utilized to solve the set of system equations analytically if the periodical perturbation of the in-plane edge excitations is much smaller as compared with the static tension of the plate, from which the stability boundaries of the moving plate are obtained. Numerical results reveal that only combination resonances of the summed-type appear under the in-plane edge excitations considered in this work.

Keywords: axially moving viscoelastic plate, in-plane periodic excitation, nonuniformly distributed edge tension, dynamic stability

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Authors: Dr., Suchita Daokar

Abstract:

Background: Successful orthodontic treatment has always relied on anchorage. The stability of the implants depends on bone quantity, mini-implant design, and placement conditions. Out of the various methods of gaining stability, Platelet concentrations are gaining popularity for various reasons. PRF is a minimally invasive method, and there are various studies that has shown its role in enhancing the stability of general implants. However, there is no literature found regarding the effect of PRF in enhancing the stability of the orthodontic implant. Therefore, this study aimed to evaluate and assess the efficacy of PRF on the stability of the orthodontic implant. Methods: The study comprised of 9 subjects aged above 18 years of age. The split mouth technique was used; Group A (where implants were coated before insertion) and group B (implant were normally inserted). The stability of the implant was measured using resonance frequency analysis at insertion (T0), 24 hours (T1), 2 weeks (T2), at 4 weeks (T3), at 6 weeks (T4), and 8 weeks (T5) after insertion. Result: Statistically significant findings were found when group A was compared to group B using ANOVA test (p<0.05). The stability of the implant of group A at each time interval was greater than group B. The implant stability was high at T0 and reduces at T2, and increasing through T3 to T5. The stability was highest at T5. Conclusion: A chairside, minimally invasive procedure ofPRF coating on implants have shown promising results in improving the stability of orthodontic implants and providing scope for future studies.

Keywords: Orthodontic implants, stablity, resonance Frequency Analysis, pre

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Authors: Sudhir Kumar Singh, Debashish Chakravarty

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Slope stability analysis is an important aspect in the field of geotechnical engineering. It is also important from safety, and economic point of view as any slope failure leads to loss of valuable lives and damage to property worth millions. This paper aims at mitigating the risk of slope failure by studying the effect of different joint sets on the stability of mine pit slopes under the influence of various external factors, namely degree of saturation, rainfall intensity, and seismic coefficients. Supervised machine learning approach has been utilized for making accurate and reliable predictions regarding the stability of slopes based on the value of Factor of Safety. Numerous cases have been studied for analyzing the stability of slopes using the popular Finite Element Method, and the data thus obtained has been used as training data for the supervised machine learning models. The input data has been trained on different supervised machine learning models, namely Random Forest, Decision Tree, Support vector Machine, and XGBoost. Distinct test data that is not present in training data has been used for measuring the performance and accuracy of different models. Although all models have performed well on the test dataset but Random Forest stands out from others due to its high accuracy of greater than 95%, thus helping us by providing a valuable tool at our disposition which is neither computationally expensive nor time consuming and in good accordance with the numerical analysis result.

Keywords: finite element method, geotechnical engineering, machine learning, slope stability

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Authors: Khelil Khadidja

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In this paper, blackness of dark solitons is considered. The exact combination between nonlinearity and dispersion is responsible of solitons stability. Dark solitons get born when dispersion is abnormal and balanced by nonlinearity, at the opposite of brillant solitons which is born by normal dispersion and nonlinearity together. Thanks to their stability, dark solitons are suitable for transmission by optical fibers. Dark solitons which are a solution of Nonlinear Schrodinger equation are simulated with Matlab to discuss the influence of coefficient of blackness. Results show that there is a direct proportion between the coefficient of blackness and the intensity of dark soliton. Those gray solitons are stable and convenient for transmission.

Keywords: abnormal dispersion, nonlinearity, optical fiber, soliton

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Authors: Arnold M. Brener, Lesbek Tashimov, Ablakim S. Muratov

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The paper deals with the special model for coagulation kernels which represents new control parameters in the Smoluchowski equation for binary aggregation. On the base of the model the new approach to evaluating aggregative stability of disperse systems has been submitted. With the help of this approach the simple estimates for aggregative stability of various types of hydrophilic nano-suspensions have been obtained.

Keywords: aggregative stability, coagulation kernels, disperse systems, mathematical model

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Authors: Jair Servín-Aguilar, Yu Tang

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We address the problem of robust attitude tracking for agile satellites under unknown bounded torque disturbances using a double-gimbal variable-speed control-moment gyro (DGVSCMG) driven by a cluster of three permanent magnet synchronous motors (PMSMs). Uniform practical asymptotic stability is achieved at the torque control level first. The desired speed of gimbals and the acceleration of the spin wheel to produce the required torque are then calculated by a velocity-based steering law and tracked at the PMSM speed-control level by designing a speed-tracking controller with compensation for the vibration caused by eccentricity and imbalance due to mechanical imperfection in the DGVSCMG. Uniform practical asymptotic stability of the overall system is ensured by loan relying on the analysis of the resulting cascaded system. Numerical simulations are included to show the performance improvement of the proposed controller.

Keywords: agile satellites, vibration compensation, internal model, stability

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Authors: Burak Yildirim, Muhsin Tunay Gencoglu

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This publication shows the effects of Microgrid (MG) integration on the power systems oscillating stability. Generated MG model power systems were applied to the IEEE 14 bus test system which is widely used in stability studies. Stability studies were carried out with the help of eigenvalue analysis over linearized system models. In addition, Hopf bifurcation point detection was performed to show the effect of MGs on the system loadability margin. In the study results, it is seen that MGs affect system stability positively by increasing system loadability margin and has a damper effect on the critical modes of the system and the electromechanical local modes, but they make the damping amount of the electromechanical interarea modes reduce.

Keywords: Eigenvalue analysis, microgrid, Hopf bifurcation, oscillatory stability

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Authors: Hosein Falahaty, Hitoshi Gotoh, Abbas Khayyer

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Performance of a Hamiltonian based particle method in simulation of nonlinear structural dynamics is subjected to investigation in terms of stability and accuracy. The governing equation of motion is derived based on Hamilton's principle of least action, while the deformation gradient is obtained according to Weighted Least Square method. The hyper-elasticity models of Saint Venant-Kirchhoff and a compressible version similar to Mooney- Rivlin are engaged for the calculation of second Piola-Kirchhoff stress tensor, respectively. Stability along with accuracy of numerical model is verified by reproducing critical stress fields in static and dynamic responses. As the results, although performance of Hamiltonian based model is evaluated as being acceptable in dealing with intense extensional stress fields, however kinds of instabilities reveal in the case of violent collision which can be most likely attributed to zero energy singular modes.

Keywords: Hamilton's principle of least action, particle-based method, hyper-elasticity, analysis of stability

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Authors: Mohammad Sadeghian, Mohsen Sadeghian

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In this paper, planning catamaran and mono-hull vessels resistance and trim in calm waters were considered. Hydrodynamic analysis of fast mono-hull planning vessel was also investigated. For hull form geometry optimization, numerical methods of different parameters were used for this type of vessels. Hull material was selected as carbon fiber composite. Exact architectural aspects were specified and stability calculations were performed, as well. Hydrodynamic calculations to extract the resistance force using semi-analytical methods and numerical modeling were carried out. Free surface numerical analysis of vessel in designed draft using finite volume method and double phase were evaluated and verified by experimental tests.

Keywords: fast vessel, hydrostatic and hydrodynamic optimization, free surface flow, computational fluid dynamics

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Authors: Sabir Messalti, Ahmed Gherbi, Ahmed Bouchlaghem

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This paper presents comparative study for power systems transient stability improvement using three FACTS devices: the SVC(Static Var Compensator), the Thyristor Control Breaking Resistor (TCBR) and superconducting fault current limiter (SFCL)The transient stability is assessed by the criterion of relative rotor angles. Critical Clearing Time (CCT) is used as an index for evaluated transient stability. The present study is tested on the WSCC3 nine-bus system in the case of three-phase short circuit fault on one transmission line.

Keywords: SVC, TCBR, SFCL, power systems transient stability improvement

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Authors: M. J. Park, S. H. Lee, C. H. Lee, O. M. Kwon

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This paper investigates stability problem for linear systems of neutral type with time-varying delay. By constructing various Lyapunov-Krasovskii functional, and utilizing some mathematical techniques, the sufficient stability conditions for the systems are established in terms of linear matrix inequalities (LMIs), which can be easily solved by various effective optimization algorithms. Finally, some illustrative examples are given to show the effectiveness of the proposed criterion.

Keywords: neutral systems, time-delay, stability, Lyapnov method, LMI

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Authors: Haowei Chen, Kaiqi Xiong

Abstract:

This paper aims to answer how malware will propagate in Wireless Mesh Networks (WMNs) and how communication radius and distributed density of nodes affects the process of spreading. The above analysis is essential for devising network-wide strategies to counter malware. We answer these questions by developing an improved dynamical system that models malware propagation in the area where nodes were uniformly distributed. The proposed model captures both the spatial and temporal dynamics regarding the malware spreading process. Equilibrium and stability are also discussed based on the threshold of the system. If the threshold is less than one, the infected nodes disappear, and if the threshold is greater than one, the infected nodes asymptotically stabilize at the endemic equilibrium. Numerical simulations are investigated about communication radius and distributed density of nodes in WMNs, which allows us to draw various insights that can be used to guide security defense.

Keywords: Bluetooth security, malware propagation, wireless mesh networks, stability analysis

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Authors: Ahlem Mougaida, Hedi Bel Hadj Salah

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Several methods are suggested to improve the numerical integration in Galerkin weak form for Meshless methods. In fact, integrating without taking into account the characteristics of the shape functions reproduced by Meshless methods (rational functions, with compact support etc.), causes a large integration error that influences the PDE’s approximate solution. Comparisons between different methods of numerical integration for rational functions are discussed and compared. The algorithms are implemented in Matlab. Finally, numerical results were presented to prove the efficiency of our algorithms in improving results.

Keywords: adaptive methods, meshless, numerical integration, rational quadrature

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Authors: Somveer Singh, Vineet Kumar Singh

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We present a new model based on viscoelasticity for the Non-Newtonian fluids.We use a matrix formulated algorithm to approximate solutions of a class of partial integro-differential equations with the given initial and boundary conditions. Some numerical results are presented to simplify application of operational matrix formulation and reduce the computational cost. Convergence analysis, error estimation and numerical stability of the method are also investigated. Finally, some test examples are given to demonstrate accuracy and efficiency of the proposed method.

Keywords: Legendre Wavelets, operational matrices, partial integro-differential equation, viscoelasticity

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Authors: Mohammad Ali Badri, Pouya Molana, Amin Rezvanpour

Abstract:

In this paper, planning catamaran and mono-hull vessels resistance and trim in calm waters were considered. Hydrodynamic analysis of fast mono-hull planning vessel was also investigated. In order to hull form geometry optimization, numerical methods of different parameters were used for this type of vessels. Hull material was selected in carbon fiber composite. Exact architectural aspects were specified and stability calculations were performed as well. Hydrodynamic calculations to extract the resistance force using semi-analytical methods and numerical modeling were carried out. Free surface numerical analysis of vessel in designed draft using finite volume method and double phase were evaluated and verified by experimental tests.

Keywords: fast vessel, hydrostatic and hydrodynamic optimization, free surface flow, computational fluid dynamics

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Authors: Sudhakar Kadiyala, Sripad R. Naik

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Large cavern in Bhutan Himalayas is being monitored since the construction period. The behavior of the cavern is being monitored for last 16 years. Instrumentation includes measurement of convergence of high walls by geodetic monitoring, load on the support systems with load cells and instrumented bolts. Analysis of the results of instrumentation showed that during the construction period of the cavern, the convergence of the cavern varied from 181 - 233 mm in the unit bay area with maximum convergence rate of 2.80mm/day. Whereas during the operational period the total convergence observed was in the range of 21 to 45 mm during a period of 11.30 years with convergence rate of 0.005 to 0.011 mm/day. During the last five years, there were no instances of high tensile stress recorded by the instrumented bolts. Load on the rock bolts have shown stabilization trend at most of the locations. This paper discusses in detail the results of long-term monitoring using the geotechnical instruments and how the data is being used in 3D numerical model to confirm the stability of the cavern.

Keywords: convergence, displacements, geodetic monitoring, long-term stability

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Authors: Gregor Kosec

Abstract:

Simple and robust numerical approach for solving flow problems is presented, where involved physical fields are represented through the local approximation functions, i.e., the considered field is approximated over a local support domain. The approximation functions are then used to evaluate the partial differential operators. The type of approximation, the size of support domain, and the type and number of basis function can be general. The solution procedure is formulated completely through local computational operations. Besides local numerical method also the pressure velocity is performed locally with retaining the correct temporal transient. The complete locality of the introduced numerical scheme has several beneficial effects. One of the most attractive is the simplicity since it could be understood as a generalized Finite Differences Method, however, much more powerful. Presented methodology offers many possibilities for treating challenging cases, e.g. nodal adaptivity to address regions with sharp discontinuities or p-adaptivity to treat obscure anomalies in physical field. The stability versus computation complexity and accuracy can be regulated by changing number of support nodes, etc. All these features can be controlled on the fly during the simulation. The presented methodology is relatively simple to understand and implement, which makes it potentially powerful tool for engineering simulations. Besides simplicity and straightforward implementation, there are many opportunities to fully exploit modern computer architectures through different parallel computing strategies. The performance of the method is presented on the lid driven cavity problem, backward facing step problem, de Vahl Davis natural convection test, extended also to low Prandtl fluid and Darcy porous flow. Results are presented in terms of velocity profiles, convergence plots, and stability analyses. Results of all cases are also compared against published data.

Keywords: fluid flow, meshless, low Pr problem, natural convection

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Authors: Abdullahi Mohammed Auwal

Abstract:

Formation and change or decamping from one political party to another have now become a common trend in Nigeria. Many of the parties’ members who could not secure positions and or win elections in their parties or are not very much satisfied with the trends occurring in the party’s internal democratic principles and mechanisms, change their respective parties. This paper developed/presented and analyzed the used of non linear mathematical model for defections between two political parties using epidemiological approach. The whole population was assumed to be a constant and homogeneously mixed. Equilibria have been analytically obtained and their local and global stability discussed. Conditions for the co-existence of both the political parties have been determined, in the study of defections between People Democratic Party (PDP) and All Progressive Congress (APC) in Nigeria using numerical simulations to support the analytical results.

Keywords: model, political parties, deffection, stability, equilibrium, epidemiology

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Authors: Hooman Dabirmanesh, Attila M. Zsaki

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Traditionally, rock slope stability is carried out using limit equilibrium analysis when investigating toppling failure. In these equilibrium methods, internal forces exerted between columns are not clearly defined, and to the authors’ best knowledge, there is no consensus in literature with respect to the results of analysis. A discrete element method-based numerical model was developed and applied to simulate the behavior of rock layers subjected to toppling failure. Based on this calibrated numerical model, a study of the location and distribution of internal forces that result in equilibrium was carried out. The sum of side forces was applied at a point on a block which properly represents the force to determine the inter-column force distribution. In terms of the side force distribution coefficient, the result was compared to those obtained from laboratory centrifuge tests. The results of the simulation show the suitable criteria to select the correct position for the internal exerted force between rock layers. In addition, the numerical method demonstrates how a theoretical method could be reliable by considering the interaction between the rock layers.

Keywords: contact bond, discrete element, force distribution, limit equilibrium, tensile stress

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Authors: Micke Didit, Xiwen Zhang, Weidong Zhu

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Slope stability is one of the most important subjects of geotechnics. The slope top-loading plays a key role in the stability of slopes in hill slope areas. Therefore, it is of great importance to study the relationship between the load and the stability of the slope. This study aims to analyze the influence of the building load applied on the top of the slope and deduces its effect on the slope stability. For this purpose, a three-dimensional slope model under different building loads with different distances to the slope shoulder was established using the finite-difference analysis software Flac3D. The results show that the loads applied at different distances on the top of the slope have different effects on the slope stability. The slope factor of safety (fos) increases with the increase of the distance between the top-loading and the slope shoulder, resulting in the decrease of the coincidence area between the load-deformation and the potential sliding surface. The slope is no longer affected by the potential risk of sliding at approximately 20 m away from the slope shoulder.

Keywords: building load, finite-difference analysis, FLAC3D software, slope factor of safety, slope stability

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Authors: A. Chellil, A. Nour, S. Lecheb , H. Mechakra, A. Bouderba, H. Kebir

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The study of the rotor dynamic in transient system allowed to determine the vibratory responses due to various excitations. This work presents a coupled gyroscopic effect in the defects of a rotor under dynamic loading. Calculations of different energies and virtual work from the various elements of the rotor are developed. To treat real systems a model of finite element was developed. This model of the rotor makes it possible to extract the frequencies and modal deformed, and to calculate the stresses in the critical zone. The study of the rotor in transient system allowed to determine the vibratory responses due to the unbalances, crack and various excitations.

Keywords: rotor, defect, finite element, numerical

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

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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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Authors: Owolabi Kolade Matthew

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In this work, we investigate both the analytical and numerical studies of the dynamical model comprising of three species system. We analyze the linear stability of stationary solutions in the one-dimensional multi-system modeling the interactions of two predators and one prey species. The stability analysis has a lot of implications for understanding the various spatiotemporal and chaotic behaviors of the species in the spatial domain. The analysis results presented have established the possibility of the three interacting species to coexist harmoniously, this feat is achieved by combining the local and global analyzes to determine the global dynamics of the system. In the presence of diffusion, a viable exponential time differencing method is applied to multi-species nonlinear time-dependent partial differential equation to address the points and queries that may naturally arise. The scheme is described in detail, and justified by a number of computational experiments.

Keywords: asymptotically stable, coexistence, exponential time differencing method, global and local stability, predator-prey model, nonlinear, reaction-diffusion system

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Authors: Ju-Young Choi, Ki-Il Song, Kyoung-Yul Kim

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During Tunnel Boring Machine (TBM) tunnel excavation, backfill grout should be injected after the installation of segment lining to ensure the stability of the tunnel and to minimize ground deformation. If grouting is not sufficient to fill the gap between the segments and rock mass, hydraulic pressures occur in the void, which can negatively influence the stability of the tunnel. Recently the tendency to use TBM tunnelling method to replace the drill and blast(NATM) method is increasing. However, there are only a few studies of evaluation of backfill grout. This study evaluates the TBM tunnel backfill state using Impact-Echo(IE). 3-layers, segment-grout-rock mass, are simulated by FLAC 2D, FDM-based software. The signals obtained from numerical analysis and IE test are analyzed by Short-Time Fourier Transform(STFT) in time domain, frequency domain, and time-frequency domain. The result of this study can be used to evaluate the quality of backfill grouting in tail void.

Keywords: tunnel boring machine, backfill grout, impact-echo method, time-frequency domain analysis, finite difference method

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Authors: Beata Jackowska-Zduniak

Abstract:

We formulate and analyze a mathematical model describing dynamics of the hypothalamus-pituitary-thyroid homoeostatic mechanism in endocrine system. We introduce to this system two types of couplings and delay. In our model, feedback controls the secretion of thyroid hormones and delay reflects time lags required for transportation of the hormones. The influence of delayed feedback on the stability behaviour of the system is discussed. Analytical results are illustrated by numerical examples of the model dynamics. This system of equations describes normal activity of the thyroid and also a couple of types of malfunctions (e.g. hyperthyroidism).

Keywords: mathematical modeling, ordinary differential equations, endocrine system, delay differential equation

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Authors: Jui-Ting Hsu, Heng-Li Huang, Ming-Tzu Tsai, Kuo-Chih Su, Lih-Jyh Fuh

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The objectives of this study were to measure the initial stability of the dental implant (ISQ and PTV) in the artificial foam bone block with three different quality levels. In addition, the 3D bone to implant contact percentage (BIC%) was measured based on the micro-computed tomography images. Furthermore, the relation between the initial stability of dental implant (ISQ and PTV) and BIC% were calculated. The experimental results indicated that enhanced the material property of the artificial foam bone increased the initial stability of the dental implant. The Pearson’s correlation coefficient between the BIC% and the two approaches (ISQ and PTV) were 0.652 and 0.745.

Keywords: dental implant, implant stability quotient, peak insertion torque, bone-implant contact, micro-computed tomography

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Authors: Hassan Al Salman, Ahmed Al Ghafli

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In this study we consider a nonlinear in time finite element approximation of a reaction diffusion system of lambda-omega type. We use a fixed point theorem to prove existence of the approximations. Then, we derive some essential stability estimates and discuss the uniqueness of the approximations. Also, we prove an optimal error bound in time for d=1, 2 and 3 space dimensions. Finally, we present some numerical experiments to verify the theoretical results.

Keywords: reaction diffusion system, finite element approximation, fixed point theorem, an optimal error bound

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Authors: P.-W. Tsai, C.-Y. Chen, C.-W. Chen

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In this paper, the stability analysis of a GA-Based adaptive fuzzy sliding model controller for a nonlinear system is discussed. First, a nonlinear plant is well-approximated and described with a reference model and a fuzzy model, both involving FLC rules. Then, FLC rules and the consequent parameter are decided on via an Evolved Bat Algorithm (EBA). After this, we guarantee a new tracking performance inequality for the control system. The tracking problem is characterized to solve an eigenvalue problem (EVP). Next, an adaptive fuzzy sliding model controller (AFSMC) is proposed to stabilize the system so as to achieve good control performance. Lyapunov’s direct method can be used to ensure the stability of the nonlinear system. It is shown that the stability analysis can reduce nonlinear systems into a linear matrix inequality (LMI) problem. Finally, a numerical simulation is provided to demonstrate the control methodology.

Keywords: adaptive fuzzy sliding mode control, Lyapunov direct method, swarm intelligence, evolved bat algorithm

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