Search results for: nonlinear equation system

Authors: Cheng-En Tsai, Chung-Chun Hsiao, Fu-Yuan Chang, Liang-Lun Lan, Jia-Ying Tu

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New design of three dimensional (3D) flywheel system based on gimbal and gyro mechanics is proposed. The 3D flywheel device utilizes the rotational motion of three spherical shells and the conservation of angular momentum to achieve planar locomotion. Actuators mounted to the ring-shape frames are installed within the system to drive the spherical shells to rotate, for the purpose of steering and stabilization. Similar to the design of 2D flywheel system, it is expected that the spherical shells may function like a “flyball” to store and supply mechanical energy; additionally, in comparison with typical single-wheel and spherical robots, the 3D flywheel can be used for developing omnidirectional robotic systems with better mobility. The Lagrangian method is applied to derive the equation of motion of the 3D flywheel system, and simulation studies are presented to verify the proposed design.

Keywords: Gimbal, spherical robot, gyroscope, Lagrangian formulation, flyball

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Authors: N. Ould cherchali, M. S. Boucherit, L. Barazane, A. Morsli

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Photovoltaic power is widely used to supply isolated or unpopulated areas (lighting, pumping, etc.). Great advantage is that this source is inexhaustible, it offers great safety in use and it is clean. But the dynamic models used to describe a photovoltaic system are complicated and nonlinear and due to nonlinear I-V and P–V characteristics of photovoltaic generators, a maximum power point tracking technique (MPPT) is required to maximize the output power. In this paper, two online techniques of maximum power point tracking using robust controller for photovoltaic systems are proposed, the first technique use fuzzy logic controller (FLC) and the second use sliding mode controller (SMC) for photovoltaic systems. The two maximum power point tracking controllers receive the partial derivative of power as inputs, and the output is the duty cycle corresponding to maximum power. A Photovoltaic generator with Boost converter is developed using MATLAB/Simulink to verify the preferences of the proposed techniques. SMC technique provides a good tracking speed in fast changing irradiation and when the irradiation changes slowly or is constant the panel power of FLC technique presents a much smoother signal with less fluctuations.

Keywords: fuzzy logic controller, maximum power point, photovoltaic system, tracker, sliding mode controller

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Authors: Galih Permana, Yuskar Lase

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In recent years, damping device has been experimentally studied to replace diagonally reinforced coupling beams, to mitigate rebar congestion problem. This study focuses on evaluating the effectiveness of various damping devices in a high-rise building. The type of damping devices evaluated is Viscoelastic Damper (VCD) and Rotational Friction Damper (RFD), with study case of a 15-story reinforced concrete apartment building with a dual system (column-beam and shear walls). The analysis used is a nonlinear time history analysis with 11 pairs of ground motions matched to the Indonesian response spectrum based on ASCE 41-17 and ASCE 7-16. In this analysis, each damper will be varied with a different position, namely the first model, the damper will be installed on the entire floor and in the second model, the damper will be installed on the 5th floor to the 9th floor, which is the floor with the largest drift. The results show that the model using both dampers increases the level of structural performance both globally and locally in the building, which will reduce the level of damage to the structural elements. But between the two dampers, the coupling beam that uses RFD is more effective than using VCD in improving building performance. The damper on the coupling beam has a good role in dissipating earthquakes and also in terms of ease of installation.

Keywords: building, coupling beam, damper, nonlinear time history analysis

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Authors: Amit Kumar, Archana Gupta, Poonam Tandon, E. D. D’Silva

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Nonlinear optical (NLO) materials are the key materials for the fast processing of information and optical data storage applications. In the last decade, materials showing nonlinear optical properties have been the object of increasing attention by both experimental and computational points of view. Chalcones are one of the most important classes of cross conjugated NLO chromophores that are reported to exhibit good SHG efficiency, ultra fast optical nonlinearities and are easily crystallizable. The basic structure of chalcones is based on the π-conjugated system in which two aromatic rings are connected by a three-carbon α, β-unsaturated carbonyl system. Due to the overlap of π orbitals, delocalization of electronic charge distribution leads to a high mobility of the electron density. On a molecular scale, the extent of charge transfer across the NLO chromophore determines the level of SHG output. Hence, the functionalization of both ends of the π-bond system with appropriate electron donor and acceptor groups can enhance the asymmetric electronic distribution in either or both ground and excited states, leading to an increased optical nonlinearity. In this research, the experimental and theoretical study on the structure and vibrations of (2E)-3-[4-(methylsulfanyl) phenyl]-1-(3-bromophenyl) prop-2-en-1-one (3Br4MSP) is presented. The FT-IR and FT-Raman spectra of the NLO material in the solid phase have been recorded. Density functional theory (DFT) calculations at B3LYP with 6-311++G(d,p) basis set were carried out to study the equilibrium geometry, vibrational wavenumbers, infrared absorbance and Raman scattering activities. The interpretation of vibrational features (normal mode assignments, for instance) has an invaluable aid from DFT calculations that provide a quantum-mechanical description of the electronic energies and forces involved. Perturbation theory allows one to obtain the vibrational normal modes by estimating the derivatives of the Kohn−Sham energy with respect to atomic displacements. The molecular hyperpolarizability β plays a chief role in the NLO properties, and a systematical study on β has been carried out. Furthermore, the first order hyperpolarizability (β) and the related properties such as dipole moment (μ) and polarizability (α) of the title molecule are evaluated by Finite Field (FF) approach. The electronic α and β of the studied molecule are 41.907×10-24 and 79.035×10-24 e.s.u. respectively, indicating that 3Br4MSP can be used as a good nonlinear optical material.

Keywords: DFT, MEP, NLO, vibrational spectra

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Authors: Gyu-Jin Kim, Hyo-Gyoung Kwak

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In this research, the effect of prestressing force on the nonlinearity of concrete was investigated by an experimental study. For the measurement of ultrasonic nonlinearity, a prestressed concrete beam was prepared and a nonlinear resonant ultrasound method was adopted. When the prestressing force changes, the stress state of the concrete inside the beam is affected, which leads to the occurrence of micro-cracks and changes in mechanical properties. Therefore, it is necessary to introduce nonlinear ultrasonic technology which sensitively reflects microstructural changes. Repetitive prestressing load history, including maximum levels of 45%, 60% and 75%, depending on the compressive strength, is designed to evaluate the impact of loading levels on the nonlinearity. With the experimental results, the possibility of ultrasonic nonlinearity as a trial indicator of stress was evaluated.

Keywords: micro crack, nonlinear ultrasonic resonant spectroscopy, prestressed concrete beam, prestressing force, ultrasonic nonlinearity

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Authors: Khashayar Kazemzadeh, Mohammad Hanif Dasoomi

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According to the increasing volume of traffic, lane changing plays a crucial role in traffic flow. Lane changing in traffic depends on several factors including road geometrical design, speed, drivers’ behavioral characteristics, etc. A great deal of research has been carried out regarding these fields. Despite of the other significant factors, the drivers’ behavioral characteristics of lane changing has been emphasized in this paper. This paper has predicted the effective equation based on personal characteristics of lane changing by regression models.

Keywords: effective equation, lane changing, drivers’ behavioral characteristics, regression models

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Authors: Labane Chrif

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A nonlinear approach to the automatic pitch attitude control problem for aircraft transportation is presented. A nonlinear model describing the longitudinal equations of motion in strict feedback form is derived. Backstepping is utilized for the construction of a globally stabilizing controller with a number of free design parameters. The controller is evaluated using the aircraft transportation. The adaptation scheme proposed allowed us to design an explicit controller with a minimal knowledge of the aircraft aerodynamics. Finally, the simulation results will show that backstepping controller have better dynamic performance, simpler design, higher precision, easier implement, etc. At the same time, the control effect will be significantly improved. In addition, backstepping control is superior in short transition, good stability, anti-disturbance and good control.

Keywords: nonlinear control, backstepping, aircraft control, Lyapunov function, longitudinal model

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Authors: Hui-Min Lai, Chin-Pin Chen, Yung-Fu Chang

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The expectation-confirmation model (ECM) is one of the most widely used models for evaluating information system continuance, and this model has been extended to other study backgrounds, or expanded with other theoretical perspectives. However, combining ECM with other theories or investigating the background problem may produce some disparities, thus generating inaccurate conclusions. Habit is considered to be an important factor that influences the user’s continuance behavior. This paper thus critically examines seven pairs of relationships from the original ECM and the habit variable. A meta-analysis was used to tackle the development of ECM research over the last 10 years from a range of journals and conference papers published in 2005–2014. Forty-six journal articles and 19 conference papers were selected for analysis. The results confirm our prediction that a high effect size for the seven pairs of relationships was obtained (ranging from r=0.386 to r=0.588). Furthermore, a meta-analytic structural equation modeling was performed to simultaneously test all relationships. The results show that habit had a significant positive effect on continuance intention at p<=0.05 and that the six other pairs of relationships were significant at p<0.10. Based on the findings, we refined our original research model and an alternative model was proposed for understanding and predicting information system continuance. Some theoretical implications are also discussed.

Keywords: Expectation-confirmation theory, Expectation-confirmation model, Meta-analysis, meta-analytic structural equation modeling.

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Authors: Fadi Eleiwi, Taous Meriem Laleg-Kirati

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This paper presents a complete dynamic modeling of a membrane distillation process. The model contains two consistent dynamic models. A 2D advection-diffusion equation for modeling the whole process and a modified heat equation for modeling the membrane itself. The complete model describes the temperature diffusion phenomenon across the feed, membrane, permeate containers and boundary layers of the membrane. It gives an online and complete temperature profile for each point in the domain. It explains heat conduction and convection mechanisms that take place inside the process in terms of mathematical parameters, and justify process behavior during transient and steady state phases. The process is monitored for any sudden change in the performance at any instance of time. In addition, it assists maintaining production rates as desired, and gives recommendations during membrane fabrication stages. System performance and parameters can be optimized and controlled using this complete dynamic model. Evolution of membrane boundary temperature with time, vapor mass transfer along the process, and temperature difference between membrane boundary layers are depicted and included. Simulations were performed over the complete model with real membrane specifications. The plots show consistency between 2D advection-diffusion model and the expected behavior of the systems as well as literature. Evolution of heat inside the membrane starting from transient response till reaching steady state response for fixed and varying times is illustrated.

Keywords: membrane distillation, dynamical modeling, advection-diffusion equation, thermal equilibrium, heat equation

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Authors: Woo-Tai Jung, Sung-Yong Choi, Young-Hwan Park

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The composite pavement system considered in this paper is composed of a functional surface layer, a fiber reinforced asphalt middle layer and a fiber reinforced lean concrete base layer. The mix design of the fiber reinforced lean concrete corresponds to the mix composition of conventional lean concrete but reinforced by fibers. The quasi-absence of research on the durability or long-term performances (fatigue, creep, etc.) of such mix design stresses the necessity to evaluate experimentally the long-term characteristics of this layer composition. This study tests the creep characteristics as one of the long-term characteristics of the fiber reinforced lean concrete layer for composite pavement using a new creep device. The test results reveal that the lean concrete mixed with fiber reinforcement and fly ash develops smaller creep than the conventional lean concrete. The results of the application of the CEB-FIP prediction equation indicate that a modified creep prediction equation should be developed to fit with the new mix design of the layer.

Keywords: creep, lean concrete, pavement, fiber reinforced concrete, base

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Authors: Sherwan Kher Alden Yakub Alsofy

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In this paper, we consider the relativistic Hamilton-Jacobi (HJ) equation and study the Hawking radiation (HR) of scalar particles from uncharged Grumiller black hole (GBH) which is affordable for testing in astrophysics. GBH is also known as Rindler modified Schwarzschild BH. Our aim is not only to investigate the effect of the Rindler parameter A on the Hawking temperature (TH ), but to examine whether there is any discrepancy between the computed horizon temperature and the standard TH as well. For this purpose, in addition to its naive coordinate system, we study on the three regular coordinate systems which are Painlev´-Gullstrand (PG), ingoing Eddington- Finkelstein (IEF) and Kruskal-Szekeres (KS) coordinates. In all coordinate systems, we calculate the tunneling probabilities of incoming and outgoing scalar particles from the event horizon by using the HJ equation. It has been shown in detail that the considered HJ method is concluded with the conventional TH in all these coordinate systems without giving rise to the famous factor- 2 problem. Furthermore, in the PG coordinates Parikh-Wilczek’s tunneling (PWT) method is employed in order to show how one can integrate the quantum gravity (QG) corrections to the semiclassical tunneling rate by including the effects of self-gravitation and back reaction. We then show how these corrections yield a modification in the TH.

Keywords: ingoing Eddington, Finkelstein, coordinates Parikh-Wilczek’s, Hamilton-Jacobi equation

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Authors: H. Bonakdari, I. Ebtehaj

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The prediction of scour depth around bridge piers is frequently considered in river engineering. One of the key aspects in efficient and optimum bridge structure design is considered to be scour depth estimation around bridge piers. In this study, scour depth around bridge piers is estimated using two methods, namely the Adaptive Neuro-Fuzzy Inference System (ANFIS) and Artificial Neural Network (ANN). Therefore, the effective parameters in scour depth prediction are determined using the ANN and ANFIS methods via dimensional analysis, and subsequently, the parameters are predicted. In the current study, the methods’ performances are compared with the nonlinear regression (NLR) method. The results show that both methods presented in this study outperform existing methods. Moreover, using the ratio of pier length to flow depth, ratio of median diameter of particles to flow depth, ratio of pier width to flow depth, the Froude number and standard deviation of bed grain size parameters leads to optimal performance in scour depth estimation.

Keywords: adaptive neuro-fuzzy inference system (ANFIS), artificial neural network (ANN), bridge pier, scour depth, nonlinear regression (NLR)

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Authors: Aleksandr I. Korobov, Natalia V. Shirgina, Aleksey I. Kokshaiskiy, Vyacheslav M. Prokhorov

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The paper presents the results of an experimental study of the effect of reverse mechanical load-unloading on the mechanical, linear, and nonlinear elastic properties of n-AMg6/C60 nanocomposite. Samples for experimental studies of n-AMg6/C60 nanocomposite were obtained by grinding AMg6 polycrystalline alloy in a planetary mill with 0.3 wt % of C60 fullerite in an argon atmosphere. The resulting product consisted of 200-500-micron agglomerates of nanoparticles. X-ray coherent scattering (CSL) method has shown that the average nanoparticle size is 40-60 nm. The resulting preform was extruded at high temperature. Modifications of C60 fullerite interferes the process of recrystallization at grain boundaries. In the samples of n-AMg6/C60 nanocomposite, the load curve is measured: the dependence of the mechanical stress σ on the strain of the sample ε under its multi-cycle load-unloading process till its destruction. The hysteresis dependence σ = σ(ε) was observed, and insignificant residual strain ε < 0.005 were recorded. At σ≈500 MPa and ε≈0.025, the sample was destroyed. The destruction of the sample was fragile. Microhardness was measured before and after destruction of the sample. It was found that the loading-unloading process led to an increase in its microhardness. The effect of the reversible mechanical stress on the linear and nonlinear elastic properties of the n-AMg6/C60 nanocomposite was studied experimentally by ultrasonic method on the automated complex Ritec RAM-5000 SNAP SYSTEM. In the n-AMg6/C60 nanocomposite, the velocities of the longitudinal and shear bulk waves were measured with the pulse method, and all the second-order elasticity coefficients and their dependence on the magnitude of the reversible mechanical stress applied to the sample were calculated. Studies of nonlinear elastic properties of the n-AMg6/C60 nanocomposite at reversible load-unloading of the sample were carried out with the spectral method. At arbitrary values of the strain of the sample (up to its breakage), the dependence of the amplitude of the second longitudinal acoustic harmonic at a frequency of 2f = 10MHz on the amplitude of the first harmonic at a frequency f = 5MHz of the acoustic wave is measured. Based on the results of these measurements, the values of the nonlinear acoustic parameter in the n-AMg6/C60 nanocomposite sample at different mechanical stress were determined. The obtained results can be used in solid-state physics, materials science, for development of new techniques for nondestructive testing of structural materials using methods of nonlinear acoustic diagnostics. This study was supported by the Russian Science Foundation (project №14-22-00042).

Keywords: nanocomposite, generation of acoustic harmonics, nonlinear acoustic parameter, hysteresis

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Authors: A. R. Nezamabadi, M. Veiskarami

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This paper studies free vibration of simply supported functionally graded beams with piezoelectric layers based on the first order shear deformation theory. The Young's modulus of beam is assumed to be graded continuously across the beam thickness. The governing equation is established. Resulting equation is solved using the Euler's equation. The effects of the constituent volume fractions, the influences of applied voltage on the vibration frequency are presented. To investigate the accuracy of the present analysis, a compression study is carried out with a known data.

Keywords: mechanical buckling, functionally graded beam, first order shear deformation theory, free vibration

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Authors: Mohammad Karimi Moridani, Mohammad Abdi Zadeh, Zahra Shahiazar Mazraeh

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In recent years, the use of intelligent systems in biomedical engineering has increased dramatically, especially in the diagnosis of various diseases. Also, due to the relatively simple recording of the electrocardiogram signal (ECG), this signal is a good tool to show the function of the heart and diseases associated with it. The aim of this paper is to design an intelligent system for automatically detecting a normal electrocardiogram signal from abnormal one. Using this diagnostic system, it is possible to identify a person's heart condition in a very short time and with high accuracy. The data used in this article are from the Physionet database, available in 2016 for use by researchers to provide the best method for detecting normal signals from abnormalities. Data is of both genders and the data recording time varies between several seconds to several minutes. All data is also labeled normal or abnormal. Due to the low positional accuracy and ECG signal time limit and the similarity of the signal in some diseases with the normal signal, the heart rate variability (HRV) signal was used. Measuring and analyzing the heart rate variability with time to evaluate the activity of the heart and differentiating different types of heart failure from one another is of interest to the experts. In the preprocessing stage, after noise cancelation by the adaptive Kalman filter and extracting the R wave by the Pan and Tampkinz algorithm, R-R intervals were extracted and the HRV signal was generated. In the process of processing this paper, a new idea was presented that, in addition to using the statistical characteristics of the signal to create a return map and extraction of nonlinear characteristics of the HRV signal due to the nonlinear nature of the signal. Finally, the artificial neural networks widely used in the field of ECG signal processing as well as distinctive features were used to classify the normal signals from abnormal ones. To evaluate the efficiency of proposed classifiers in this paper, the area under curve ROC was used. The results of the simulation in the MATLAB environment showed that the AUC of the MLP and SVM neural network was 0.893 and 0.947, respectively. As well as, the results of the proposed algorithm in this paper indicated that the more use of nonlinear characteristics in normal signal classification of the patient showed better performance. Today, research is aimed at quantitatively analyzing the linear and non-linear or descriptive and random nature of the heart rate variability signal, because it has been shown that the amount of these properties can be used to indicate the health status of the individual's heart. The study of nonlinear behavior and dynamics of the heart's neural control system in the short and long-term provides new information on how the cardiovascular system functions, and has led to the development of research in this field. Given that the ECG signal contains important information and is one of the common tools used by physicians to diagnose heart disease, but due to the limited accuracy of time and the fact that some information about this signal is hidden from the viewpoint of physicians, the design of the intelligent system proposed in this paper can help physicians with greater speed and accuracy in the diagnosis of normal and patient individuals and can be used as a complementary system in the treatment centers.

Keywords: neart rate variability, signal processing, linear and non-linear features, classification methods, ROC Curve

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Authors: Motahar Reza, Rajni Chahal, Neha Sharma

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This article addresses the boundary layer flow and heat transfer of Casson fluid over a nonlinearly permeable stretching surface with chemical reaction in the presence of variable magnetic field. The effect of thermal radiation is considered to control the rate of heat transfer at the surface. Using similarity transformations, the governing partial differential equations of this problem are reduced into a set of non-linear ordinary differential equations which are solved by finite difference method. It is observed that the velocity at fixed point decreases with increasing the nonlinear stretching parameter but the temperature increases with nonlinear stretching parameter.

Keywords: boundary layer flow, nonlinear stretching, Casson fluid, heat transfer, radiation

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Authors: Somnath Bhattacharyya

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The mobile adsorbed surface charge on hydrophobic surfaces can modify the velocity slip condition as well as create a Marangoni stress at the interface. The functionalized hydrophobic walls of micro/nanopores, e.g., graphene nanochannels, may possess physio-sorbed ions. The lateral mobility of the physisorbed absorbed ions creates a friction force as well as an electric force, leading to a modification in the velocity slip condition at the hydrophobic surface. In addition, the non-uniform distribution of these surface ions creates a surface tension gradient, leading to a Marangoni stress. The impact of the mobile surface charge on streaming potential and electrochemical energy conversion efficiency in a pressure-driven flow of ionized liquid through the nanopore is addressed. Also, enhanced electro-osmotic flow through the hydrophobic nanochannel is also analyzed. The mean-filed electrokinetic model is modified to take into account the short-range non-electrostatic steric interactions and the long-range Coulomb correlations. The steric interaction is modeled by considering the ions as charged hard spheres of finite radius suspended in the electrolyte medium. The electrochemical potential is modified by including the volume exclusion effect, which is modeled based on the BMCSL equation of state. The electrostatic correlation is accounted for in the ionic self-energy. The extremal of the self-energy leads to a fourth-order Poisson equation for the electric field. The ion transport is governed by the modified Nernst-Planck equation, which includes the ion steric interactions; born force arises due to the spatial variation of the dielectric permittivity and the dielectrophoretic force on the hydrated ions. This ion transport equation is coupled with the Navier-Stokes equation describing the flow of the ionized fluid and the 3fourth-order Poisson equation for the electric field. We numerically solve the coupled set of nonlinear governing equations along with the prescribed boundary conditions by adopting a control volume approach over a staggered grid arrangement. In the staggered grid arrangements, velocity components are stored on the midpoint of the cell faces to which they are normal, whereas the remaining scalar variables are stored at the center of each cell. The convection and electromigration terms are discretized at each interface of the control volumes using the total variation diminishing (TVD) approach to capture the strong convection resulting from the highly enhanced fluid flow due to the modified model. In order to link pressure to the continuity equation, we adopt a pressure correction-based iterative SIMPLE (Semi-Implicit Method for Pressure-Linked Equations) algorithm, in which the discretized continuity equation is converted to a Poisson equation involving pressure correction terms. Our results show that the physisorbed ions on a hydrophobic surface create an enhanced slip velocity when streaming potential, which enhances the convection current. However, the electroosmotic flow attenuates due to the mobile surface ions.

Keywords: microfluidics, electroosmosis, streaming potential, electrostatic correlation, finite sized ions

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Authors: Hyun-Woo Cho

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Unexpected events may occur with serious impacts on industrial process. This work utilizes a data representation technique to model and to analyze process data pattern for the purpose of diagnosis. In this work, the use of triangular representation of process data is evaluated using simulation process. Furthermore, the effect of using different pre-treatment techniques based on such as linear or nonlinear reduced spaces was compared. This work extracted the fault pattern in the reduced space, not in the original data space. The results have shown that the non-linear technique based diagnosis method produced more reliable results and outperforms linear method.

Keywords: process monitoring, data analysis, pattern modeling, fault, nonlinear techniques

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Authors: Reza Soleimanpour, Ching Tai Ng

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Fibre-composites are widely used in various structures due to their attractive properties such as higher stiffness to mass ratio and better corrosion resistance compared to metallic materials. However, one serious weakness of this composite material is delamination, which is a subsurface separation of laminae. A low level of this barely visible damage can cause a significant reduction in residual compressive strength. In the last decade, the application of guided waves for damage detection has been a topic of significant interest for many researches. Among all guided wave techniques, nonlinear guided wave has shown outstanding sensitivity and capability for detecting different types of damages, e.g. cracks and delaminations. So far, most of researches on applications of nonlinear guided wave have been dedicated to isotropic material, such as aluminium and steel, while only a few works have been done on applications of nonlinear characteristics of guided waves in anisotropic materials. This study investigates the nonlinear interactions of the fundamental antisymmetric lamb wave (A0) with delamination in composite laminates using three-dimensional (3D) explicit finite element (FE) simulations. The nonlinearity considered in this study arises from interactions of two interfaces of sub-laminates at the delamination region, which generates contact acoustic nonlinearity (CAN). The aim of this research is to investigate the phenomena of CAN in composite laminated beams by a series of numerical case studies. In this study interaction of fundamental antisymmetric lamb wave with delamination of different sizes are studied in detail. The results show that the A0 lamb wave interacts with the delaminations generating CAN in the form of higher harmonics, which is a good indicator for determining the existence of delaminations in composite laminates.

Keywords: contact acoustic nonlinearity, delamination, fibre reinforced composite beam, finite element, nonlinear guided waves

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Authors: Masoud Ghermezi

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Studying the sheet metals is one of the most important research areas in the field of metal forming due to their extensive applications in the aerospace industries. A useful method for determining the forming limit of these materials and consequently preventing the rupture of sheet metals during the forming process is the use of the forming limit curve (FLC). In addition to specifying the forming limit, this curve also delineates a boundary for the allowed values of strain in sheet metal forming; these characteristics of the FLC along with its accuracy of computation and wide range of applications have made this curve the basis of research in the present paper. This study presents a new model that not only agrees with the results obtained from the above mentioned theory, but also eliminates its shortcomings. In this theory, like in the M-K theory, a thin sheet with an inhomogeneity as a gradient thickness reduction with a sinusoidal function has been chosen and subjected to two-dimensional stress. Through analytical evaluation, ultimately, a governing differential equation has been obtained. The numerical solution of this equation for the range of positive strains (stretched region) yields the results that agree with the results obtained from M-K theory. Also the solution of this equation for the range of negative strains (tension region) completes the FLC curve. The findings obtained by applying this equation on two alloys with the hardening exponents of 0.4 and 0.24 indicate the validity of the presented equation.

Keywords: sheet metal, metal forming, forming limit curve (FLC), M-K theory

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Authors: N. Manoj

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The aeroelastic behavior of engine nacelle strake when subjected to unsteady aerodynamic flows is investigated in this paper. Geometric nonlinear characteristics and modal parameters of nacelle strake are studied when it is under dynamic loading condition. Here, an N-S based Finite Volume solver is coupled with Finite Element (FE) based nonlinear structural solver to investigate the nonlinear characteristics of nacelle strake over a range of dynamic pressures at various phases of flight like takeoff, climb, and cruise conditions. The combination of high fidelity models for both aerodynamics and structural dynamics is used to predict the nonlinearities of strake (chine). The methodology adopted for present aeroelastic analysis is partitioned-based time domain coupled CFD and CSD solvers and it is validated by the consideration of experimental and numerical comparison of aeroelastic data for a cropped delta wing model which has a proven record. The present strake geometry is derived from theoretical formulation. The amplitude and frequency obtained from the coupled solver at various dynamic pressures is discussed, which gives a better understanding of its impact on aerodynamic design-sizing of strake.

Keywords: aeroelasticity, finite volume, geometric nonlinearity, limit cycle oscillations, strake

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Authors: Alexander P. Smirnov, Sergey A. Matveev, Dmitry A. Zheltkov, Eugene E. Tyrtyshnikov

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We propose a new computational technique for multidimensional (multicomponent) Smoluchowski coagulation equation. Using low-rank approximations in Tensor Train format of both the solution and the coagulation kernel, we accelerate the classical finite-difference Runge-Kutta scheme keeping its level of accuracy. The complexity of the taken finite-difference scheme is reduced from O(N^2d) to O(d^2 N log N ), where N is the number of grid nodes and d is a dimensionality of the problem. The efficiency and the accuracy of the new method are demonstrated on concrete problem with known analytical solution.

Keywords: tensor train decomposition, multicomponent Smoluchowski equation, runge-kutta scheme, convolution

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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: Farid Nouioua, Abdelouaheb Ardjouni

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In this article, we study the existence of positive periodic solutions of certain delay differential equations. In the process we convert the differential equation into an equivalent integral equation after which appropriate mappings are constructed. We then employ Krasnoselskii's fixed point theorem to obtain sufficient conditions for the existence of a positive periodic solution of the differential equation. The obtained results improve and extend the results in the literature. Finally, an example is given to illustrate our results.

Keywords: delay differential equations, positive periodic solutions, integral equations, Krasnoselskii fixed point theorem

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Authors: Jaime E. Munoz, Jose C. Arcos, Oscar E. Bautista, Ivan E. Campos

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The influence of slippage phenomenon over the destabilization and atomization mechanisms induced via surface acoustic waves on a Newtonian, millimeter-sized, drop deposited on a hydrophilic substrate is studied theoretically. By implementing the Navier-slip model and a lubrication-type approach into the equations which govern the dynamic response of a drop exposed to acoustic stress, a highly nonlinear evolution equation for the air-liquid interface is derived in terms of the acoustic capillary number and the slip coefficient. By numerically solving such an evolution equation, the Spatio-temporal deformation of the drop's free surface is obtained; in this context, atomization of the initial drop into micron-sized droplets is predicted at our numerical model once the acoustically-driven capillary waves reach a critical value: the instability length. Our results show slippage phenomenon at systems with partial and complete wetting favors the formation of capillary waves at the free surface, which traduces in a major volume of liquid being atomized in comparison to the no-slip case for a given time interval. In consequence, slippage at the wall possesses the capability to affect and improve the atomization rate for a drop exposed to a high-frequency acoustic field.

Keywords: capillary instability, lubrication theory, navier-slip condition, SAW atomization

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Authors: Mohammad R. Jalali

Abstract:

Movement of liquid with a free surface in a container is known as slosh. For instance, slosh occurs when water in a closed tank is set in motion by a free surface displacement, or when liquid natural gas in a container is vibrated by an external driving force, such as an earthquake or movement induced by transport. Slosh is also derived from resonant switching of a natural basin. During sloshing, different types of motion are produced by energy exchange between the liquid and its container. In present study, a numerical model is developed to simulate the nonlinear even harmonic oscillations of free surface sloshing of an initial disturbance to the free surface of a liquid in a closed square basin. The response of the liquid free surface is affected by amplitude and motion frequencies of its container; therefore, sloshing involves complex fluid-structure interactions. In the present study, nonlinear interaction of free surface sloshing of an initial Gaussian hump with its uneven container is predicted numerically. For this purpose, Green-Naghdi (GN) equations are applied as governing equation of fluid field to produce nonlinear second-order and higher-order wave interactions. These equations reduce the dimensions from three to two, yielding equations that can be solved efficiently. The GN approach assumes a particular flow kinematic structure in the vertical direction for shallow and deep-water problems. The fluid velocity profile is finite sum of coefficients depending on space and time multiplied by a weighting function. It should be noted that in GN theory, the flow is rotational. In this study, GN numerical simulations of initial Gaussian hump are compared with Fourier series semi-analytical solutions of the linearized shallow water equations. The comparison reveals that satisfactory agreement exists between the numerical simulation and the analytical solution of the overall free surface sloshing patterns. The resonant free surface motions driven by an initial Gaussian disturbance are obtained by Fast Fourier Transform (FFT) of the free surface elevation time history components. Numerically predicted velocity vectors and magnitude contours for the free surface patterns indicate that interaction of Gaussian hump with its container has localized effect. The result of this sloshing is applicable to the design of stable liquefied oil containers in tankers and offshore platforms.

Keywords: fluid-structure interactions, free surface sloshing, Gaussian hump, Green-Naghdi equations, numerical predictions

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Authors: Clarinda Vitorino Nhangumbe, Ercília Sousa

Abstract:

Weather derivatives are financial products used to cover non catastrophic weather events with a weather index as the underlying asset. The rainfall weather derivative pricing model is modeled based in the assumption that the rainfall dynamics follows Ornstein-Uhlenbeck process, and the partial differential equation approach is used to derive the convection-diffusion two dimensional time dependent partial differential equation, where the spatial variables are the rainfall index and rainfall depth. To compute the approximation solutions of the partial differential equation, the appropriate boundary conditions are suggested, and an explicit numerical method is proposed in order to deal efficiently with the different choices of the coefficients involved in the equation. Being an explicit numerical method, it will be conditionally stable, then the stability region of the numerical method and the order of convergence are discussed. The model is tested for real precipitation data.

Keywords: finite differences method, ornstein-uhlenbeck process, partial differential equations approach, rainfall derivatives

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Authors: Hassan J. Al Salman, Ahmed A. Al Ghafli

Abstract:

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 at each time level. Then, we derive some essential stability estimates and discuss the uniqueness of the approximations. In addition, we employ Nochetto mathematical framework to prove an optimal error bound in time for d= 1, 2 and 3 space dimensions. Finally, we present some numerical experiments to verify the obtained theoretical results.

Keywords: reaction diffusion system, finite element approximation, stability estimates, error bound

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Authors: Subha D. Puthankattil, Paul K. Joseph

Abstract:

Analyzing brain signals of the patients suffering from the state of depression may lead to interesting observations in the signal parameters that is quite different from a normal control. The present study adopts two different methods: Time frequency domain and nonlinear method for the analysis of EEG signals acquired from depression patients and age and sex matched normal controls. The time frequency domain analysis is realized using wavelet entropy and approximate entropy is employed for the nonlinear method of analysis. The ability of the signal processing technique and the nonlinear method in differentiating the physiological aspects of the brain state are revealed using Wavelet entropy and Approximate entropy.

Keywords: EEG, depression, wavelet entropy, approximate entropy, relative wavelet energy, multiresolution decomposition

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Authors: Anton S. Perin, Vladimir M. Shandarov

Abstract:

Compensation for the nonlinear diffraction of narrow laser beams with wavelength of 532 and the formation of photonic waveguides and waveguide circuits due to the contribution of pyroelectric effect to the nonlinear response of lithium niobate crystal have been experimentally demonstrated. Complete compensation for the linear and nonlinear diffraction broadening of light beams is obtained upon uniform heating of an undoped sample from room temperature to 55 degrees Celsius. An analysis of the light-field distribution patterns and the corresponding intensity distribution profiles allowed us to estimate the spacing for the channel waveguides. The observed behavior of bright soliton beams may be caused by their coherent interaction, which manifests itself in repulsion for anti-phase light fields and in attraction for in-phase light fields. The experimental results of this study showed a fundamental possibility of forming optically complex waveguide structures in lithium niobate crystals with pyroelectric mechanism of nonlinear response. The topology of these structures is determined by the light field distribution on the input face of crystalline sample. The optical induction of channel waveguide elements by interacting spatial solitons makes it possible to design optical systems with a more complex topology and a possibility of their dynamic reconfiguration.

Keywords: self-action, soliton, lithium niobate, piroliton, photorefractive effect, pyroelectric effect

Procedia PDF Downloads 139