Search results for: nonlinear evolution of ultrasonic pulses
1371 Nonlinear Simulation of Harmonically Coupled Two-Beam Free-Electron Laser
Authors: M. Zahedian, B. Maraghechi, M. H. Rouhani
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A nonlinear model of two-beam free-electron laser (FEL) in the absence of slippage is presented. The two beams are assumed to be cold with different energies and the fundamental resonance of the higher energy beam is at the third harmonic of lower energy beam. By using Maxwell-s equations and full Lorentz force equations of motion for the electron beams, coupled differential equations are derived and solved numerically by the fourth order Runge–Kutta method. In this method a considerable growth of third harmonic electromagnetic field in the XUV and X-ray regions is predicted.Keywords: Free-electron laser, Higher energy beam, Lowerenergy beam, Two-beam
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 13361370 Nonlinear Stability of Convection in a Thermally Modulated Anisotropic Porous Medium
Authors: M. Meenasaranya, S. Saravanan
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Conditions corresponding to the unconditional stability of convection in a mechanically anisotropic fluid saturated porous medium of infinite horizontal extent are determined. The medium is heated from below and its bounding surfaces are subjected to temperature modulation which consists of a steady part and a time periodic oscillating part. The Brinkman model is employed in the momentum equation with the Bousinessq approximation. The stability region is found for arbitrary values of modulational frequency and amplitude using the energy method. Higher order numerical computations are carried out to find critical boundaries and subcritical instability regions more accurately.Keywords: Convection, porous medium, anisotropy, temperature modulation, nonlinear stability.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 8641369 Investigation of Improved Chaotic Signal Tracking by Echo State Neural Networks and Multilayer Perceptron via Training of Extended Kalman Filter Approach
Authors: Farhad Asadi, S. Hossein Sadati
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This paper presents a prediction performance of feedforward Multilayer Perceptron (MLP) and Echo State Networks (ESN) trained with extended Kalman filter. Feedforward neural networks and ESN are powerful neural networks which can track and predict nonlinear signals. However, their tracking performance depends on the specific signals or data sets, having the risk of instability accompanied by large error. In this study we explore this process by applying different network size and leaking rate for prediction of nonlinear or chaotic signals in MLP neural networks. Major problems of ESN training such as the problem of initialization of the network and improvement in the prediction performance are tackled. The influence of coefficient of activation function in the hidden layer and other key parameters are investigated by simulation results. Extended Kalman filter is employed in order to improve the sequential and regulation learning rate of the feedforward neural networks. This training approach has vital features in the training of the network when signals have chaotic or non-stationary sequential pattern. Minimization of the variance in each step of the computation and hence smoothing of tracking were obtained by examining the results, indicating satisfactory tracking characteristics for certain conditions. In addition, simulation results confirmed satisfactory performance of both of the two neural networks with modified parameterization in tracking of the nonlinear signals.Keywords: Feedforward neural networks, nonlinear signal prediction, echo state neural networks approach, leaking rates, capacity of neural networks.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 7471368 Auto Regressive Tree Modeling for Parametric Optimization in Fuzzy Logic Control System
Authors: Arshia Azam, J. Amarnath, Ch. D. V. Paradesi Rao
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The advantage of solving the complex nonlinear problems by utilizing fuzzy logic methodologies is that the experience or expert-s knowledge described as a fuzzy rule base can be directly embedded into the systems for dealing with the problems. The current limitation of appropriate and automated designing of fuzzy controllers are focused in this paper. The structure discovery and parameter adjustment of the Branched T-S fuzzy model is addressed by a hybrid technique of type constrained sparse tree algorithms. The simulation result for different system model is evaluated and the identification error is observed to be minimum.Keywords: Fuzzy logic, branch T-S fuzzy model, tree modeling, complex nonlinear system.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 13821367 Effects of the Mass and Damping Matrix Model in the Nonlinear Seismic Response of Steel Frames
Authors: A. Reyes-Salazar, M. D. Llanes-Tizoc, E. Bojorquez, F. Valenzuela-Beltran, J. Bojorquez, J. R. Gaxiola-Camacho, A. Haldar
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Seismic analysis of steel buildings is usually based on the use of the concentrated mass (ML) matrix and the Rayleigh damping matrix (C). Similarly, the initial stiffness matrix (KO) and the first two modes associated to lateral vibrations are commonly used to develop the matrix C. The evaluation of the accuracy of these practices for the particular case of steel buildings with moment-resisting steel frames constitutes the main objective of this research. For this, the nonlinear seismic responses of three models of steel frames, representing low-, medium- and high-rise steel buildings, are considered. Results indicate that if the ML matrix is used, shears and bending moments in columns are underestimated by up to 30% and 65%, respectively, when compared to the corresponding results obtained with the consistent mass matrix (MC). It is also shown that if KO is used in C instead the tangent stiffness matrix (Kt), axial loads in columns are underestimated by up to 80%. It is concluded that the consistent mass matrix should be used in the structural modelling of moment resisting steel frames and the tangent stiffness matrix should be used to develop the Rayleigh damping matrix.
Keywords: Moment-resisting steel frames, consistent and concentrated mass matrices, nonlinear seismic response, Rayleigh damping.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 3801366 A Multi-Population Differential Evolution with Adaptive Mutation and Local Search for Global Optimization
Authors: Zhoucheng Bao, Haiyan Zhu, Tingting Pang, Zuling Wang
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This paper presents a multi population Differential Evolution (DE) with adaptive mutation and local search for global optimization, named AMMADE in order to better coordinate the cooperation between the populations and the rational use of resources. In AMMADE, the population is divided based on the Euclidean distance sorting method at each generation to appropriately coordinate the cooperation between subpopulations and the usage of resources, such that the best-performed subpopulation will get more computing resources in the next generation. Further, an adaptive local search strategy is employed on the best-performed subpopulation to achieve a balanced search. The proposed algorithm has been tested by solving optimization problems taken from CEC2014 benchmark problems. Experimental results show that our algorithm can achieve a competitive or better result than related methods. The results also confirm the significance of devised strategies in the proposed algorithm.
Keywords: Differential evolution, multi-mutation strategies, memetic algorithm, adaptive local search.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 4271365 Exact Three-wave Solutions for High Nonlinear Form of Benjamin-Bona-Mahony-Burgers Equations
Authors: Mohammad Taghi Darvishi, Maliheh Najafi, Mohammad Najafi
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By means of the idea of three-wave method, we obtain some analytic solutions for high nonlinear form of Benjamin-Bona- Mahony-Burgers (shortly BBMB) equations in its bilinear form.
Keywords: Benjamin-Bona-Mahony-Burgers equations, Hirota's bilinear form, three-wave method.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 15651364 Bifurcation Analysis of Horizontal Platform System
Authors: C. C. Wang, N. S. Pai, H. T. Yau, T. T. Liao, M. J. Jang, C. W. Lee, W. M. Hong
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Horizontal platform system (HPS) is popularly applied in offshore and earthquake technology, but it is difficult and time-consuming for regulation. In order to understand the nonlinear dynamic behavior of HPS and reduce the cost when using it, this paper employs differential transformation method to study the bifurcation behavior of HPS. The numerical results reveal a complex dynamic behavior comprising periodic, sub-harmonic, and chaotic responses. Furthermore, the results reveal the changes which take place in the dynamic behavior of the HPS as the external torque is increased. Therefore, the proposed method provides an effective means of gaining insights into the nonlinear dynamics of horizontal platform system.Keywords: horizontal platform system, differentialtransformation method, chaotic.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 15181363 Fuzzy Boundary Layer Solution to Nonlinear Hydraulic Position Control Problem
Authors: Mustafa Resa Becan
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Sliding mode control with a fuzzy boundary layer is presented to hydraulic position control problem in this paper. A nonlinear hydraulic servomechanism which has an asymmetric cylinder is modeled and simulated first, then the proposed control scheme is applied to this model versus the conventional sliding mode control. Simulation results proved that the chattering free position control is achieved by tuning the fuzzy scaling factors properly.
Keywords: Hydraulic servomechanism, position control, sliding mode control, chattering, fuzzy boundary layer.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 18151362 A TFETI Domain Decompositon Solver for Von Mises Elastoplasticity Model with Combination of Linear Isotropic-Kinematic Hardening
Authors: Martin Cermak, Stanislav Sysala
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In this paper we present the efficient parallel implementation of elastoplastic problems based on the TFETI (Total Finite Element Tearing and Interconnecting) domain decomposition method. This approach allow us to use parallel solution and compute this nonlinear problem on the supercomputers and decrease the solution time and compute problems with millions of DOFs. In our approach we consider an associated elastoplastic model with the von Mises plastic criterion and the combination of linear isotropic-kinematic hardening law. This model is discretized by the implicit Euler method in time and by the finite element method in space. We consider the system of nonlinear equations with a strongly semismooth and strongly monotone operator. The semismooth Newton method is applied to solve this nonlinear system. Corresponding linearized problems arising in the Newton iterations are solved in parallel by the above mentioned TFETI. The implementation of this problem is realized in our in-house MatSol packages developed in MatLab.
Keywords: Isotropic-kinematic hardening, TFETI, domain decomposition, parallel solution.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 17481361 Torque Ripple Minimization in Switched Reluctance Motor Using Passivity-Based Robust Adaptive Control
Authors: M.M. Namazi, S.M. Saghaiannejad, A. Rashidi
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In this paper by using the port-controlled Hamiltonian (PCH) systems theory, a full-order nonlinear controlled model is first developed. Then a nonlinear passivity-based robust adaptive control (PBRAC) of switched reluctance motor in the presence of external disturbances for the purpose of torque ripple reduction and characteristic improvement is presented. The proposed controller design is separated into the inner loop and the outer loop controller. In the inner loop, passivity-based control is employed by using energy shaping techniques to produce the proper switching function. The outer loop control is employed by robust adaptive controller to determine the appropriate Torque command. It can also overcome the inherent nonlinear characteristics of the system and make the whole system robust to uncertainties and bounded disturbances. A 4KW 8/6 SRM with experimental characteristics that takes magnetic saturation into account is modeled, simulation results show that the proposed scheme has good performance and practical application prospects.Keywords: Switched Reluctance Motor, Port HamiltonianSystem, Passivity-Based Control, Torque Ripple Minimization
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 16711360 New Stabilization for Switched Neutral Systems with Perturbations
Authors: Lianglin Xiong, Shouming Zhong, Mao Ye
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This paper addresses the stabilization issues for a class of uncertain switched neutral systems with nonlinear perturbations. Based on new classes of piecewise Lyapunov functionals, the stability assumption on all the main operators or the convex combination of coefficient matrices is avoid, and a new switching rule is introduced to stabilize the neutral systems. The switching rule is designed from the solution of the so-called Lyapunov-Metzler linear matrix inequalities. Finally, three simulation examples are given to demonstrate the significant improvements over the existing results.
Keywords: Switched neutral system, piecewise Lyapunov functional, nonlinear perturbation, Lyapunov-Metzler linear matrix inequality.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 16481359 Dynamic Study on the Evaluation of the Settlement of Soil under Sea Dam
Authors: Faroudja Meziani, Amar Kahil
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In order to study the variation in settlement of soil under a dyke dam, the modelisation in our study consists of applying an imposed displacement at the base of the mass of soil (consisting of a saturated sand). The imposed displacement follows the evolution of acceleration of the earthquake of Boumerdes 2003 in Algeria. Moreover, the gravity load is taken into consideration by taking account the specific weight of the materials constituting the dyke. The results obtained show that the gravity loads have a direct influence on the evolution of settlement, especially at the center of the dyke where these loads are higher.
Keywords: Settlement, dynamic analysis, rockfill dam, effect of earthquake, soil dynamics.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 7711358 Modeling the Saltatory Conduction in Myelinated Axons by Order Reduction
Authors: Ruxandra Barbulescu, Daniel Ioan, Gabriela Ciuprina
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The saltatory conduction is the way the action potential is transmitted along a myelinated axon. The potential diffuses along the myelinated compartments and it is regenerated in the Ranvier nodes due to the ion channels allowing the flow across the membrane. For an efficient simulation of populations of neurons, it is important to use reduced order models both for myelinated compartments and for Ranvier nodes and to have control over their accuracy and inner parameters. The paper presents a reduced order model of this neural system which allows an efficient simulation method for the saltatory conduction in myelinated axons. This model is obtained by concatenating reduced order linear models of 1D myelinated compartments and nonlinear 0D models of Ranvier nodes. The models for the myelinated compartments are selected from a series of spatially distributed models developed and hierarchized according to their modeling errors. The extracted model described by a nonlinear PDE of hyperbolic type is able to reproduce the saltatory conduction with acceptable accuracy and takes into account the finite propagation speed of potential. Finally, this model is again reduced in order to make it suitable for the inclusion in large-scale neural circuits.Keywords: Saltatory conduction, action potential, myelinated compartments, nonlinear, Ranvier nodes, reduced order models, POD.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 8261357 Nonlinear Static Analysis of Laminated Composite Hollow Beams with Super-Elliptic Cross-Sections
Authors: G. Akgun, I. Algul, H. Kurtaran
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In this paper geometrically nonlinear static behavior of laminated composite hollow super-elliptic beams is investigated using generalized differential quadrature method. Super-elliptic beam can have both oval and elliptic cross-sections by adjusting parameters in super-ellipse formulation (also known as Lamé curves). Equilibrium equations of super-elliptic beam are obtained using the virtual work principle. Geometric nonlinearity is taken into account using von-Kármán nonlinear strain-displacement relations. Spatial derivatives in strains are expressed with the generalized differential quadrature method. Transverse shear effect is considered through the first-order shear deformation theory. Static equilibrium equations are solved using Newton-Raphson method. Several composite super-elliptic beam problems are solved with the proposed method. Effects of layer orientations of composite material, boundary conditions, ovality and ellipticity on bending behavior are investigated.
Keywords: Generalized differential quadrature, geometric nonlinearity, laminated composite, super-elliptic cross-section.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 13771356 A Sum Operator Method for Unique Positive Solution to a Class of Boundary Value Problem of Nonlinear Fractional Differential Equation
Authors: Fengxia Zheng, Chuanyun Gu
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By using a fixed point theorem of a sum operator, the existence and uniqueness of positive solution for a class of boundary value problem of nonlinear fractional differential equation is studied. An iterative scheme is constructed to approximate it. Finally, an example is given to illustrate the main result.Keywords: Fractional differential equation, Boundary value problem, Positive solution, Existence and uniqueness, Fixed point theorem of a sum operator.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 14771355 Oscillation Criteria for Nonlinear Second-order Damped Delay Dynamic Equations on Time Scales
Authors: Da-Xue Chen, Guang-Hui Liu
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In this paper, we establish several oscillation criteria for the nonlinear second-order damped delay dynamic equation r(t)|xΔ(t)|β-1xΔ(t)Δ + p(t)|xΔσ(t)|β-1xΔσ(t) + q(t)f(x(τ (t))) = 0 on an arbitrary time scale T, where β > 0 is a constant. Our results generalize and improve some known results in which β > 0 is a quotient of odd positive integers. Some examples are given to illustrate our main results.
Keywords: Oscillation, damped delay dynamic equation, time scale.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 12671354 Existence of Solutions for a Nonlinear Fractional Differential Equation with Integral Boundary Condition
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This paper deals with a nonlinear fractional differential equation with integral boundary condition of the following form: Dαt x(t) = f(t, x(t),Dβ t x(t)), t ∈ (0, 1), x(0) = 0, x(1) = 1 0 g(s)x(s)ds, where 1 < α ≤ 2, 0 < β < 1. Our results are based on the Schauder fixed point theorem and the Banach contraction principle.
Keywords: Fractional differential equation, Integral boundary condition, Schauder fixed point theorem, Banach contraction principle.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 16471353 Hippocampus Segmentation using a Local Prior Model on its Boundary
Authors: Dimitrios Zarpalas, Anastasios Zafeiropoulos, Petros Daras, Nicos Maglaveras
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Segmentation techniques based on Active Contour Models have been strongly benefited from the use of prior information during their evolution. Shape prior information is captured from a training set and is introduced in the optimization procedure to restrict the evolution into allowable shapes. In this way, the evolution converges onto regions even with weak boundaries. Although significant effort has been devoted on different ways of capturing and analyzing prior information, very little thought has been devoted on the way of combining image information with prior information. This paper focuses on a more natural way of incorporating the prior information in the level set framework. For proof of concept the method is applied on hippocampus segmentation in T1-MR images. Hippocampus segmentation is a very challenging task, due to the multivariate surrounding region and the missing boundary with the neighboring amygdala, whose intensities are identical. The proposed method, mimics the human segmentation way and thus shows enhancements in the segmentation accuracy.Keywords: Medical imaging & processing, Brain MRI segmentation, hippocampus segmentation, hippocampus-amygdala missingboundary, weak boundary segmentation, region based segmentation, prior information, local weighting scheme in level sets, spatialdistribution of labels, gradient distribution on boundary.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 17431352 Optimization Approach to Estimate Hammerstein–Wiener Nonlinear Blocks in Presence of Noise and Disturbance
Authors: Leili Esmaeilani, Jafar Ghaisari, Mohsen Ahmadian
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Hammerstein–Wiener model is a block-oriented model where a linear dynamic system is surrounded by two static nonlinearities at its input and output and could be used to model various processes. This paper contains an optimization approach method for analysing the problem of Hammerstein–Wiener systems identification. The method relies on reformulate the identification problem; solve it as constraint quadratic problem and analysing its solutions. During the formulation of the problem, effects of adding noise to both input and output signals of nonlinear blocks and disturbance to linear block, in the emerged equations are discussed. Additionally, the possible parametric form of matrix operations to reduce the equation size is presented. To analyse the possible solutions to the mentioned system of equations, a method to reduce the difference between the number of equations and number of unknown variables by formulate and importing existing knowledge about nonlinear functions is presented. Obtained equations are applied to an instance H–W system to validate the results and illustrate the proposed method.Keywords: Identification, Hammerstein-Wiener, optimization, quantization.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 7921351 Trajectory Estimation and Control of Vehicle using Neuro-Fuzzy Technique
Authors: B. Selma, S. Chouraqui
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Nonlinear system identification is becoming an important tool which can be used to improve control performance. This paper describes the application of adaptive neuro-fuzzy inference system (ANFIS) model for controlling a car. The vehicle must follow a predefined path by supervised learning. Backpropagation gradient descent method was performed to train the ANFIS system. The performance of the ANFIS model was evaluated in terms of training performance and classification accuracies and the results confirmed that the proposed ANFIS model has potential in controlling the non linear system.
Keywords: Adaptive neuro-fuzzy inference system (ANFIS), Fuzzy logic, neural network, nonlinear system, control
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 17731350 Experimental Study of Boost Converter Based PV Energy System
Authors: T. Abdelkrim, K. Ben seddik, B. Bezza, K. Benamrane, Aeh. Benkhelifa
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This paper proposes an implementation of boost converter for a resistive load using photovoltaic energy as a source. The model of photovoltaic cell and operating principle of boost converter are presented. A PIC microcontroller is used in the close loop control to generate pulses for controlling the converter circuit. To performance evaluation of boost converter, a variation of output voltage of PV panel is done by shading one and two cells.
Keywords: Boost converter, Microcontroller, Photovoltaic power generation, Shading cells.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 39891349 Characterisation and Classification of Natural Transients
Authors: Ernst D. Schmitter
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Monitoring lightning electromagnetic pulses (sferics) and other terrestrial as well as extraterrestrial transient radiation signals is of considerable interest for practical and theoretical purposes in astro- and geophysics as well as meteorology. Managing a continuous flow of data, automisation of the detection and classification process is important. Features based on a combination of wavelet and statistical methods proved efficient for analysis and characterisation of transients and as input into a radial basis function network that is trained to discriminate transients from pulse like to wave like.Keywords: transient signals, statistics, wavelets, neural networks
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 14371348 Concrete Gravity Dams and Traveling Wave Effect along Reservoir Bottom
Authors: H. Mirzabozorg, M. Varmazyari
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In the present article, effect of non-uniform excitation of reservoir bottom on nonlinear response of concrete gravity dams is considered. Anisotropic damage mechanics approach is used to model nonlinear behavior of mass concrete in 2D space. The tallest monolith of Pine Flat dam is selected as a case study. The horizontal and vertical components of 1967 Koyna earthquake is used to excite the system. It is found that crest response and stresses within the dam body decrease significantly when the reservoir is excited nonuniformly. In addition, the crack profiles within the dam body and in vicinity of the neck decreases.Keywords: Concrete gravity dam, dam-reservoir-foundation interaction, traveling wave, damage mechanics.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 18021347 A New Particle Filter Inspired by Biological Evolution: Genetic Filter
Authors: S. Park, J. Hwang, K. Rou, E. Kim
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In this paper, we consider a new particle filter inspired by biological evolution. In the standard particle filter, a resampling scheme is used to decrease the degeneracy phenomenon and improve estimation performance. Unfortunately, however, it could cause the undesired the particle deprivation problem, as well. In order to overcome this problem of the particle filter, we propose a novel filtering method called the genetic filter. In the proposed filter, we embed the genetic algorithm into the particle filter and overcome the problems of the standard particle filter. The validity of the proposed method is demonstrated by computer simulation.Keywords: Particle filter, genetic algorithm, evolutionary algorithm.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 24831346 Observer Based Control of a Class of Nonlinear Fractional Order Systems using LMI
Authors: Elham Amini Boroujeni, Hamid Reza Momeni
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Design of an observer based controller for a class of fractional order systems has been done. Fractional order mathematics is used to express the system and the proposed observer. Fractional order Lyapunov theorem is used to derive the closed-loop asymptotic stability. The gains of the observer and observer based controller are derived systematically using the linear matrix inequality approach. Finally, the simulation results demonstrate validity and effectiveness of the proposed observer based controller.Keywords: Fractional order calculus, Fractional order observer, Linear matrix inequality, Nonlinear Systems, Observer based Controller.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 28671345 The Existence and Uniqueness of Positive Solution for Nonlinear Fractional Differential Equation Boundary Value Problem
Authors: Chuanyun Gu, Shouming Zhong
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In this paper, the existence and uniqueness of positive solutions for nonlinear fractional differential equation boundary value problem is concerned by a fixed point theorem of a sum operator. Our results can not only guarantee the existence and uniqueness of positive solution, but also be applied to construct an iterative scheme for approximating it. Finally, the example is given to illustrate the main result.
Keywords: Fractional differential equation, Boundary value problem, Positive solution, Existence and uniqueness, Fixed point theorem of a sum operator
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 14811344 No one Set of Parameter Values Can Simulate the Epidemics Due to SARS Occurring at Different Localities
Authors: Weerachi Sarakorn, I-Ming Tang
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A mathematical model for the transmission of SARS is developed. In addition to dividing the population into susceptible (high and low risk), exposed, infected, quarantined, diagnosed and recovered classes, we have included a class called untraced. The model simulates the Gompertz curves which are the best representation of the cumulative numbers of probable SARS cases in Hong Kong and Singapore. The values of the parameters in the model which produces the best fit of the observed data for each city are obtained by using a differential evolution algorithm. It is seen that the values for the parameters needed to simulate the observed daily behaviors of the two epidemics are different.
Keywords: SARS, mathematical modelling, differential evolution algorithm.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 14391343 Nonlinear Structural Behavior of Micro- and Nano-Actuators Using the Galerkin Discretization Technique
Authors: Hassen M. Ouakad
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In this paper, the influence of van der Waals, as well as electrostatic forces on the structural behavior of MEMS and NEMS actuators, has been investigated using of a Euler-Bernoulli beam continuous model. In the proposed nonlinear model, the electrostatic fringing-fields and the mid-plane stretching (geometric nonlinearity) effects have been considered. The nonlinear integro-differential equation governing the static structural behavior of the actuator has been derived. An original Galerkin-based reduced-order model has been developed to avoid problems arising from the nonlinearities in the differential equation. The obtained reduced-order model equations have been solved numerically using the Newton-Raphson method. The basic design parameters such as the pull-in parameters (voltage and deflection at pull-in), as well as the detachment length due to the van der Waals force of some investigated micro- and nano-actuators have been calculated. The obtained numerical results have been compared with some other existing methods (finite-elements method and finite-difference method) and the comparison showed good agreement among all assumed numerical techniques.
Keywords: MEMS, NEMS, fringing-fields, mid-plane stretching, Galerkin method.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 14291342 Nonlinear Effects in Stiffness Modeling of Robotic Manipulators
Authors: A. Pashkevich, A. Klimchik, D. Chablat
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The paper focuses on the enhanced stiffness modeling of robotic manipulators by taking into account influence of the external force/torque acting upon the end point. It implements the virtual joint technique that describes the compliance of manipulator elements by a set of localized six-dimensional springs separated by rigid links and perfect joints. In contrast to the conventional formulation, which is valid for the unloaded mode and small displacements, the proposed approach implicitly assumes that the loading leads to the non-negligible changes of the manipulator posture and corresponding amendment of the Jacobian. The developed numerical technique allows computing the static equilibrium and relevant force/torque reaction of the manipulator for any given displacement of the end-effector. This enables designer detecting essentially nonlinear effects in elastic behavior of manipulator, similar to the buckling of beam elements. It is also proposed the linearization procedure that is based on the inversion of the dedicated matrix composed of the stiffness parameters of the virtual springs and the Jacobians/Hessians of the active and passive joints. The developed technique is illustrated by an application example that deals with the stiffness analysis of a parallel manipulator of the Orthoglide familyKeywords: Robotic manipulators, Stiffness model, Loaded mode, Nonlinear effects, Buckling, Orthoglide manipulator
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1448