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  • Articles  (5,473)
  • Hindawi  (5,473)
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  • Articles  (5,473)
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  • Hindawi  (5,473)
  • American Meteorological Society
  • Blackwell Publishing Ltd
  • Copernicus
  • Institute of Electrical and Electronics Engineers
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  • Mathematics  (5,473)
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  • 1
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    A New Numerical Procedure for Vibration Analysis of Beam under Impulse and Multiharmonics Piezoelectric Actuators (2020)
    Hindawi
    Details
    Publication Date: 2020-08-28
    Description: The dynamic behavior of structures with piezoelectric patches is governed by partial differential equations with strong singularities. To directly deal with these equations, well adapted numerical procedures are required. In this work, the differential quadrature method (DQM) combined with a regularization procedure for space and implicit scheme for time discretization is used. The DQM is a simple method that can be implemented with few grid points and can give results with a good accuracy. However, the DQM presents some difficulties when applied to partial differential equations involving strong singularities. This is due to the fact that the subsidiaries of the singular functions cannot be straightforwardly discretized by the DQM. A methodological approach based on the regularization procedure is used here to overcome this difficulty and the derivatives of the Dirac-delta function are replaced by regularized smooth functions. Thanks to this regularization, the resulting differential equations can be directly discretized using the DQM. The efficiency and applicability of the proposed approach are demonstrated in the computation of the dynamic behavior of beams for various boundary conditions and excited by impulse and Multiharmonics piezoelectric actuators. The obtained numerical results are well compared to the developed analytical solution.
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    Electronic ISSN: 1687-0042
    Topics: Mathematics
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  • 2
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    Computing the q-Numerical Range of Differential Operators (2020)
    Hindawi
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    Publication Date: 2020-08-28
    Description: A linear operator on a Hilbert space may be approximated with finite matrices by choosing an orthonormal basis of thez Hilbert space. In this paper, we establish an approximation of the q-numerical range of bounded and unbounnded operator matrices by variational methods. Application to Schrödinger operator, Stokes operator, and Hain-Lüst operator is given.
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  • 3
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    Computation of Invariant Measures and Stationary Expectations for Markov Chains with Block-Band Transition Matrix (2020)
    Hindawi
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    Publication Date: 2020-07-08
    Description: This paper deals with the computation of invariant measures and stationary expectations for discrete-time Markov chains governed by a block-structured one-step transition probability matrix. The method generalizes in some respect Neuts’ matrix-geometric approach to vector-state Markov chains. The method reveals a strong relationship between Markov chains and matrix continued fractions which can provide valuable information for mastering the growing complexity of real-world applications of large-scale grid systems and multidimensional level-dependent Markov models. The results obtained are extended to continuous-time Markov chains.
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  • 4
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    A New Class of Halley’s Method with Third-Order Convergence for Solving Nonlinear Equations (2020)
    Hindawi
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    Publication Date: 2020-07-02
    Description: In this paper, we present a new family of methods for finding simple roots of nonlinear equations. The convergence analysis shows that the order of convergence of all these methods is three. The originality of this family lies in the fact that these sequences are defined by an explicit expression which depends on a parameter p where p is a nonnegative integer. A first study on the global convergence of these methods is performed. The power of this family is illustrated analytically by justifying that, under certain conditions, the method convergence’s speed increases with the parameter p. This family’s efficiency is tested on a number of numerical examples. It is observed that our new methods take less number of iterations than many other third-order methods. In comparison with the methods of the sixth and eighth order, the new ones behave similarly in the examples considered.
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  • 5
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    Firefly Algorithm for Polynomial Bézier Surface Parameterization (2013)
    Hindawi
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    Publication Date: 2013-09-12
    Description: A classical issue in many applied fields is to obtain an approximating surface to a given set of data points. This problem arises in Computer-Aided Design and Manufacturing (CAD/CAM), virtual reality, medical imaging, computer graphics, computer animation, and many others. Very often, the preferred approximating surface is polynomial, usually described in parametric form. This leads to the problem of determining suitable parametric values for the data points, the so-called surface parameterization. In real-world settings, data points are generally irregularly sampled and subjected to measurement noise, leading to a very difficult nonlinear continuous optimization problem, unsolvable with standard optimization techniques. This paper solves the parameterization problem for polynomial Bézier surfaces by applying the firefly algorithm, a powerful nature-inspired metaheuristic algorithm introduced recently to address difficult optimization problems. The method has been successfully applied to some illustrative examples of open and closed surfaces, including shapes with singularities. Our results show that the method performs very well, being able to yield the best approximating surface with a high degree of accuracy.
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  • 6
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    A Common Fixed Point Theorem in Metric Space under General Contractive Condition (2013)
    Hindawi
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    Publication Date: 2013-09-16
    Description: We prove a common fixed point theorem for two pairs of compatible and subsequentially continuous (alternately subcompatible and reciprocally continuous) mappings satisfying a general contractive condition in a metric space. Some illustrative examples are furnished to highlight the realized improvements. Our result improves the main result of Sedghi and Shobe (2007).
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  • 7
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    Modeling of Location Estimation for Object Tracking in WSN (2013)
    Hindawi
    Details
    Publication Date: 2013-09-17
    Description: Location estimation for object tracking is one of the important topics in the research of wireless sensor networks (WSNs). Recently, many location estimation or position schemes in WSN have been proposed. In this paper, we will propose the procedure and modeling of location estimation for object tracking in WSN. The designed modeling is a simple scheme without complex processing. We will use Matlab to conduct the simulation and numerical analyses to find the optimal modeling variables. The analyses with different variables will include object moving model, sensing radius, model weighting value α, and power-level increasing ratio k of neighboring sensor nodes. For practical consideration, we will also carry out the shadowing model for analysis.
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  • 8
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    Stability Analysis of Networked Control Systems with Random Time Delays and Packet Dropouts Modeled by Markov Chains (2013)
    Hindawi
    Details
    Publication Date: 2013-09-17
    Description: This paper investigates the stability analysis problem for a class of discrete-time networked control systems (NCSs) with random time delays and packet dropouts based on unified Markov jump model. The random time delays and packet dropouts existed in feedback communication link are modeled by two independent Markov chains; the resulting closed-loop system is described by a new Markovian jump linear system (MJLS) with Markov delays. Sufficient conditions of the stochastic stability for NCSs is obtained by constructing a novel Lyapunov functional, and the mode-dependent output feedback controller design method is presented based on linear matrix inequality (LMI) technique. A numerical example is given to illustrate the effectiveness of the proposed method.
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  • 9
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    Modeling and Control for Giant Magnetostrictive Actuators with Rate-Dependent Hysteresis (2013)
    Hindawi
    Details
    Publication Date: 2013-09-17
    Description: The rate-dependent hysteresis in giant magnetostrictive materials is a major impediment to the application of such material in actuators. In this paper, a relevance vector machine (RVM) model is proposed for describing the hysteresis nonlinearity under varying input current. It is possible to construct a unique dynamic model in a given rate range for a rate-dependent hysteresis system using the sinusoidal scanning signals as the training set input signal. Subsequently, a proportional integral derivative (PID) control scheme combined with a feedforward compensation is implemented on a giant magnetostrictive actuator (GMA) for real-time precise trajectory tracking. Simulations and experiments both verify the effectiveness and the practicality of the proposed modeling and control methods.
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  • 10
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    A Unified Elastoplastic Model of Unsaturated Soils Considering Capillary Hysteresis (2013)
    Hindawi
    Details
    Publication Date: 2013-09-17
    Description: Unlike its saturated counterparts, the mechanical behavior of an unsaturated soil depends not only upon its stress history but also upon its hydraulic history. In this paper, a soil-water characteristic relationship which is capable of describing the effect of capillary hysteresis is introduced to characterize the influence of hydraulic history on the skeletal deformation. The capillary hysteresis is viewed as a phenomenon associated with the internal structural rearrangements in unsaturated soils, which can be characterized by using a set of internal state variables. It is shown that both capillary hysteresis and plastic deformation can be consistently addressed in a unified theoretical framework. Within this context, a constitutive model of unsaturated soils is developed by generalizing the modified Cam-Clay model. A hardening function is introduced, in which both the matric suction and the degree of saturation are explicitly included as hardening variables, so that the effect of hydraulic history on the mechanical response can be properly addressed. The proposed model is capable of capturing the main features of the unsaturated soil behavior. The new model has a hierarchical structure, and, depending upon application, it can describe the stress-strain relation and the soil-water characteristics in a coupled or uncoupled manner.
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