• Title/Summary/Keyword: linear differential systems

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An Amperometric Proton Selective Sensor with an Elliptic Microhole Liquid/Gel Interface for Vitamin-C Quantification

  • Faisal, Shaikh Nayeem;Hossain, Md. Mokarrom;Lee, Hye-Jin
    • Journal of Electrochemical Science and Technology
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    • v.1 no.2
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    • pp.121-126
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    • 2010
  • An amperometric ascorbic acid selective sensor utilizing the transfer reaction of proton liberated from the dissociation of ascorbic acid in aqueous solution across an elliptic micro-hole water/organic gel interface is demonstrated. This redox inactive sensing platform offers an alternative way for the detection of ascorbic acid to avoid a fouling effect which is one of the major concerns in redox based sensing systems. The detection principle is simply measuring the current change with respect to the assisted transfer of protons by a proton selective ionophore (e.g., ETH 1778) across the micro-hole interface between the water and the polyvinylchloride-2-nitrophenyloctylether gel phase. The assisted transfer reaction of protons generated from ascorbic acid across the polarized micro-hole interface was first characterized using cyclic voltammetry. An improved sensitivity for the quantitative analysis of ascorbic acid was achieved using differential pulse stripping voltammetry with a linear response ranging from 1 to $100\;{\mu}M$ concentrations of ascorbic acid. As a demonstration, the developed sensor was applied for analyzing the content of vitamin-C in different types of commercial pharmaceutical tablets and syrups, and a satisfactory recovery from these samples were also obtained.

An Improved Poincaré-like Carleman Linearization Approach for Power System Nonlinear Analysis

  • Wang, Zhou-Qiang;Huang, Qi;Zhang, Chang-Hua
    • Journal of Electrical Engineering and Technology
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    • v.8 no.2
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    • pp.271-281
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    • 2013
  • In order to improve the performance of analysis, it is important to consider the nonlinearity in power system. The Carleman embedding technique (linearization procedure) provides an effective approach in reduction of nonlinear systems. In the approach, a group of differential equations in which the state variables are formed by the original state variables and the vector monomials one can build with products of positive integer powers of them, is constructed. In traditional Carleman linearization technique, the tensor matrix is truncated to form a square matrix, and then regular linear system theory is used to solve the truncated system directly. However, it is found that part of nonlinear information is neglected when truncating the Carleman model. This paper proposes a new approach to solve the problem, by combining the Poincar$\acute{e}$ transformation with the Carleman linearization. Case studies are presented to verify the proposed method. Modal analysis shows that, with traditional Carleman linearization, the calculated contribution factors are not symmetrical, while such problems are avoided in the improved approach.

Slender piezoelectric beams with resistive-inductive electrodes - modeling and axial wave propagation

  • Schoeftner, Juergen;Buchberger, Gerda;Benjeddou, Ayech
    • Smart Structures and Systems
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    • v.18 no.2
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    • pp.335-354
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    • 2016
  • This contribution presents an extended one-dimensional theory for piezoelectric beam-type structures with non-ideal electrodes. For these types of electrodes the equipotential area condition is not satisfied. The main motivation of our research is originated from passive vibration control: when an elastic structure is covered by several piezoelectric patches that are linked via resistances and inductances, vibrational energy is efficiently dissipated if the electric network is properly designed. Assuming infinitely small piezoelectric patches that are connected by an infinite number of electrical, in particular resistive and inductive elements, one obtains the Telegrapher's equation for the voltage across the piezoelectric transducer. Embedding this outcome into the framework of Bernoulli-Euler, the final equations are coupled to the wave equations for the longitudinal motion of a bar and to the partial differential equations for the lateral motion of the beam. We present results for the wave propagation of a longitudinal bar for several types of electrode properties. The frequency spectra are computed (phase angle, wave number, wave speed), which point out the effect of resistive and inductive electrodes on wave characteristics. Our results show that electrical damping due to the resistivity of the electrodes is different from internal (=strain velocity dependent) or external (=velocity dependent) mechanical damping. Finally, results are presented, when the structure is excited by a harmonic single force, yielding that resistive-inductive electrodes are suitable candidates for passive vibration control that might be of great interest for practical applications in the future.

Bi-stability in a vertically excited rectangular tank with finite liquid depth

  • Spandonidis, Christos C.;Spyrou, Kostas J.
    • Ocean Systems Engineering
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    • v.2 no.3
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    • pp.229-238
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    • 2012
  • We discuss the bi - stability that is possibly exhibited by a liquid free surface in a parametrically - driven two-dimensional (2D) rectangular tank with finite liquid depth. Following the method of adaptive mode ordering, assuming two dominant modes and retaining polynomial nonlinearities up to third-order, a nonlinear finite-dimensional nonlinear modal system approximation is obtained. A "continuation method" of nonlinear dynamics is then used in order to elicit efficiently the instability boundary in parameters' space and to predict how steady surface elevation changes as the frequency and/or the amplitude of excitation are varied. Results are compared against those of the linear version of the system (that is a Mathieu-type model) and furthermore, against an intermediate model also derived with formal mode ordering, that is based on a second - order ordinary differential equation having nonlinearities due to products of elevation with elevation velocity or acceleration. The investigation verifies that, in parameters space, there must be a region, inside the quiescent region, where liquid surface instability is exhibited. There, behaviour depends on initial conditions and a wave form would be realised only if the free surface was substantially disturbed initially.

Numerical simulation of single-phase two-components flow in naturally fractured oil reservoirs

  • Debossam, Joao Gabriel Souza;dos Santos Heringer, Juan Diego;de Souza, Grazione;Souto, Helio Pedro Amaral
    • Coupled systems mechanics
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    • v.8 no.2
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    • pp.129-146
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    • 2019
  • The main goal of this work is to develop a numerical simulator to study an isothermal single-phase two-component flow in a naturally fractured oil reservoir, taking into account advection and diffusion effects. We use the Peng-Robinson equation of state with a volume translation to evaluate the properties of the components, and the discretization of the governing partial differential equations is carried out using the Finite Difference Method, along with implicit and first-order upwind schemes. This process leads to a coupled non-linear algebraic system for the unknowns pressure and molar fractions. After a linearization and the use of an operator splitting, the Conjugate Gradient and Bi-conjugated Gradient Stabilized methods are then used to solve two algebraic subsystems, one for the pressure and another for the molar fraction. We studied the effects of fractures in both the flow field and mass transport, as well as in computing time, and the results show that the fractures affect, as expected, the flow creating a thin preferential path for the mass transport.

The effect of impact with adjacent structure on seismic behavior of base-isolated buildings with DCFP bearings

  • Bagheri, Morteza;Khoshnoudiana, Faramarz
    • Structural Engineering and Mechanics
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    • v.51 no.2
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    • pp.277-297
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    • 2014
  • Since the isolation bearings undergo large displacements in base-isolated structures, impact with adjacent structures is inevitable. Therefore, in this investigation, the effect of impact on seismic response of isolated structures mounted on double concave friction pendulum (DCFP) bearings subjected to near field ground motions is considered. A non-linear viscoelastic model of collision is used to simulate structural pounding more accurately. 2-, 4- and 8-story base-isolated buildings adjacent to fixed-base structures are modeled and the coupled differential equations of motion related to these isolated systems are solved in the MATLAB environment using the SIMULINK toolbox. The variation of seismic responses such as base shear, displacement in the isolation system and superstructure (top floor) is computed to study the impact condition. Also, the effects of variation of system parameters: isolation period, superstructure period, size of seismic gap between two structures, radius of curvature of the sliding surface and friction coefficient of isolator are contemplated in this study. It is concluded that the normalized base shear, bearing and top floor displacement increase due to impact with adjacent structure. When the distance between two structures decreases, the base shear and displacement increase comparing to no impact condition. Besides, the increase in friction coefficient difference also causes the normalized base shear and displacement in isolation system and superstructure increase in comparison with bi-linear hysteretic behavior of base isolation system. Totally, the comparison of results indicates that the changes in values of friction coefficient have more significant effects on 2-story building than 4- and 8-story buildings.

Nonlinear Anisotropic Diffusion Using Adaptive Weighted Median Filters (적응 가중 미디언 필터를 이용한 영상 확산 알고리즘)

  • Hwang, In-Ho;Lee, Kyung-Hoon;Kim, Woong-Hee
    • The Journal of Korean Institute of Communications and Information Sciences
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    • v.32 no.5C
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    • pp.542-549
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    • 2007
  • Recently, many research activities in the image processing area are concentrated on developing new algorithms by finding the solution of the 'diffusion equation'. The diffusion algorithms are expected to be utilized in numerous applications including noise removal and image restoration, edge detection, segmentation, etc. In this paper, at first, it will be shown that the anisotropic diffusion algorithms have the similar structure with the adaptive FIR filters with cross-shaped 5-tap kernel, and this relatively small-sized kernel causes many iterating procedure for satisfactory filtering effects. Moreover, it will also be shown that lots of modifications which are adopted to the conventional Gaussian diffusion method in order to weaken the edge blurring nature of the linear filtering process increases another computational burden. We propose a new Median diffusion scheme by replacing the adaptive linear filters in the diffusion process with the AWM (Adaptive Weighted Median) filters. A diffusion-equation-based adaptation scheme is also proposed. With the proposed scheme, the size of the diffusion kernel can be increased, and thus diffusion speed greatly increases. Simulation results shows that the proposed Median diffusion scheme outperforms in noise removal (especially impulsive noise), and edge preservation.

Design of a Force Applying System for a Smart-phone Curved Glass Molding System and Its Characteristic Test (스마트폰 곡면유리 성형시스템의 가압장치 설계 및 곡면유리 성형특성실험)

  • Kim, Hyeon-Min;Hong, Tae-Kyung;Jung, Dong-Yean;Lee, Yeon-Hyeong;Park, Jea-Hyun;Kim, Gab-Soon
    • Journal of Institute of Control, Robotics and Systems
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    • v.20 no.5
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    • pp.570-577
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    • 2014
  • This paper describes the design of a force applying system for a smart phone curved glass molding system and its characteristic test. The force applying system is composed of a motor and gear, a rectilinear movement structure, a force sensor, an LVDT (Linear Variable Differential Transformer) sensor, an up and down moving block, and so on. The system precisely controls the applying force and time to the plane glass because the glass can be easily destroyed under applied force, and can be bent imperfectly. As a result of the characteristic test, the curved glass can be manufactured using this system, and the holding time under 0N force, the applying force to the plane glass, the time for applying from 0N to maximum force, and the holding time under maximum force at the manufacture feasible temperature $620^{\circ}C$ were found.

Unknown-Parameter Identification for Accurate Control of 2-Link Manipulator using Dual Extended Kalman Filter (2링크 매니퓰레이터 제어를 위한 듀얼 확장 칼만 필터 기반의 미지 변수 추정 기법)

  • Seung, Ji Hoon;Park, Jung Kil;Yoo, Sung Goo
    • Journal of the Korea Convergence Society
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    • v.9 no.6
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    • pp.53-60
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    • 2018
  • In this paper, we described the unknown parameter identification using Dual Extended Kalman Filter for precise control of 2-link manipulator. 2-link manipulator has highly non-linear characteristic with changed parameter thought tasks. The parameter kinds of mass and inertia of system is important to handle with the manipulator robustly. To solve the control problem by estimating the state and unknown parameters of the system through the proposed method. In order to verify the performance of proposed method, we simulate the implementation using Matlab and compare with results of RLS algorithm. At the results, proposed method has a better performance than those of RLS and verify the estimation performance in the parameter estimation.

Static bending response of axially randomly oriented functionally graded carbon nanotubes reinforced composite nanobeams

  • Ahmed Amine Daikh;Ahmed Drai;Mohamed Ouejdi Belarbi;Mohammed Sid Ahmed Houari;Benoumer Aour;Mohamed A. Eltaher;Norhan A. Mohamed
    • Advances in nano research
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    • v.16 no.3
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    • pp.289-301
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    • 2024
  • In this work, an analytical model employing a new higher-order shear deformation beam theory is utilized to investigate the bending behavior of axially randomly oriented functionally graded carbon nanotubes reinforced composite nanobeams. A modified continuum nonlocal strain gradient theory is employed to incorporate both microstructural effects and geometric nano-scale length scales. The extended rule of mixture, along with molecular dynamics simulations, is used to assess the equivalent mechanical properties of functionally graded carbon nanotubes reinforced composite (FG-CNTRC) beams. Carbon nanotube reinforcements are randomly distributed axially along the length of the beam. The equilibrium equations, accompanied by nonclassical boundary conditions, are formulated, and Navier's procedure is used to solve the resulting differential equation, yielding the response of the nanobeam under various mechanical loadings, including uniform, linear, and sinusoidal loads. Numerical analysis is conducted to examine the influence of inhomogeneity parameters, geometric parameters, types of loading, as well as nonlocal and length scale parameters on the deflections and stresses of axially functionally graded carbon nanotubes reinforced composite (AFG CNTRC) nanobeams. The results indicate that, in contrast to the nonlocal parameter, the beam stiffness is increased by both the CNTs volume fraction and the length-scale parameter. The presented model is applicable for designing and analyzing microelectromechanical systems (MEMS) and nanoelectromechanical systems (NEMS) constructed from carbon nanotubes reinforced composite nanobeams.