• Title/Summary/Keyword: Matrix exponential

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Probe Diffusion and Viscosity Properties in Dimethyl Sulfoxide Solution of Poly(vinyl alcohol) with High Degree of Hydrolysis (고검화도의 폴리(비닐 알코올)/디메틸설폭사이드 용액에서의 점성도 특성과 탐침입자의 확산)

  • Eom, Hyo-Sang;Park, Il-Hyun
    • Polymer(Korea)
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    • v.34 no.5
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    • pp.415-423
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    • 2010
  • Poly(vinyl alcohol)(PVA) with high degree of hydrolysis of above 98% was dissolved in dimethyl sulfoxide(DMSO), and the shear viscosity was measured up to $C{\simeq}0.14\;g/mL$ in the semi-dilute solution regime. Next, as probe particle, polystyrene(PS) latex was introduced into this matrix system and its delayed diffusion due to polymer concentration was investigated by means of dynamic light scattering. When the solution viscosity of PVA/DMSO was plotted against the reduced concentration $C[{\eta}]$, which is scaled by the intrinsic viscosity, the molecular weight dependence was strongly appeared at C$[{\eta}]$ >2. Some heterogeneties in polymer solution were considered as its source. Contrary, the diffusion of probe particle in the matrix solution was observed as a single mode motion at whole concentration range but its ratio of its diffusion coefficient at solution to that at solvent, D/Do did not show any molecular weight dependence at all. However, the application limit of the stretched exponential function was disclosed at C$[{\eta}]$ >2.5.

Dosimetrical Analysis of Reactor Leakage Gamma-rays by Means of Scintillation Spectrometry

  • Jun, Jae-Shik
    • Nuclear Engineering and Technology
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    • v.5 no.4
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    • pp.291-309
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    • 1973
  • Exposure rates due to leakage gamma-rays from operating reactors TRIGA Mark II and III were measured in a horizontal plane by means of scintillation spectrometry using a 3"$\times$3" cylindrical Nal(T1) detector associated with a 400 channel pulse height analyzer under varied conditions of reactor operation. In determining exposure rate due to the leakage gamma-rays at each point of measurement, Moriuchi's spectrum-exposure rate conversion theory was applied instead of using conventional responce matrix method which necessitates very complicated procedures to convert a spectrum into exposure rate. The results show that a basic pattern of "typical" spectrum of the reactor leakage gamma-rays is neither affected by thermal output of the reactor, nor influenced by overall attenuation in radiation intensity. It was indicated that he attenuation of the leakage gamma-rays in air in terms of exposure rate as a whole follows an exponential law, and the total exposure rate due to the leakage gamma-rays at a certain point is nearly proportional to thermal output of the reactor. The complexity in spectrum measured for a movable core reactor, TRIGA Mark III, was analyzed through spectrum resolution, and proper judgement of the leakage gamma-rays in a complex spectrum was discussed.ctrum was discussed.

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Numerically Efficient Evaluation of MoM Matrix in Conjunction with the Closed-form Green s Functions in Analysis of Multi-layered Planar Structures (다층 평판구조체 해석시 Closed-form 그린함수와 함께한 모멘트 행렬의 효율적인 수치계산)

  • 이영순;김병철;조영기
    • The Journal of Korean Institute of Electromagnetic Engineering and Science
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    • v.12 no.1
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    • pp.92-98
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    • 2001
  • When analyzing the scatting problem of multi-layered planar structures using closed-form Green's function, one of the main difficulties is that the numerical integrations for the evaluation of diagonal matrix elements converge slowly and are not so stable. Accordingly, even when the integration fur the singularity of type $e^{-jkr}/{\gamma}$, corresponding to the source dipole itself, is performed using such a method, this difficulty persists in the integration corresponding to the finite number of complex images. In order to resolve this difficulty, a new technique based upon the Gaussian quadrature in polar coordinates for the evaluation of the two-dimensional generalized exponential integral is presented. Stability of the algorithm and convergence is discussed. Performance is demonstrated for the example of a microstrip patch antenna.

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Fuzzy H2/H Controller Design for Delayed Nonlinear Systems with Saturating Input (포화입력을 가지는 시간지연 비선형 시스템의 퍼지 H2/H 제어기 설계)

  • Cho, Hee-Soo;Lee, Kap-Rai;Park, Hong-Bae
    • Journal of the Korean Institute of Intelligent Systems
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    • v.12 no.3
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    • pp.239-245
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    • 2002
  • In this Paper, we present a method for designing fuzzy $H_2/H_{\infty}$ controllers of delayed nonlinear systems with saturating input. Takagi-Sugeno fuzzy model is employed to represent delayed nonlinear systems with saturating input. The fuzzy control systems utilize the concept of the so-called parallel distributed compensation(PDC). Using a single quadratic Lyapunov function, the globally exponential stability and $H_2/H_{\infty}$ performance problem are discussed. And a sufficient condition for the existence of fuzzy $H_2/H_{\infty}$ controllers is given in terms of linear matrix inequalities(LMIs). The designing fuzzy $H_2/H_{\infty}$ controllers minimize an upper bound on a linear quadratic performance measure. Finally, a design example of fuzzy $H_2/H_{\infty}$ controller for uncertain delayed nonlinear systems with saturating input.

Performance Evaluation of a Two-Product CONWIP System with Poisson Demand Processes (Poisson 수요과정을 갖는 두 품목 콘윕시스템의 성능평가)

  • Park, Chan-Woo;Kim, Su-Min;Bang, Woo-Hyung;Lee, Hyo-Seong
    • Journal of Korean Institute of Industrial Engineers
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    • v.39 no.3
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    • pp.172-182
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    • 2013
  • In this study we consider a flow line CONWIP system in which two types of product are produced. The processing times of each product type at each station follow an independent exponential distribution and the demands for the finished products of each type arrive according to a Poisson process. The demands that are not satisfied instantaneously are either backordered or lost according to the number of unsatisfied demands that exist at their arrival instants. For this system we develop an approximation method to obtain the performance measures such as steady state probabilities of the number of parts of each product type at each station, mean waiting times of backordered demands and the proportion of backordered demands. For the analysis of the proposed CONWIP system, we model the CONWIP system as a two class closed queueing network with a synchronization station and analyze the closed queueing network using a product-form approximation method for multiple classes developed by Baynat and Dallery. In the approximation method, each subsystem is analyzed using a matrix geometric method. Comparisons with simulation show that the approximation method provides fairly good results for all performance measures.

Simulation of the Phase-Type Distribution Based on the Minimal Laplace Transform (최소 표현 라플라스 변환에 기초한 단계형 확률변수의 시뮬레이션에 관한 연구)

  • Sunkyo Kim
    • Journal of the Korea Society for Simulation
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    • v.33 no.1
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    • pp.19-26
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    • 2024
  • The phase-type, PH, distribution is defined as the time to absorption into a terminal state in a continuous-time Markov chain. As the PH distribution includes family of exponential distributions, it has been widely used in stochastic models. Since the PH distribution is represented and generated by an initial probability vector and a generator matrix which is called the Markovian representation, we need to find a vector and a matrix that are consistent with given set of moments if we want simulate a PH distribution. In this paper, we propose an approach to simulate a PH distribution based on distribution function which can be obtained directly from moments. For the simulation of PH distribution of order 2, closed-form formula and streamlined procedures are given based on the Jordan decomposition and the minimal Laplace transform which is computationally more efficient than the moment matching methods for the Markovian representation. Our approach can be used more effectively than the Markovian representation in generating higher order PH distribution in queueing network simulation.

Critical buckling analyses of nonlinear FG-CNT reinforced nano-composite beam

  • Zerrouki, Rachid;Karas, Abdelkader;Zidour, Mohamed
    • Advances in nano research
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    • v.9 no.3
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    • pp.211-220
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    • 2020
  • This paper investigates the effect of linear and non-linear distribution of carbon nanotube volume fraction in the FG-CNTRC beams on the critical buckling by using higher-order shear deformation theories. Here, the material properties of the CNTRC beams are assumed to be graded in the thickness direction according to a new exponential power law distribution in terms of the carbon nanotube volume fractions. The single-walled carbon nanotube is aligned and distributed in the polymeric matrix with different patterns of reinforcement; the material properties of the CNTRC beams are described by using the rule of mixture. The governing equations are derived through using Hamilton's principle. The Navier solution method is used under the specified boundary conditions for simply supported CNTRC beams. The mathematical models provided in this work are numerically validated by comparison with some available results. New results of critical buckling with the non-linear distribution of CNT volume fraction in different patterns are presented and discussed in detail, and compared with the linear distribution. Several aspects of beam types, CNT volume fraction, exponent degree (n), aspect ratio, etc., are taken into this investigation. It is revealed that the influences of non-linearity distribution in the beam play an important role to improve the mechanical properties, especially in buckling behavior. The results show that the X-Beam configuration is the strongest among all different types of CNTRC beams in supporting the buckling loads.

Multiscale Simulation for a Crack Behavior in Heterogeneous Materials (비균질 재료에서의 균열거동평가를 위한 멀티스케일 수치해석)

  • Fatoni, Nurul Fajriyah;Kwon, Oh Heon
    • Journal of the Korean Society of Safety
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    • v.32 no.4
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    • pp.1-6
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    • 2017
  • Functionally Graded Materials (FGM) as advanced heterogeneous composite materials have a higher performance than a conventional composite or bimaterial composite under some severe environments. As a heterogeneous material, FGM is commonly used in spacecraft, defense, nuclear and automotive industries due to its excellent properties. The purposes of this study are to evaluate the stress distribution and crack behaviors by the multiscale simulation. FGM contains two or more than two materials that the composition is structured continuously. Two types of FGM model are suggested, which are created by arbitrary prediction of the volume fraction and the exponential function. Aluminum as the metal matrix constituent and silicon carbide as the ceramic particle constituent are structured gradually by two types and the three point bending test also estimated. Moreover, two kinds of crack location were introduced in order to get the influences of material property distribution on the stress intensity factor. From the results we found that the stress intensity factors are increased in the case from softer to stiffer material, while vice versa.

Thermal effects on nonlinear dynamic characteristics of polymer-CNT-fiber multiscale nanocomposite structures

  • Ebrahimi, Farzad;Habibi, Sajjad
    • Structural Engineering and Mechanics
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    • v.67 no.4
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    • pp.403-415
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    • 2018
  • In the present study, nonlinear dynamic response of polymer-CNT-fiber multiscale nanocomposite plate resting on elastic foundations in thermal environments using the finite element method is performed. In this regard, the governing equations are derived based on Inverse Hyperbolic Shear Deformation Theory and von $K{\acute{a}}rm{\acute{a}}n$ geometrical nonlinearity. Three type of distribution of temperature through the thickness of the plate namely, uniform linear and nonlinear are considered. The considered element is C1-continuous with 15 DOF at each node. The effective material properties of the multiscale composite are calculated using Halpin-Tsai equations and fiber micromechanics in hierarchy. The carbon nanotubes are assumed to be uniformly distributed and randomly oriented through the epoxy resin matrix. Five types of impulsive loads are considered, namely the step, sudden, triangular, half-sine and exponential pulses. After examining the validity of the present work, the effects of the weight percentage of SWCNTs and MWCNTs, nanotube aspect ratio, volume fraction of fibers, plate aspect, temperature, elastic foundation parameters, distribution of temperature and shape of impulsive load on nonlinear dynamic response of CNT reinforced multi-phase laminated composite plate are studied in details.

Output Feedback Robust $H^infty$ Control for Uncertain Fuzzy Dynamic Systems (불확실성을 갖는 퍼지 시스템의 출력궤환 견실 $H^infty$ 제어)

  • Lee, Kap-Lai;Kim, Jong-Hae;Park, Hong-Bae
    • Journal of the Institute of Electronics Engineers of Korea SC
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    • v.37 no.6
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    • pp.15-24
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    • 2000
  • This paper presents an output feedback robust H$\infty$ control problem for a class of uncertain nonlinear systems, which can be represented by an fuzzy dynamic model. The nonlinear system is represented by Takagi-Sugeno fuzzy model, and the control design is carried out on the basis of the fuzzy model. Using a single quadratic Lyapunov function, the globally exponential stability and disturance attenuation of the closed-loop fuzzy control system are discussed. Sufficient conditions for the existence of robust H$\infty$ controllers are given in terms of linear matrix inequalities(LMIs). Constructive algorithm for design of robust H$\infty$ controller is also developed. The resulting controller is nonlinear and automatically tuned based on fuzzy operation.

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