• Title/Summary/Keyword: Integral equation

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Closed Integral Form Expansion for the Highly Efficient Analysis of Fiber Raman Amplifier (라만증폭기의 효율적인 성능분석을 위한 라만방정식의 적분형 전개와 수치해석 알고리즘)

  • Choi, Lark-Kwon;Park, Jae-Hyoung;Kim, Pil-Han;Park, Jong-Han;Park, Nam-Kyoo
    • Korean Journal of Optics and Photonics
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    • v.16 no.3
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    • pp.182-190
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    • 2005
  • The fiber Raman amplifier(FRA) is a distinctly advantageous technology. Due to its wider, flexible gain bandwidth, and intrinsically lower noise characteristics, FRA has become an indispensable technology of today. Various FRA modeling methods, with different levels of convergence speed and accuracy, have been proposed in order to gain valuable insights for the FRA dynamics and optimum design before real implementation. Still, all these approaches share the common platform of coupled ordinary differential equations(ODE) for the Raman equation set that must be solved along the long length of fiber propagation axis. The ODE platform has classically set the bar for achievable convergence speed, resulting exhaustive calculation efforts. In this work, we propose an alternative, highly efficient framework for FRA analysis. In treating the Raman gain as the perturbation factor in an adiabatic process, we achieved implementation of the algorithm by deriving a recursive relation for the integrals of power inside fiber with the effective length and by constructing a matrix formalism for the solution of the given FRA problem. Finally, by adiabatically turning on the Raman process in the fiber as increasing the order of iterations, the FRA solution can be obtained along the iteration axis for the whole length of fiber rather than along the fiber propagation axis, enabling faster convergence speed, at the equivalent accuracy achievable with the methods based on coupled ODEs. Performance comparison in all co-, counter-, bi-directionally pumped multi-channel FRA shows more than 102 times faster with the convergence speed of the Average power method at the same level of accuracy(relative deviation < 0.03dB).

Aerodynamic noise reduction of fan motor unit of cordless vacuum cleaner by optimal designing of splitter blades for impeller (임펠라 스플리터 날개 최적 설계를 통한 무선진공청소기 팬 모터 단품의 공력 소음 저감)

  • Kim, Kunwoo;Ryu, Seo-Yoon;Cheong, Cheolung;Seo, Seongjin;Jang, Cheolmin;Seol, Hanshin
    • The Journal of the Acoustical Society of Korea
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    • v.39 no.6
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    • pp.524-532
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    • 2020
  • In this study, noise radiated from a high-speed fan-motor unit for a cordless vacuum cleaner is reduced by designing splitter blades on the existing impeller. First of all, in order to investigate the flow field through a fan-motor unit, especially impeller, the unsteady incompressible Reynolds-Averaged Navier-Stokes (RANS) equations are numerically solved by using computational fluid dynamic technique. With predicted flow field results as input, the Ffowcs Williams-Hawkings (FW-H) integral equation is solved to predict aerodynamic noise radiated from the impeller. The validity of the numerical methods is confirmed by comparing the predicted sound pressure spectrum with the measured one. Further analysis of the predicted flow field shows that the strong vortex is formed between the impeller blades. As the vortex induces the loss of the flow field and acts as an aerodynamic noise source, supplementary splitter blades are designed to the existing impeller to suppress the identified vortex. The length and position of splitter are selected as design factors and the effect of each design factor on aerodynamic noise is numerically analyzed by using the Taguchi method. From this results, the optimum location and length of splitter for minimum radiated noise is determined. The finally selected design shows lower noise than the existing one.

A study on the estimation of bubble size distribution using an acoustic inversion method (음향 역산법을 이용한 기포의 크기 분포 추정 연구)

  • Park, Cheolsoo;Jeong, So Won;Kim, Gun Do;Moon, Ilsung;Yim, Geuntae
    • The Journal of the Acoustical Society of Korea
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    • v.39 no.3
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    • pp.151-162
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    • 2020
  • This paper presents an acoustic inversion method for estimating the bubble size distribution. The estimation error of the attenuation coefficient represented by a Fredholm integral equation of the first kind is defined as an objective function, and an optimal solution is found by applying the Levenberg-Marquardt (LM) method. In order to validate the effectiveness of the inversion method, numerical simulations using two types of bubble distribution are performed. In addition, a series of experiments are carried out in a water tank (1.0 m × 0.54 m × 0.6 m), using bubbles generated by three different generators. Images of the distributed bubbles are obtained by a high-speed camera, and the insertion losses of the bubble layer are measured using a source and a hydrophone. The image is post-processed to glance a distribution characteristics of each bubble generator. Finally, the size distribution of bubbles is estimated by applying the inversion method to the measured insertion loss. From the inversion results, it was observed that the number of bubbles increases exponentially as the bubble size decreases, and then increases again after the local peak at 70 ㎛ - 120 ㎛.

A Simulation of Temperature Control of Greenhouse with Hot-Water Heating System (온수난방시스템 온실의 온도제어 시뮬레이션)

  • 정태상;하종규;민영봉
    • Journal of Bio-Environment Control
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    • v.8 no.3
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    • pp.152-163
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    • 1999
  • It is required to analyze the controlled response of air temperature in greenhouse according to control techniques for precise control. In this study, a mathematical model was established for air heating of greenhouse with hot-water heating system The parameters of the model were decided by regression analysis using reference data measured at the greenhouse being heated In the simulation for the digital control of air temperature in the greenhouse, the mathematical model to evaluate the control performances was used. Tested control methods were ON-OFF contpol, p control, rl control and PID control. The mathematical model represented by inside air temperature ( T$_{i}$), hot-water temperature (T$_{w}$) in heating pipe and outside air temperature (T$_{o}$) was expressed as a following discrete time equation ; T$_{i}$($textsc{k}$+1)= 0.851.T$_{i}$($textsc{k}$)+0.055.T$_{w}$($textsc{k}$)+0.094.T$_{o}$($textsc{k}$) Control simulations for various control methods showed the settling time, the overshoot and the steady state nor as follows; infinite time, 3.5$0^{\circ}C$, 3.5$0^{\circ}C$ for ON-OFF control : 30min 2.37$^{\circ}C$, 0.51$^{\circ}C$ for P control; 21min, 0.0$0^{\circ}C$, 0.23$^{\circ}C$ for PI control; 18min 0.0$0^{\circ}C$, 0.23$^{\circ}C$ for PID control, respectively. PI and PID controls appeared to be optimal control methods. There was no effect of differential gain on the heating process but much effect of integral gain on it.on it.

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Structural Analysis and Magnctic Propcrics of Amorphous $Fe_{78}Si_{9}B_{13}$ Alloy (비정질 $Fe_{78}Si_{9}B_{13}$ 합금의 구조와 자성 연구)

  • 이희복;송인명;유성초;임우영
    • Journal of the Korean Magnetics Society
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    • v.3 no.3
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    • pp.179-184
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    • 1993
  • The X-ray diffraction pattern of amorphous $Fe_{78}Si_{9}B_{13}$ alloy was analyzed to obtain the radial distribution function (RDF) where the first peak was in the form of Gaussian function. The calculated coordination number of the form of Gaussian functiono The calculated coordination number of the sample is 13.5, the mean distance betweeon near-neighbor atoms $r_{0}$ is $2.595{\AA}$ and a Gaussian parametet ${\delta}r$ indicating near-neighbor atomic distri-bution is $0.27{\AA}$. The temperature dependence of saturated magnetization at low temperature could be explained by spin wave excitations theory yielding the spin wave stiffness constant as $117.8\;meV\;{\AA}^2$. Also, we tried to fit the observed temperature dependence of saturated magnetization with the Handrich's equation of the modified molecular field theory for the amorphous ferromagnet. Nice fittings are obtained when we used the parameters ${\Delta}=0.32$(S=1/2) and ${\Delta}=0.23$(S=1), respectively. Finally, the calculated spin wave stiffness constant using the parameters and the structural data are $149\;meV\;{\AA}^2$ for S=1/2 and $138\;meV\;{\AA}^2$ for S=1, respectively. The mean exchange coupling integral between near-neighbor atoms was estimated to be 17.9 meV for S=1/2 and 6.7 meV for S=1.

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Response Analysis of Data Acquired by Marine Loop Electromagnetic System Using Three-Dimensional Modeling Based on Integral Equation (적분방정식 기반의 3차원 모델링을 이용한 소형 루프형 해양 전자탐사 자료의 반응 분석)

  • Ko, Hwicheol;Park, In Hwa;Lee, Seong Kon
    • Geophysics and Geophysical Exploration
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    • v.17 no.1
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    • pp.21-27
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    • 2014
  • We analyzed response patterns of test field data acquired with new small loop electromagnetic (EM) system using three-dimensional (3D) electromagnetic modeling code. The size and shape of a conductor was adopted as experimental parameters for EM modeling to understand influencing factors of the response patterns due to a metallic object on the seafloor. Obtaining the responses for four models of difference sizes and shapes through 3D EM modeling, we confirmed that the shape of the object have a more critical factor on the response pattern than size. We also calculated "ppm" values with respect to different altitudes of the sensor and source frequencies. The modeling results show that the consistency of sensor altitude is important and imaginary part of ppm response is more sensitive than real part. We also visualized the contour map of the real and imaginary part of ppm value as a function of frequency and altitude so that we can estimate proper altitude for source frequency band of our survey system. The results of this paper are anticipated to give proper parameters in survey construction for seafloor massive sulfide deposit.

An efficient 2.5D inversion of loop-loop electromagnetic data (루프-루프 전자탐사자료의 효과적인 2.5차원 역산)

  • Song, Yoon-Ho;Kim, Jung-Ho
    • Geophysics and Geophysical Exploration
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    • v.11 no.1
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    • pp.68-77
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    • 2008
  • We have developed an inversion algorithm for loop-loop electromagnetic (EM) data, based on the localised non-linear or extended Born approximation to the solution of the 2.5D integral equation describing an EM scattering problem. Source and receiver configuration may be horizontal co-planar (HCP) or vertical co-planar (VCP). Both multi-frequency and multi-separation data can be incorporated. Our inversion code runs on a PC platform without heavy computational load. For the sake of stable and high-resolution performance of the inversion, we implemented an algorithm determining an optimum spatially varying Lagrangian multiplier as a function of sensitivity distribution, through parameter resolution matrix and Backus-Gilbert spread function analysis. Considering that the different source-receiver orientation characteristics cause inconsistent sensitivities to the resistivity structure in simultaneous inversion of HCP and VCP data, which affects the stability and resolution of the inversion result, we adapted a weighting scheme based on the variances of misfits between the measured and calculated datasets. The accuracy of the modelling code that we have developed has been proven over the frequency, conductivity, and geometric ranges typically used in a loop-loop EM system through comparison with 2.5D finite-element modelling results. We first applied the inversion to synthetic data, from a model with resistive as well as conductive inhomogeneities embedded in a homogeneous half-space, to validate its performance. Applying the inversion to field data and comparing the result with that of dc resistivity data, we conclude that the newly developed algorithm provides a reasonable image of the subsurface.

A Study on the Design of Ship′s Bow Form using Surface Panel Method (판요소법을 이용한 선수형상 설계에 관한 연구[1])

  • Jae-Hoon Yoo;Hyo-Chul Kim
    • Journal of the Society of Naval Architects of Korea
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    • v.33 no.3
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    • pp.35-47
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    • 1996
  • A surface panel method treating a boundary-value problem of the Dirichlet type is presented to design a three dimensional body with free surface corresponding to a prescribed pressure distribution. An integral equation is derived from Green's theorem, giving a relation between total potential of known strength and the unknown local flux. Upon discretization, a system of linear simultaneous equations is formed including free surface boundary condition and is solved for an assumed geometry. The pseudo local flux, present due to the incorrect positioning of the assumed geometry, plays a role f the geometry corrector, with which the new geometry is computed for the next iteration. Sample designs for submerged spheroids and Wigley hull and carried out to demonstrate the stable convergence, the effectiveness and the robustness of the method. For the calculation of the wave resistance, normal dipoles and Rankine sources are distributed on the body surface and Rankine sources on the free surface. The free surface boundary condition is linearized with respect to the oncoming flow. Four-points upwind finite difference scheme is used to compute the free surface boundary condition. A hyperboloidal panel is adopted to represent the hull surface, which can compensate the defects of the low-order panel method. The design of a 5500TEU container carrier is performed with respect to reduction of the wave resistance. To reduce the wave resistance, calculated pressure on the hull surface is modified to have the lower fluctuation, and is applied as a Dirichlet type dynamic boundary condition on the hull surface. The designed hull form is verified to have the lower wave resistance than the initial one not only by computation but by experiment.

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Thermal Stability and Mechanical Interfacial Properties of DGEBA/PMR-15 Blend System Initiated by Cationic Latent Thermal Catalyst (잠재성 양이온 개시제를 이용한 DGEBA/PMR-15 블렌드계의 열안정성 및 기계적 계면 특성에 관한 연구)

  • Park, Soo-Jin;Lee, Hwa-Young;Han, Mijeong;Hong, Sung-Kwon
    • Journal of Adhesion and Interface
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    • v.5 no.1
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    • pp.3-11
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    • 2004
  • In this work, the cure behaviors of the DGEBA/PMR-15 blends initiated by N-benzylpyrazinium hexafluoroantimonate (BPH) as a cationic latent catalyst were performed in DSC and DMA analyses. And, the thermal stabilities were carried out by TGA analysis and their mechanical interfacial properties of blends were measured in the context of critical stress intensity factor ($K_{IC}$). As a result, the curing activation energy ($E_a$) determined from Ozawa's equation in DSC and the relaxation activation energy ($E_r$) from DMA were increased with increasing PMA-15 content. Also, the thermal stabilities obtained from the integral procedural decomposition temperature (IPDT) and the glass transition temperature ($T_g$) were highly improved with increasing the PMR-15 content, which were probably due to the high heat resistance. And, the $K_{IC}$ showed a similar behavior with $E_a$, which was attributed to the improving of the interfacial adhesion or hydrogen bondings between intermolecular chains.

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Optimal design of impeller in fan motor unit of cordless vacuum cleaner for improving flow performance and reducing aerodynamic noise (무선진공청소기 팬 모터 단품의 유량성능 향상과 공력소음 저감을 위한 임펠라 최적설계)

  • Kim, KunWoo;Ryu, Seo-Yoon;Cheong, Cheolung;Seo, Seongjin;Jang, Cheolmin
    • The Journal of the Acoustical Society of Korea
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    • v.39 no.5
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    • pp.379-389
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    • 2020
  • In this study, the flow and noise performances of high-speed fan motor unit for cordless vacuum cleaner is improved by optimizing the impeller which drives the suction air through flow passage of the cordless vacuum cleaner. Firstly, the unsteady incompressible Reynolds averaged Navier-Stokes (RANS) equations are solved to investigate the flow through the fan motor unit using the computational fluid dynamics techniques. Based on flow field results, the Ffowcs-Williams and Hawkings (FW-H) integral equation is used to predict flow noise radiated from the impeller. Predicted results are compared to the measured ones, which confirms the validity of the numerical method used. It is found that the strong vortex is formed around the mid-chord region of the main blades where the blade curvature change rapidly. Given that vortex acts as a loss for flow and a noise source for noise, impeller blade is redesigned to suppress the identified vortex. The response surface method using two factors is employed to determine the optimum inlet and outlet sweep angles for maximum flow rate and minimum noise. Further analysis of finally selected design confirms the improved flow and noise performance.