• Title/Summary/Keyword: Numerical Approximation

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VOIDS LENSING OF THE CMB AT HIGH RESOLUTION

  • SANGKA, ANUT;SAWANGWIT, UTANE;SANGUANSAK, NUANWAN
    • Publications of The Korean Astronomical Society
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    • v.30 no.2
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    • pp.397-399
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    • 2015
  • Recently, cosmic voids have been recognized as a powerful cosmological probe. A number of studies have focused on the effects of the gravitational lensing by voids on the temperature (and in some cases polarization) anisotropy of the Cosmic Microwave Background (CMB) background at relatively large to medium scales, l ~ 1000. Many of these studies attempt to explain the unusually large cold spot in CMB temperature maps and dynamical evidence of dark energy via detections of late-time integrated Sachs Wolfe (ISW) effect. Here, the effects of lensing by voids on the CMB temperature anisotropy at small scales, up to l = 3000, will be investigated. This work is carried out in the light of the benefits of adding large catalogues of cosmic voids, to be identified by future large galaxy surveys such as EUCLID and LSST, to the analysis of CMB data such as those from Planck mission. Our numerical simulation utilizes two methods, namely, the small-de ectionangle approximation and full ray-tracing analysis. Using the fitted void density profiles and radius (RV ) distribution available in the literature from N-body simulations, we simulated the secondary temperature anisotropy (lensing) of CMB photons induced by voids along a line of sight from redshift 0 to 2. Each line of sight contains approximately 1000 voids of effective radius $RV_{,eff}=35h^{-1}Mpc$ with randomly distributed radial and projected positions. Both methods are used to generate temperature maps. The two methods will be compared for their accuracy and effciency in the implementation of theoretical modeling.

Direct Non-stepwise Multiple Quantum Excitations in Translation-Vibration Energy Transfer (竝進-振動에너지 變換에 있어서의 多量子 直接 振動 勵起)

  • Yoo Hang Kim;Hyung Kyu Shin
    • Journal of the Korean Chemical Society
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    • v.20 no.2
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    • pp.97-110
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    • 1976
  • Effects of direct multiple quantum excitations in vibrational energy transfer were investigated. Vibrational transition probabilities for 0${\rightarrow}$2, 0${\rightarrow}$3, and 0${\rightarrow}$4 excitations were explicitly formulated including both direct 0→n excitations and stepwise single quantum processes. For the formulation the perturbing force was derived from the exponential potential including terms up to fourth order in the vibrational amplitude. The head-on collinear collision model between a harmonic oscillator and an incident particle was employed, and the formulation was based on the semiclassical approximation. Numerical results were obtained for five different collision systems (Ar${\cdots}$O-N, He${\cdots}$H-H, He${\cdots}$H-Cl, 5${\cdots}$1-2, 2${\cdots}$12-12). Comparison between the present results and those obtained using the linearized interaction potential showed that the overall effect of including the direct multiple quantum transition is to decrease the probabilities at low collision energies and to increase them at high energies. The present results were found to be significantly different from those obtained using the linearized potential for collision systems He${\cdots}$H-H, He${\cdots}$H-Cl, and 5${\cdots}$1-2. For systems Ar${\cdots}$O-N and 2${\cdots}$12-12 the differences were negligible.

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Axisymmetric Modeling of Dome Tendons in Nuclear Containment Building I. Theoretical Derivations (원전 격납건물 돔 텐던의 축대칭 모델링 기법 I. 이론식의 유도)

  • Jeon Se-Jin;Chung Chul-Hun
    • Journal of the Korea Concrete Institute
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    • v.17 no.4 s.88
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    • pp.521-526
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    • 2005
  • Prestressing tendons in a nuclear containment building dome are non-axisymmetrically arranged in most cases. However, simple axisymmetric modeling of the containment has been often employed in practice to estimate structural behavior for the axisymmetric loadings such as an internal pressure. In this case, the axisymmetric approximation is required for the actual tendon arrangements in the dome. Some procedures are proposed that can implement the actual 3-dimensional tendon stiffness and prestressing effect into the axisymmetric model. Prestressing tendons, which are arranged in 3 or 2-ways depending on a containment type, are converted into an equivalent layer to consider the stiffness contribution in meridional and hoop directions. In order to reflect the prestressing effect, equivalent load method and initial stress method are devised and the corresponding loads or stresses are derived in terms of the axisymmetric model. In a companion paper, the proposed schemes are applied into CANDU and KSNP(Korean Standard Nuclear Power Plant) type containments and are verified through some numerical examples comparing the analysis results with those of the actual 3-dimensional model.

Tight Bounds and Invertible Average Error Probability Expressions over Composite Fading Channels

  • Wang, Qian;Lin, Hai;Kam, Pooi-Yuen
    • Journal of Communications and Networks
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    • v.18 no.2
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    • pp.182-189
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    • 2016
  • The focus in this paper is on obtaining tight, simple algebraic-form bounds and invertible expressions for the average symbol error probability (ASEP) of M-ary phase shift keying (MPSK) in a class of composite fading channels. We employ the mixture gamma (MG) distribution to approximate the signal-to-noise ratio (SNR) distributions of fading models, which include Nakagami-m, Generalized-K ($K_G$), and Nakagami-lognormal fading as specific examples. Our approach involves using the tight upper and lower bounds that we recently derived on the Gaussian Q-function, which can easily be averaged over the general MG distribution. First, algebraic-form upper bounds are derived on the ASEP of MPSK for M > 2, based on the union upper bound on the symbol error probability (SEP) of MPSK in additive white Gaussian noise (AWGN) given by a single Gaussian Q-function. By comparison with the exact ASEP results obtained by numerical integration, we show that these upper bounds are extremely tight for all SNR values of practical interest. These bounds can be employed as accurate approximations that are invertible for high SNR. For the special case of binary phase shift keying (BPSK) (M = 2), where the exact SEP in the AWGN channel is given as one Gaussian Q-function, upper and lower bounds on the exact ASEP are obtained. The bounds can be made arbitrarily tight by adjusting the parameters in our Gaussian bounds. The average of the upper and lower bounds gives a very accurate approximation of the exact ASEP. Moreover, the arbitrarily accurate approximations for all three of the fading models we consider become invertible for reasonably high SNR.

Numerical Analysis of Natural Convection-Radiation Heat Transfer in an Enclosure Containing Absorbing, emitting and Linear Anisotropic Scattering Medium (흡수,방사 및 선형비등방 산란 매질을 포함하는 밀폐공간내의 자연대류- 복사열전달에 대한 수치해석)

  • 차상명;김종열;박희용
    • Transactions of the Korean Society of Mechanical Engineers
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    • v.16 no.5
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    • pp.952-964
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    • 1992
  • The interaction of natural convection and radiation heat transfer in a two dimensional square enclosure containing absorbing, emitting and linear anisotropically scattering gray medium is numerically analyzed. P-1 and P-3 approximation is introduced to calculate radiation heat transfer. The effects of scattering albedo, wall emissivity, scattering anisotropy, and optical thickness on the characteristics of the flow and temperature field and heat transfer are investigated. Temperature and velocity profiles depend a great deal on the scattering albedo, and the importance of this effect increases with decrease in albelo. Planck number is another important parameter in radiation heat transfer. The increase in scattering albedo increases convection heat transfer and decreases radiation heat transfer at hot wall. However, the increase in scattering albedo decreases both convection and radiation heat transfer at cold wall. The increase in optical thickness decreases radiation heat transfer. The scattering anisotropy has important effects on the radiation heat transfer only. The highly forward scattering leads to an increase of radiation heat transfer whereas the highly backward scattering leads to an decrease of radiation heat transfer. The effect of scattering anisotropy decreases when reducing the wall emissivity.

A Terrain Surface Approximation Using the Hermite Function (Hermite함수를 이용한 지형곡면근사)

  • 문두열;정범석;이용희
    • Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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    • v.20 no.3
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    • pp.265-272
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    • 2002
  • By this time, many methods have been developed for computing the pit excavation volumes, ranging from a simple formula to more complicated numerical methods. Earlier the standard methods for pit excavation volume computation requires that the considered area be divided the boundary ranges of x and y directions into a rectangular grid. whereas these methods may not calculate the estimation of pit excavation volume that is often required in many surveying situation exactly. In Easa methods(1998), the rectangular grid is divided into the same linear in the range x and y directions respectively. This method employs a cubic Hermite polynomial for individual intervals in both directions of the grid. Because the height data over the same boundary of x and y interval ranges have to be exist, it is not possible to choose the governing points of the terrain boundary such as points of maximum and minimum height. In this study, a method of volume computation, that combines the advantages of Easa methods(1998) and avoids the drawbacks of it, is presented. The proposed method employs a cubic Hermite polynomial for individual intervals in both directions of the non-grid, the all over intervals of it may be unequal grid x in width and y in length y, partially. The new proposed method should produce better accuracy than the other conventional methods.

Fuzzy Nonlinear Adaptive Control of Overhead Cranes for Anti-Sway Trajectory Tracking and High-Speed Hoisting Motion (고속 권상운동과 흔들림억제 궤적추종을 위한 천정주행 크레인의 퍼지 비선형 적응제어)

  • Park, Mun-Soo;Chwa, Dong-Kyoung;Hong, Suk-Kyo
    • Journal of the Korean Institute of Intelligent Systems
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    • v.17 no.5
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    • pp.582-590
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    • 2007
  • Nonlinear adaptive control of overhead cranes is investigated for anti-sway trajectory tracking with high-speed hoisting motion. The sway dynamics of two dimensional underactuated overhead cranes is heavily coupled with the trolley acceleration, hoisting rope length, and the hoisting velocity which is an obstacle in the design of decoupling control based anti-sway trajectory tracking control law To cope with this obstacle. we propose a fuzzy nonlinear adaptive anti-sway trajectory tracking control law guaranteeing the uniform ultimate boundedness of the sway dynamics even in the presence of uncertainties in such a way that it cancels the effect of the trolley acceleration and hoisting velocity on the sway dynamics. In particular. system uncertainties, including system parameter uncertainty unmodelled dynamics, and external disturbances, are compensated in an adaptive manner by utilizing fuzzy uncertainty observers. Accordingly, the ultimate bound of the tracking errors and the sway angle decrease to zero when the fuzzy approximation errors decrease to zero. Finally, numerical simulations are performed to confirm the effectiveness of the proposed scheme.

Analytical Model for Multi-Fiber WDM Networks with Sparse and Limited Wavelength Conversion (다수의 광심유와 산재한 제한 영역 파장 변환기로 구성된 파장분할다중화 광통신항의 성능 분석 모형)

  • Jeong, Han-You;Seo, Seung-Woo;Choi, Yoon-Ho
    • The Journal of Korean Institute of Communications and Information Sciences
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    • v.34 no.4B
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    • pp.394-402
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    • 2009
  • In this paper, we present a new analytical model for estimating the blocking performance of multi-fiber WDM networt:s with sparse and limited wavelength conversion (SLWC). The proposed model is a reduced-load approximation model that can obtain accurate estimates of blocking probability of such networks. Our model employs three new recurrence formulae to obtain the free wavelength distribution on a multi-fiber link, the free wavelength distribution after limited-range wavelength conversion and the end-to-end blocking probability of a multi-hop path, respectively. From the numerical results on the NSFNET, we demonstrate that the blocking performance of two-fiber NSFNET with three wavelength-convertible nodes, each of which translates an input wavelength to its adjacent output wavelengths, closely approximates the blocking performance of full wavelength conversion.

Criticality Safety Determination of Spent Fuel Storage Vault (기사용(旣使用) 핵연료저장시(核燃料貯藏時) 핵임계(核臨界) 안전성(安全性) 결정(決定))

  • Yook, Chong-Chul
    • Journal of Radiation Protection and Research
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    • v.4 no.1
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    • pp.1-4
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    • 1979
  • Effective multiplication factor has been calculated for one PWR fresh fuel assembly immersed in a spent fuel storage vault on the basis of the neutron transport theory. A numerical calculation has been carried out by means of Sn approximation. The method employed in this study is that the energy domain is broken into 16 groups, the angular variable is divided into four discrete direction, i.e., $S_4$, and the spatial variable which is divided into fine meshes at the interface between different materials is discretized into 27 mesh points. The calculated $K_{eff}$ value of 0.6145 seems to be far small in comparison with the value obtained by other author for an infinite array of fuel assemblies.

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Analysis of Stokes flows by Carrera unified formulation

  • Varello, Alberto;Pagani, Alfonso;Guarnera, Daniele;Carrera, Erasmo
    • Advances in aircraft and spacecraft science
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    • v.5 no.3
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    • pp.363-383
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    • 2018
  • One-dimensional (1D) models of incompressible flows, can be of interest for many applications in which fast resolution times are demanded, such as fluid-structure interaction of flows in compliant pipes and hemodynamics. This work proposes a higher-order 1D theory for the flow-field analysis of incompressible, laminar, and viscous fluids in rigid pipes. This methodology is developed in the domain of the Carrera Unified Formulation (CUF), which was first employed in structural mechanics. In the framework of 1D modelling, CUF allows to express the primary variables (i.e., velocity and pressure fields in the case of incompressible flows) as arbitrary expansions of the generalized unknowns, which are functions of the 1D computational domain coordinate. As a consequence, the governing equations can be expressed in terms of fundamental nuclei, which are invariant of the theory approximation order. Several numerical examples are considered for validating this novel methodology, including simple Poiseuille flows in circular pipes and more complex velocity/pressure profiles of Stokes fluids into non-conventional computational domains. The attention is mainly focused on the use of hierarchical McLaurin polynomials as well as piece-wise nonlocal Lagrange expansions of the generalized unknowns across the pipe section. The preliminary results show the great advantages in terms of computational costs of the proposed method. Furthermore, they provide enough confidence for future extensions to more complex fluid-dynamics problems and fluid-structure interaction analysis.