• Title/Summary/Keyword: integrals

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Effects of Temperature, Photoperiod and Light Intensity on Growth and Flowering in Eustoma grandiflorum

  • Oh, Wook
    • Horticultural Science & Technology
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    • v.33 no.3
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    • pp.349-355
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    • 2015
  • Lisianthus (Eustoma grandiflorum) is relatively sensitive to temperature and light conditions. For year round production of good quality potted plants and energy saving, it is necessary to understand the growth and flowering response to the combined conditions of these environmental factors. This study was conducted to examine the growth and flowering responses to temperature, photoperiod, and light intensity during the post-seedling stage. 'El Paso Deep Blue' lisianthus plants with four true leaf pairs were grown in growth chambers maintained at average daily temperatures (ADT) of 14, 20, and $26^{\circ}C$ and provided with three photosynthetic photon fluxes [PPF; 100, 200, and $400{\mu}mol{\cdot}m^{-2}{\cdot}s^{-1}$] for 8 (08:00-16:00) and 16 hours (08:00-24:00) by fluorescent and incandescent lamps, resulting in four daily light integrals (DLI): about 3, 6 (two photoperiods), 12 (two photoperiods), and $24mol{\cdot}m^{-2}{\cdot}d^{-1}$. After treatment for three weeks followed by growth for one week in a greenhouse of $20{\pm}3^{\circ}C$, growth and development were measured. Higher temperature, higher PPF, and longer photoperiod promoted plant growth and flowering; however the impacts of PPF and photoperiod were smaller than those of temperature. As ADT and DLI increased, the number of leaves, number of flowers, lateral shoot length, and shoot dry weight increased. An increase of about $1mol{\cdot}m^{-2}{\cdot}d^{-1}$ DLI could constitute an increase of 0.40 to $0.76^{\circ}C$ ADT depending on these crop characteristics when ADT and DLI are above $20^{\circ}C$ and $12mol{\cdot}m^{-2}{\cdot}d^{-1}$, respectively. Therefore, growers can select a regimen of heating or supplemental lighting without delaying harvesting time or decreasing crop quality.

Shape Optimal Design by P-version of Finite Element Method (p-Version 유한요소법에 의한 형상 최적화설계)

  • Kim, Haeng Joon;Woo, Kwang Sung
    • KSCE Journal of Civil and Environmental Engineering Research
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    • v.14 no.4
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    • pp.729-740
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    • 1994
  • In the shape optimal design based on h-version of FEM, the ideal mesh for the initial geometry most probably will not be suitable for the final analysis. Thus, it is necessary to remesh the geometry of the model at each stage of optimization. However, the p-version of FEM appears to be a very attractive alternative for use in shape optimization. The main advantages are as follows; firstly, the elements are not sensitive to distortion for interpolation polynomials of order $p{\geq}3$; secondly, even singular problems can be solved more efficiently with p-version than with the h-version by proper mesh design; thirdly, the initial mesh design are identical. The 2-D p-version model for shape optimization is presented on the basis of Bezier's curve fitting, gradient projection method, and integrals of Legendre polynomials. The numerical results are performed by p-version software RASNA.

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Noise Analysis for Large Silencers of Ships and Off-shore Plants using Energy Flow Analysis

  • Kim, Tae-Gyoung;Song, Jee-Hun;Hong, Suk-Yoon
    • Journal of the Korean Society of Marine Environment & Safety
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    • v.26 no.3
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    • pp.297-307
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    • 2020
  • In the study, energy flow analysis is performed to predict the performance of silencers. To date, deterministic approaches such as finite element method have been widely used for silencer analysis. However, they have limitations in analyzing large structures and mid-high frequency ranges due to unreasonable computational costs and errors. However, silencers used for ships and off-shore plants are much larger than those used in other engineering fields. Hence, energy governing equation, which is significantly efficient for systems with high modal density, is solved for silencers in ships and off-shore plants. The silencer is divided into two different acoustic media, air and absorption materials. The discontinuity of energy density at interfaces is solved via hypersingular integrals for the 3-D modified Helmholtz equation to analyze multi-domain problems with the energy flow boundary element method. The method is verified by comparing the measurements and analysis results for ship silencers over mid-high frequency ranges. The comparisons confirm good agreement between the measurement and analysis results. We confirm that the applied analysis method is useful for large silencers in mid-high frequency ranges. With the proven procedures, energy flow analysis can be performed for various types of silencer used in ships and off-shore plants in the first stage of the design.

Improvement of Einstein's Suspended Load Equation (Einstein 부유사량 산정식의 개선)

  • Yu, Dong-Hun;Sin, Seung-Ho;Im, Hak-Su
    • Journal of Korea Water Resources Association
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    • v.33 no.6
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    • pp.815-825
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    • 2000
  • In the present work Einstein's(l942) suspended load equation IS refined in vanous aspects. After checking the flow characteristics a new method is presented for the estimation of zero velocity point at the condition of smooth turbulent flow, and non-dimensional number of suspended load is introduced for the clear representation of suspended load equation. And a recent equation of bed load is employed in order to calculate accurately the sediment concentration at a reference point. Several approximation equations are also developed to compute directly or explicitly two integrals introduced in the equations. The refined equation has been tested against the measurement data collected by Brownlie(l981) in comparison with Einstein's original equation.uation.

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Estimates of Partial Safety Factors of Circumferential Through-Wall Cracked Pipes Based on Elastic-Plastic Crack Initiation Criterion (탄소성 균열개시조건에 대한 원주방향 관통균열 배관의 부분안전계수 계산)

  • Lee, Jae-Bin;Huh, Nam-Su
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.38 no.11
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    • pp.1257-1264
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    • 2014
  • Efforts are presently underway for developing an optimal design methodology for GEN-IV nuclear reactors based on target failure probabilities. A typical example is the system-based code, in which the results are represented in the form of partial safety factors (PSFs). Thus, a PSF is one of the crucial elements in either component design or integrity assessment based on target failure probabilities during the operation period. In the present study, a procedure for calculating the PSF of a circumferential through-wall cracked pipe based on the elastic-plastic crack initiation criterion is established, in which the importance of each input variable is assessed. Elastic-plastic J-integrals are calculated using the GE/EPRI and reference stress methods, and the PSF values are calculated using both first- and second-order reliability methods. Moreover, the effect of statistical distributions of assessment variables on the PSF is also evaluated.

Subparametric Element Based on Partial-linear Layerwise Theory for the Analysis of Orthotropic Laminate Composites (직교이방성 적층구조 해석을 위한 부분-선형 층별이론에 기초한 저매개변수요소)

  • Ahn, Jae-Seok;Woo, Kwang-Sung
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.22 no.2
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    • pp.189-196
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    • 2009
  • This paper presents the subparametric finite element model formulated by partial-linear layerwise theory for the analysis of laminate composites. The proposed model is based on refined approximations of two dimensional plane for orthotropic thick laminate plate as well as thin case. Three dimensional problem can be reduced to two dimensional case by assuming piecewise linear variation of in-plane displacement and a constant value of out-of-plane displacement across the thickness. The integrals of Legendre polynomials are chosen to define displacement fields and Gauss-Lobatto numerical integration is implemented in order to directly obtain maximum values occurred at the nodal points of each layer without other extrapolation techniques. The validity and characteristics of the proposed model have been tested by using orthotropic multilayered plate problem as compared to the values available in the published references. In this study, the convergence test has been carried out to determine the optimal layer model in terms of central deflection and stresses. Also, the distribution of displacements and stresses across the thickness has been investigated as the number of layer is increased.

An Analytical Model of the First Eigen Energy Level for MOSFETs Having Ultrathin Gate Oxides

  • Yadav, B. Pavan Kumar;Dutta, Aloke K.
    • JSTS:Journal of Semiconductor Technology and Science
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    • v.10 no.3
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    • pp.203-212
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    • 2010
  • In this paper, we present an analytical model for the first eigen energy level ($E_0$) of the carriers in the inversion layer in present generation MOSFETs, having ultrathin gate oxides and high substrate doping concentrations. Commonly used approaches to evaluate $E_0$ make either or both of the following two assumptions: one is that the barrier height at the oxide-semiconductor interface is infinite (with the consequence that the wave function at this interface is forced to zero), while the other is the triangular potential well approximation within the semiconductor (resulting in a constant electric field throughout the semiconductor, equal to the surface electric field). Obviously, both these assumptions are wrong, however, in order to correctly account for these two effects, one needs to solve Schrodinger and Poisson equations simultaneously, with the approach turning numerical and computationally intensive. In this work, we have derived a closed-form analytical expression for $E_0$, with due considerations for both the assumptions mentioned above. In order to account for the finite barrier height at the oxide-semiconductor interface, we have used the asymptotic approximations of the Airy function integrals to find the wave functions at the oxide and the semiconductor. Then, by applying the boundary condition at the oxide-semiconductor interface, we developed the model for $E_0$. With regard to the second assumption, we proposed the inclusion of a fitting parameter in the wellknown effective electric field model. The results matched very well with those obtained from Li's model. Another unique contribution of this work is to explicitly account for the finite oxide-semiconductor barrier height, which none of the reported works considered.

The Effects of Sloshing on the Responses of an LNG Carrier Moored in a Side-by-side Configuration with an Offshore Plant (해양플랜트에 병렬 계류된 LNG 운반선의 거동에 슬로싱이 미치는 영향)

  • Lee, Seung-Jae
    • Journal of Ocean Engineering and Technology
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    • v.24 no.5
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    • pp.16-21
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    • 2010
  • During the loading/offloading operation of a liquefied natural gas carrier (LNGC) that is moored in a side-by-side configuration with an offshore plant, sloshing that occurs due to the partially filled LNG tank and the interactive effect between the two floating bodies are important factors that affect safety and operability. Therefore, a time-domain software program, called CHARM3D, was developed to consider the interactions between sloshing and the motion of a floating body, as well as the interactions between multiple bodies using the potential-viscous hybrid method. For the simulation of a floating body in the time domain, hydrodynamic coefficients and wave forces were calculated in the frequency domain using the 3D radiation/diffraction panel program based on potential theory. The calculated values were used for the simulation of a floating body in the time domain by convolution integrals. The liquid sloshing in the inner tanks is solved by the 3D-FDM Navier-Stokes solver that includes the consideration of free-surface non-linearity through the SURF scheme. The computed sloshing forces and moments were fed into the time integration of the ship's motion, and the updated motion was, in turn, used as the excitation force for liquid sloshing, which is repeated for the ensuing time steps. For comparison, a sloshing motion coupled analysis program based on linear potential theory in the frequency domain was developed. The computer programs that were developed were applied to the side-by-side offloading operation between the offshore plant and the LNGC. The frequency-domain results reproduced the coupling effects qualitatively, but, in general, the peaks were over-predicted compared to experimental and time-domain results. The interactive effects between the sloshing liquid and the motion of the vessel can be intensified further in the case of multiple floating bodies.

DIRECT PRODUCTED W*-PROBABILITY SPACES AND CORRESPONDING AMALGAMATED FREE STOCHASTIC INTEGRATION

  • Cho, Il-Woo
    • Bulletin of the Korean Mathematical Society
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    • v.44 no.1
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    • pp.131-150
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    • 2007
  • In this paper, we will define direct producted $W^*-porobability$ spaces over their diagonal subalgebras and observe the amalgamated free-ness on them. Also, we will consider the amalgamated free stochastic calculus on such free probabilistic structure. Let ($A_{j},\;{\varphi}_{j}$) be a tracial $W^*-porobability$ spaces, for j = 1,..., N. Then we can define the corresponding direct producted $W^*-porobability$ space (A, E) over its N-th diagonal subalgebra $D_{N}\;{\equiv}\;\mathbb{C}^{{\bigoplus}N}$, where $A={\bigoplus}^{N}_{j=1}\;A_{j}\;and\;E={\bigoplus}^{N}_{j=1}\;{\varphi}_{j}$. In Chapter 1, we show that $D_{N}-valued$ cumulants are direct sum of scalar-valued cumulants. This says that, roughly speaking, the $D_{N}-freeness$ is characterized by the direct sum of scalar-valued freeness. As application, the $D_{N}-semicircularityrity$ and the $D_{N}-valued$ infinitely divisibility are characterized by the direct sum of semicircularity and the direct sum of infinitely divisibility, respectively. In Chapter 2, we will define the $D_{N}-valued$ stochastic integral of $D_{N}-valued$ simple adapted biprocesses with respect to a fixed $D_{N}-valued$ infinitely divisible element which is a $D_{N}-free$ stochastic process. We can see that the free stochastic Ito's formula is naturally extended to the $D_{N}-valued$ case.

Effects of High-harmonic Components on the Rayleigh Indices in Multi-mode Thermo-acoustic Combustion Instability

  • Song, Chang Geun;Yoon, Jisu;Yoon, Youngbin;Kim, Young Jin;Lee, Min Chul
    • International Journal of Aeronautical and Space Sciences
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    • v.17 no.4
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    • pp.518-525
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    • 2016
  • This paper presents the characteristics of non-fundamental multi-mode combustion instability and the effects of high-harmonic components on the Rayleigh criterion. Phenomenological observations of multi-harmonic-mode dynamic pressure waves regarding the intensity of harmonic components and the source of wave distortion have been explained by introducing examples of second- and third-order harmonics at various amplitudes. The amplitude and order of the harmonic components distorted the wave shapes, including the peak and the amplitude, of the dynamic pressure and heat release, and consequently the temporal Rayleigh index and its integrals. A cause-and-effect analysis was used to identify the root causes of the phase delay and the amplification of the Rayleigh index. From this analysis, the skewness of the dynamic pressure turned out to be a major source in determining whether multi-mode instability is driving or damping, as well as in optimizing the combustor design, such as the mixing length and the combustor length, to avoid unstable regions. The results can be used to minimize errors in predicting combustion instability in cases of high multi-mode combustion instability. In the future, the amount of research and the number of applications will increase because new fuels, such as fast-burning syngases, are prone to generating multi-mode instabilities.