• Journal of Advanced Marine Engineering and Technology
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• 제20권5호
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• pp.39-44
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• 1996

To overcome weak poinks of the standard k-${\varepsilon}$ turbulence model when applied to complex turbulent flows, various modified models were proposed. But their effects are confined to special flow fields. They have still some problems. Recently, an anisotropic k-${\varepsilon}$ turbulence model was also proposed to solve the drawback of the standard k-${\varepsilon}$ turbulence model. This study is concentrated on the evaluation of the anisotropic k-${\varepsilon}$ turbulence model by the analysis of axisymmetric swirling turbulent flow. Results show that the anisotropic k-${\varepsilon}$ turbulence model has scarecely the fundamentally physical mechanism of predicting the swirling structure of flow.

• 대한수학회지
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• 제47권2호
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• pp.263-275
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• 2010

Let {$X_n;n\;\geq\;1$} be a strictly stationary sequence of negatively associated random variables with mean zero and finite variance. Set $S_n\;=\;{\sum}^n_{k=1}X_k$, $M_n\;=\;max_{k{\leq}n}|S_k|$, $n\;{\geq}\;1$. Suppose $\sigma^2\;=\;EX^2_1+2{\sum}^\infty_{k=2}EX_1X_k$ (0 < $\sigma$ < $\infty$). We prove that for any b > -1/2, if $E|X|^{2+\delta}$(0<$\delta$$\leq$1), then $$lim\limits_{\varepsilon\searrow0}\varepsilon^{2b+1}\sum^{\infty}_{n=1}\frac{(loglogn)^{b-1/2}}{n^{3/2}logn}E\{M_n-\sigma\varepsilon\sqrt{2nloglogn}\}_+=\frac{2^{-1/2-b}{\sigma}E|N|^{2(b+1)}}{(b+1)(2b+1)}\sum^{\infty}_{k=0}\frac{(-1)^k}{(2k+1)^{2(b+1)}}$$ and for any b > -1/2, $$lim\limits_{\varepsilon\nearrow\infty}\varepsilon^{-2(b+1)}\sum^{\infty}_{n=1}\frac{(loglogn)^b}{n^{3/2}logn}E\{\sigma\varepsilon\sqrt{\frac{\pi^2n}{8loglogn}}-M_n\}_+=\frac{\Gamma(b+1/2)}{\sqrt{2}(b+1)}\sum^{\infty}_{k=0}\frac{(-1)^k}{(2k+1)^{2b+2'}}$$, where $\Gamma(\cdot)$ is the Gamma function and N stands for the standard normal random variable.

• 대한전기학회:학술대회논문집
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• 대한전기학회 1989년도 하계종합학술대회 논문집
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• pp.356-358
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• 1989

Linear and nonlinear complex permittivities have been measured for an alternating copolymer of vinylidene cyanide(VSCN) with vinyl propionale(VPr). It is found that the third order permittivity ${\varepsilon}_3$ depends upon frequency according to a function V ${\varepsilon}_3$/ ${1+(j{\omega}{\tau}_3)^{\beta}}^3$ while the linear permittivity ${\varepsilon}_1$obeys a Debye type function ${\nabla}{\varepsilon}_1$/ {1+$(j{\omega}{\tau}_1)^{\beta}$}. Experimental results are well fitled by predicted functions except at low frequency where dc conduction dominates. The relaxation times ${\tau}_1$ and ${\tau}_3$ at same teperature are nealy equal and depend upon temperature according to WLF form. The relaxation strengths ${\nabla}{\varepsilon}_1$ and ${\nabla}{\varepsilon}_3$ have a peak at the vicinity of glass transition temperature (Tg). The strength ${\nabla}{\varepsilon}_1$ has a value of -9 order and ${\nabla}{\varepsilon}_3$ has a negative value of -25 order. The analysis of mechanism by combined knowledge about linear and nonlinear permittivities and dipole moment gives us an imformation of the electrical and thermal dipolar motions in this copolymer.

• 대한음성학회:학술대회논문집
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• 대한음성학회 2005년도 춘계 학술대회 발표논문집
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• pp.59-62
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• 2005

One's mother tongue can have an effect on learning a foreign language, especially on pronunciation. Investigating and comparing English vowels /${\varepsilon}$/ and /${\ae}$/, and their- supposedly- corresponding vowels in Korean /에/ and /애/, this study addresses the following questions: Can Koreans distinguish /에/ and /애/? Can they distinguish /${\varepsilon}$/ and /${\ae}$/ in English? And what is the relationship between the Korean vowels and the English vowels? That is, is the conventional correspondence of /에/-/${\varepsilon}$/ and /애/-/${\ae}$/ appropriate? The results showed that most Korean students distinguish neither Korean /에/ and /애/, nor English /${\varepsilon}$/ and /${\ae}$/. While not distinguishable within a language, Korean /에/ and /애/ still form a separate group from English /${\varepsilon}$/ and /${\ae}$/. Therefore the correspondence between /에/-/${\varepsilon}$/ and /애/-/${\ae}$/ is not appropriate. Strategies for teaching English pronunciation should be designed accordingly.

• 대한수학회보
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• 제49권6호
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• pp.1223-1240
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• 2012

The system $$\dot{x}=(A+{\varepsilon}Q(t,{\varepsilon}))x+{\varepsilon}g(t,{\varepsilon})+h(x,t,{\varepsilon}),$$ where A is elliptic whose eigenvalues are not necessarily simple and $h$ is $\mathcal{O}(x^2)$. It is proved that, under suitable hypothesis of analyticity, for most values of the frequencies, the system is reducible.

• Journal of the Korean Statistical Society
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• 제22권1호
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• pp.39-54
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• 1993

In the three-factor nested variance component model with equal numbers in the cells given by $y_{ijkm} = \mu + A_i + B_{ij} + C_{ijk} + \varepsilon_{ijkm}$, the exact confidence intervals of the variance component of $\sigma^2_A, \sigma^2_B, \sigma^2_C, \sigma^2_{\varepsilon}, \sigma^2_A/\sigma^2_{\varepsilon}, \sigma^2_B/\sigma^2_{\varepsilon}, \sigma^2_C/\sigma^2_{\varepsilon}, \sigma^2_A/\sigma^2_C, \sigma^2_B/\sigma^2_C$ and $\sigma^2_A/\sigma^2_B$ are not found out yet. In this paper approximate lower and upper confidence intervals are presented.

• 해양환경안전학회지
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• 제25권3호
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• pp.344-353
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• 2019

The wakes behind a square cylinder were simulated using two-equation turbulence models, $k-{\varepsilon}$ and RNG $k-{\varepsilon}$ models. For comparisons between the model predictions and analytical solutions, we employed three skill assessments:, the correlation coefficient for the similarity of the wake shape, the error of maximum velocity difference (EMVD) of the accuracy of wake velocity, and the ratio of drag coefficient (RDC) for the flow patterns as in the authors' previous study. On the basis of the calculated results, we discussed the feasibility of each model for wake simulation and suggested a suitable value for an eddy viscosity related constant in each turbulence model. The $k-{\varepsilon}$ model underestimated the drag coefficient by over 40 %, and its performance was worse than that in the previous study with one-equation and mixing length models, resulting from the empirical constants in the ${\varepsilon}-equation$. In the RNG $k-{\varepsilon}$ model experiments, when an eddy viscosity related constant was six times higher than the suggested value, the model results were yielded good predictions compared with the analytical solutions. Then, the values of EMVD and RDC were 3.8 % and 3.2 %, respectively. The results of the turbulence model simulations indicated that the RNG $k-{\varepsilon}$ model results successfully represented wakes behind the square cylinder, and the mean error for all skill assessments was less than 4 %.

• 설비공학논문집
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• 제8권3호
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• pp.375-385
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• 1996

Turbulent flow and heat transfer characteristics around staggered tube banks were studied using the 3-D Navier-Stokes equations and energy equation governing a steady incompressible flow, which were reformulated in a non-orthogonal coordinate system with cartesian velocity components and discretized by the finite volume method with a non-staggered variable arrangement. The predicted turbulent kinetic energy using RNG $k-{\varepsilon}$ model was lower than that of standard $k-{\varepsilon}$ model but showed same result for mean flow field quantities. The prediction of the skin friction coefficient using RNG $k-{\varepsilon}$ model showed better trend with experimental data than standard $k-{\varepsilon}$ model result. The inclined flow showed higher velocity and skin friction coefficient than transverse flow because of extra strain rate ($\frac{{\partial}w}{{\partial}y}$). Also, this was why the inclined flow showed higher local heat transfer coefficient than the transverse flow.

• 대한수학회보
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• 제43권2호
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• pp.309-318
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• 2006

Let X and Y be real Banach spaces and ${\varepsilon}\;>\;0$, p > 1. Let f : $X\;{\to}\;Y$ be a bijective mapping with f(0) = 0 satisfying $$|\;{\parallel}f(x)-f(y){\parallel}-{\parallel}{x}-y{\parallel}\;|\;{\leq}{\varepsilon}{\parallel}{x}-y{\parallel}^p$$ for all $x\;{\in}\;X$ and, let $f^{-1}\;:\;Y\;{\to}\;X$ be uniformly continuous. Then there exist a constant ${\delta}\;>\;0$ and N(${\varepsilon},p$) such that lim N(${\varepsilon},p$)=0 and a unique surjective isometry I : X ${\to}$ Y satisfying ${\parallel}f(x)-I(x){\parallel}{\leq}N({\varepsilon,p}){\parallel}x{\parallel}^p$ for all $x\;{\in}\;X\;with\;{\parallel}x{\parallel}{\leq}{\delta}$.

• 한국전산유체공학회:학술대회논문집
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• 한국전산유체공학회 2008년도 춘계학술대회논문집
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• pp.168-171
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• 2008

In the present study, turbulent flows around cubic and L-shape buildings were simulated numerically. Standard ${\kappa}$-$\varepsilon$, RNG ${\kappa}$-$\varepsilon$, LES turbulence models were adopted for the present simulation. The wind pressure coefficients from these results were compared with the available experimental data. The result of RNG ${\kappa}$-$\varepsilon$ and LES turbulent models gave better prediction than that of standard ${\kappa}$-$\varepsilon$ turbulent model which is widely used in the turbulent flow simulation.