• Journal of applied mathematics & informatics
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• 제28권5_6호
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• pp.1143-1156
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• 2010

In this paper, we study the following p&q-Laplacian problem with critical Sobolev and Hardy exponents {$-{\Delta}_pu-{\Delta}_qu={\mu}\frac{{\mid}u{\mid}^{p^*(s)-2}u}{{\mid}x{\mid}^s}+{\lambda}f(x,\;u)$, in $\Omega$, u=0, on $\Omega$, where ${\Omega}\;{\subset}\;\mathbb{R}^{\mathbb{N}}$ is a bounded domain and ${\Delta}_ru=div({\mid}{\nabla}u{\mid}^{r-2}{\nabla}u)$ is the r-Laplacian of u. By using the variational method and concentration-compactness principle, we obtain the existence of infinitely many small solutions for above problem which are the complement of previously known results.

• 한국전산유체공학회:학술대회논문집
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• 한국전산유체공학회 2003년도 추계 학술대회논문집
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• pp.158-163
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• 2003

This paper assesses the two-equation turbulence models available in a commercial code, FLUENT, for heat transfer in a turbulent heated pipe flow. In case of flow under $Re_D=10,000$, Standard $\kappa-\epsilon$ and Realizable $\kappa-\epsilon$ models overpredict the Nusselt number about $20\%$ compared with the experimental correlation, and RNG $\kappa-\epsilon$ model overpredicts about $30\%$ when the two-layer zonal method is employed. When wall function method is adopted, all $\kappa-\epsilon$ models show better predictions. Standard $\kappa-\omega$ and SST $\kappa-\omega$ models have the dependency on the first grid point ($0.3). As Reynolds number becomes high, the predictions of all $\kappa-\epsilon$ and $\kappa-\omega$ models are in a good agreement with the experimental correlation.

• 환경위생공학
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• 제16권4호
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• pp.62-68
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• 2001

The advantages of hydrogen peroxide dissolution method were no discharge of noxious matter when dissolution of iron wire which used as the center supporter, reactions occur in room temperature and easy to recover dissolved iron. This study was aimed at gathering the basic data of iron wire dissolution- recovery process and proposes the reaction condition of iron wire dissolution- recovery process rind the factors influencing those reactions. The results were as follows : 1 . Hydrogen peroxide dissolution method used hydrochloric acid as the catalyst. 1. In the dissolution of iron wire(1.668 g), the condition of reaction was E1702(30 ml), HCI(20 ml) and $H_2O$(200 ml) ; time of the reaction was 18 min. P.W.(Piece weight) was 7.75 mg, and C.R. was $2.34{\;}{\Omega}$ 2. In the dissolution of iron wire(1.529 g), the condition of reaction was H7O2(30 ml), HCI(20 ml) and $H_2O$(200 ml), time of the reaction was 21 min., P.W.(Piece weight) was 7.73 mg, and C.R. was $2.35{\;}{\Omega}$. Hydrogen peroxide dissolution method used sulfuric acid as the catalyst. 1. In the dissolution of iron wire(0.834 g), the condition of reaction was $H_2O$(65 ml), $H_2SO_4$(5 ml) and 1702(5 ml) ; time of the reaction was 5 min.30 sec, P.W.(Piece weight) was 7.74 mg, and C.R. was $2.33{\;}{\Omega}$ 2. In the dissolution of iron wire(1.112 g), the condition of reaction was $H_2O$(65 ml), $H_2SO_4$(5 ml) and $H_2O_2$(5 ml) ; time of the reaction was 4 min.30 sec, P.W.(Piece weight) was 7.75 mg, and C.R. was $2.33{\;}{\Omega}$. Hydrogen peroxide dissolution method used hydrochloric acid and sulfuric acid as the catalyst confirmed a clean technology, because there were not occurred a pollutant discharged in the existing method.

• Macromolecular Research
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• 제12권6호
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• pp.604-607
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• 2004

We report an important and useful method for preparing ${\omega}-sulfonated$ polystyrene-stabilized cadmium sulfide (CdS) nanoclusters. The ${\omega}-sulfonated$ polystyrene $(M_n\;=\;5000\;g/mol)$ was prepared successfully through chain-end sulfonation of poly(styryl)lithium using 1,3-propanesultone; the resulting polymer was used successfully as a polymeric stabilizing agent for the preparation of semiconductor CdS nanoclusters by reduction of cadmium acetate in a mixture of toluene and methanol (9:1, v/v). The nanoclusters that formed were characterized by a combination of transmission electron microscopy, X-ray diffraction, and UVN is spectroscopic analysis. The ${\omega}-sulfonated$ polystyrene-stabilized CdS nanoclusters synthesized in this study exhibited the cubic phase (zinc-blende phase) structure in the range of 2-8 nm.

• 한국세라믹학회지
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• 제22권6호
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• pp.87-93
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• 1985

The hematite the magetite and the maghemite thin film were prepared by oxidation and reductino of the vaccum-evaporated iron thin film. Interre;atoms between film preparation process and the electrical properties were investigated. At room temperature the electrical conductivity of the iron the hematite the magnetite and the maghemite thin film were $1{\times}10^4\Omega^{-1}cm^{-1}$, 2{\times}10^{-5}\Omega^{-1}cm^{-1}$, $3{\times}10^{-5}\Omega^{-1}cm^{-1}$, and $4{\times}10^{-5}\Omega^{-1}cm^{-1}$, resp-ectively. The surface of each thin film was dense and homogeneous. At the temperature that the iron thin film was converted into the hematite thin film the electrical conductivity decreased rapidly and the electrical con-ductivity of the hematite thin film increased as temperature increased. The hematite thin film was reduced to the magnetite thin film in H2 atmosphere. The electrical conductivity decreased rapidly at the temperature that the maghemite thin film is formed by oxidation of the magnetite thin film and the electrical conductivity of the maghemite thin film increased as temperature increased.

• 한국전산유체공학회:학술대회논문집
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• 한국전산유체공학회 2004년도 춘계 학술대회논문집
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• pp.139-145
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• 2004

A numerical study of underexpanded jet and impingement on a wall mounted at various distances from the nozzle exit is presented. The 3-dimensional Navier-Stokes equations and $\kappa-\omega$ turbulence equations are solved. The grids are constructed as overlapped grid systems to examine the distance effect. The DADI method is applied to obtain steady-state solutions. To avoid numerical instability such as the carbuncle that sometimes accompany approximate Riemann solver, the HLLE+ scheme is employed for the inviscid flux at the cell interfaces. A goal of this work is to apply a number of two-equation turbulence models based on the $\omega$ equation to the impinging jet problem.

• 대한수학회보
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• 제51권2호
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• pp.409-421
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• 2014

This paper deals with the superlinear elliptic problem without Ambrosetti and Rabinowitz type growth condition of the form: $$\{-div\((1+\frac{|{\nabla}u|^{p(x)}}{\sqrt{1+|{\nabla}u|^{2p(x)}}}})|{\nabla}u|^{p(x)-2}{\nabla}u\)={\lambda}f(x,u)\;a.e.\;in\;{\Omega}\\u=0,\;on\;{\partial}{\Omega}$$ where ${\Omega}{\subset}R^N$ is a bounded domain with smooth boundary ${\partial}{\Omega}$, ${\lambda}$ > 0 is a parameter. The purpose of this paper is to obtain the existence results of nontrivial solutions for every parameter ${\lambda}$. Firstly, by using the mountain pass theorem a nontrivial solution is constructed for almost every parameter ${\lambda}$ > 0. Then we consider the continuation of the solutions. Our results are a generalization of that of Manuela Rodrigues.

• 대한기계학회논문집B
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• 제29권2호
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• pp.232-238
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• 2005

The 'Mixing Index($D_I$)' is used as a conventional guidance measuring the degree of mixing for multiphase flows. For the case when insoluble solutions flow in a passive micromixer, a new method to calculate $D_I$ is proposed. The 'Vortex Index(${\Omega}_I$)' is suggested and formulated. We infer that ${\Omega}_I$ relates to the degree of chaotic advection. Various arbitrary shaped microchannels were tested to calculate the $D_I\;and\;{\Omega}_I$, and then a simple algebraic equation, $D_I=Aexp(B{\Omega}_I)$, is obtained. This equation may be used instead of the conventional partial differential equation, concentration equation, to estimate the degree of mixing.

• East Asian mathematical journal
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• 제14권1호
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• pp.63-76
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• 1998

we consider the hp-version to solve non-constant coefficients elliptic equations $-div(a{\nabla}u)=f$ with Dirichlet boundary conditions on a bounded polygonal domain $\Omega$ in $R^2$. In [6], M. Suri obtained an optimal error-estimate for the hp-version: ${\parallel}u-u^h_p{\parallel}_{1,\Omega}{\leq}Cp^{(\sigma-1)}h^{min(p,\sigma-1)}{\parallel}u{\parallel}_{\sigma,\Omega}$. This optimal result follows under the assumption that all integrations are performed exactly. In practice, the integrals are seldom computed exactly. The numerical quadrature rule scheme is needed to compute the integrals in the variational formulation of the discrete problem. In this paper we consider a family $G_p=\{I_m\}$ of numerical quadrature rules satisfying certain properties, which can be used for calculating the integrals. Under the numerical quadrature rules we will give the variational form of our non-constant coefficients elliptic problem and derive an error estimate of ${\parallel}u-\tilde{u}^h_p{\parallel}_{1,\Omega}$.

• 한국통신학회논문지
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• 제19권9호
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• pp.1802-1811
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• 1994

본 논문에서는 위성반사판 안테나로 사용되는 Ku-밴드 코루게이트 혼 안테나를 모드확장방법을 이용하여 해석 및 실험하였다. 모드확장법은 안테나의 복사 전자계가 각지점에서 모드의 합으로 주어지므로 임의의 위치에서 전자계 분포를 정확하게 예측할 수 있다. 모드확장법을 이용하여 전자계를 계산하는데 필요한 최소한의 항수를 제시했으며, 이를 이용하면 계산시간을 줄일 수 있을 뿐만 아니라 전자계에 대한 계산이 원거리 및 근거리에서 0.5% 이내의 오차를 가질 수 있다. 본 논문의 이론적인 타당성을 확인하기 위해서 크기가 서로 다른 3가지 형태의 안테나를 설계 제작하여 측정한 결과 설계 주파수대에서 정재파비는 평균 1.04-1.1, 입력 임피던스는 $46{\cdot}48{\Omega}$으로 50$\Omega$에 근사한 값을 가졌다.