• Title, Summary, Keyword: Critical point

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A Calculation for the Viscosity of Fluid at the Critical Point

  • Kim, Won-Soo;Chair, Tong-Seek
    • Bulletin of the Korean Chemical Society
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    • v.23 no.11
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    • pp.1524-1526
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    • 2002
  • It is very difficult to measure the fluid viscosity at the critical point, there are seldom found experimental values of fluid viscosity at the critical point. Few theories can explain the critical viscosity quantitatively. A theory of viscosity previously proposed by authors10 is applied to the fluid at the critical point. This theory can be simplified as a simple form with no adjustable parameters, allowing for easy calculation. Viscosities at the critical point for some substances have been calculated, and calculated results are satisfactory when compared with the observed values.

CRITICAL POINTS AND CONFORMALLY FLAT METRICS

  • Hwang, Seungsu
    • Bulletin of the Korean Mathematical Society
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    • v.37 no.3
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    • pp.641-648
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    • 2000
  • It has been conjectured that, on a compact 3-dimensional manifold, a critical point of the total scalar curvature functional restricted to the space of constant scalar curvature metrics of volume 1 is Einstein. In this paper we find a sufficient condition that a critical point is Einstein. This condition is equivalent for a critical point ot be conformally flat. Its relationship with the Fisher-Marsden conjecture is also discussed.

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CRITICAL POINT METRICS OF THE TOTAL SCALAR CURVATURE

  • Chang, Jeong-Wook;Hwang, Seung-Su;Yun, Gab-Jin
    • Bulletin of the Korean Mathematical Society
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    • v.49 no.3
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    • pp.655-667
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    • 2012
  • In this paper, we deal with a critical point metric of the total scalar curvature on a compact manifold $M$. We prove that if the critical point metric has parallel Ricci tensor, then the manifold is isometric to a standard sphere. Moreover, we show that if an $n$-dimensional Riemannian manifold is a warped product, or has harmonic curvature with non-parallel Ricci tensor, then it cannot be a critical point metric.

STABLE MINIMAL HYPERSURFACES IN A CRITICAL POINT EQUATION

  • HWang, Seung-Su
    • Communications of the Korean Mathematical Society
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    • v.20 no.4
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    • pp.775-779
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    • 2005
  • On a compact n-dimensional manifold $M^n$, a critical point of the total scalar curvature functional, restricted to the space of metrics with constant scalar curvature of volume 1, satifies the critical point equation (CPE), given by $Z_g\;=\;s_g^{1\ast}(f)$. It has been conjectured that a solution (g, f) of CPE is Einstein. The purpose of the present paper is to prove that every compact stable minimal hypersurface is in a certain hypersurface of $M^n$ under an assumption that Ker($s_g^{1\ast}{\neq}0$).

The Critical Point Equation on 3-dimensional α-cosymplectic Manifolds

  • Blaga, Adara M.;Dey, Chiranjib
    • Kyungpook Mathematical Journal
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    • v.60 no.1
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    • pp.177-183
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    • 2020
  • The object of the present paper is to study the critical point equation (CPE) on 3-dimensional α-cosymplectic manifolds. We prove that if a 3-dimensional connected α-cosymplectic manifold satisfies the Miao-Tam critical point equation, then the manifold is of constant sectional curvature -α2, provided Dλ ≠ (ξλ)ξ. We also give several interesting corollaries of the main result.

On-Line Calculation of the Critical Point of Voltage Collapse Based on Multiple Load Flow Solutions (다중조류계산을 이용한 전압붕괴 임계점의 On-Line 계산)

  • Nam, Hae-Kon;Kim, Dong-Jun
    • Proceedings of the KIEE Conference
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    • pp.134-136
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    • 1993
  • This paper presents a novel and efficient method to calculate the critical point of voltage collapse. Conjugate gradient and modified Newton-Raphson methods are employed to calculate two pairs of multiple load flow solutions for two operating conditions, i.e., both +mode and -mode voltages for two loading conditions respectively. Then these four voltage magnitude-load data sets of the bus which is most susceptible to voltage collapse, are fitted to third order polynomial using Lagrangian interpolation in order to represent approximate nose curve (P-V curve). This nose curve locates first estimate of the critical point of voltage collapse. The procedure described above is repeated near the critical point and the new estimate will be very close to the critical point. The proposed method is tested for the eleven bus Klos-Kerner system, with good accuracy and fast computation time.

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A Numerical Study on the Laminar Flow Field and Heat Transfer Coefficient Distribution for Supercritical Water in a Tube

  • Lee Sang-Ho
    • International Journal of Air-Conditioning and Refrigeration
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    • v.13 no.4
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    • pp.206-216
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    • 2005
  • Numerical analysis has been carried out to investigate laminar convective heat transfer at zero gravity in a tube for supercritical water near the thermodynamic critical point. Fluid flow and heat transfer are strongly coupled due to large variation of thermodynamic and transport properties such as density, specific heat, viscosity, and thermal conductivity near the critical point. Heat transfer characteristics in the developing region of the tube show transition behavior between liquid-like and gas-like phases with a peak in heat transfer coefficient distribution near the pseudo critical point. The peak of the heat transfer coefficient depends on pressure and wall heat flux rather than inlet temperature and Reynolds number. Results of the modeling provide convective heat transfer characteristics including velocity vectors, temperature, and the properties as well as the heat transfer coefficient. The effect of proximity on the critical point is considered and a heat transfer correlation is suggested for the peak of Nusselt number in the tube.

On the Critical Behavior of Phase Changes of a Forward-Scattered Light in a Nonpolar Binary Liquid Mixture

  • Kim, Kyoung-Ran;Kang, Young-Soo;Lee, Dong-J.
    • Bulletin of the Korean Chemical Society
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    • v.23 no.12
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    • pp.1749-1753
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    • 2002
  • The effect of concentration fluctuations on the changes of azimuth and ellipticity are analytically obtained in a binary chiral liquid mixture, when the incident light is completely linearly polarized above (or below) the horizontal at 45°. The important results are as follows;(1) When the binary liquid is in the critical region far from the cr5itical point, the ellipticity change is proportional to isothermal compressibility factor and the fifth order of frequency and shows the logarithmic divergence. (2) In the case that the system is in the critical region far from the critical point, the azimuth change is solely due to the molecular contribution. As the system approaches to the critical point, the effect of fluctuations becomes important. If it is in the extreme close to the critical point, the term due to the concentration fluctuations is comparable to or larger than the molecular contribution.

A Study on the Laminar Flow Field and Heat Transfer Coefficient Distribution for Supercritical Water in a Tube (초임계상태의 물에 대한 관 내 층류유동장 및 열전달계수 분포특성에 관한 연구)

  • 이상호
    • Korean Journal of Air-Conditioning and Refrigeration Engineering
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    • v.15 no.9
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    • pp.768-778
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    • 2003
  • Numerical analysis has been carried out to investigate laminar convective heat transfer in a tube for supercritical water near the thermodynamic critical point. Fluid flow and heat transfer are strongly coupled due to large variations of thermodynamic and transport properties such as density, specific heat, viscosity, and thermal conductivity near the critical point. Heat transfer characteristics in the developing region of the tube show transition behavior between liquid-like and gas-like phases with a peak in heat transfer coefficient distribution near the pseudocritical point. The peak of the heat transfer coefficient depends on pressure and wall heat flux rather than inlet temperature and Reynolds number, Results of the modeling provide convective heat transfer characteristics including velocity vectors, temperature, and the properties as well as the heat transfer coefficient. The effect of proximity to the critical point is considered and a heat transfer correlation is suggested for the peak of Nusselt number in the tube.