• Journal of Industrial Technology
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• v.19
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• pp.253-260
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• 1999

Two thermodynamic models were used to predict the partial molar volumes of solutes in supercritical carbon dioxide at infinite dilution: (1) the Peng-Robinson equation of state with various mixing rules including those based on $EOS/G^E$ (2) the Kirkwood Buff fluctuation integral with the hard sphere expansion (HSE) method. The Kirkwood-Buff fluctuation integral method, in which an equation of state for pure component and molecular parameters are required, produced better results especially near the critical point than the Peng-Robinson equation of state with the several mixing rules based an $EOS/G^E$. When the $EOS/G^E$ mixing rules were used, poorer results were obtained compared with the classical mixing rule and Kirkwood-Buff model.

• Proceedings of the Korean Society of Propulsion Engineers Conference
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• 2017.05a
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• pp.1077-1079
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• 2017

The cavitation in the turbopump inducer progresses from the inception to the critical point, and finally develops to a breakdown which sharply declined in head. In this paper, we evaluated characteristics and predicted empirical equations about the cavitation inception of a turbopump inducer. The empirical equation of the cavitation inception for the elliptical plate was relatively well predicted to the turbopump inducer. However, in case of the marine propeller, it showed a big difference due to Reynolds number under the operating point.

• Journal of the Korean Society of Propulsion Engineers
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• v.23 no.1
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• pp.93-100
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• 2019

The cavitation of a turbopump inducer develops from the inception to a critical point, and encounters breakdown finally. In this study, we evaluated the characteristics and predictions of cavitation inception for the turbopump inducer using empirical equations. The empirical equation for the elliptical plate predicted the generation of cavitation inception of the turbopump inducer relatively well. However, in case of the marine propeller, it showed a considerable difference owing to the Reynolds number of the operating point. The cavitation inception occurred earlier as the number of blades increased. However, the solidity had no major impact on the cavitation inception because the cavitation occurred locally at the tip of the leading edge.

• Journal of the Korean Mathematical Society
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• v.57 no.6
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• pp.1451-1470
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• 2020

We are concerned with the following elliptic equations: $$\{(-{\Delta})^s_pu={\lambda}f(x,u)\;{\text{in {\Omega}}},\\u=0\;{\text{on {\mathbb{R}}^N{\backslash}{\Omega}},$$ where λ are real parameters, (-∆)^s_p is the fractional p-Laplacian operator, 0 < s < 1 < p < + ∞, sp < N, and f : Ω × ℝ → ℝ satisfies a Carathéodory condition. By applying abstract critical point results, we establish an estimate of the positive interval of the parameters λ for which our problem admits at least one or two nontrivial weak solutions when the nonlinearity f has the subcritical growth condition. In addition, under adequate conditions, we establish an apriori estimate in L^∞(Ω) of any possible weak solution by applying the bootstrap argument.

• Journal of the Korean Mathematical Society
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• v.57 no.6
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• pp.1435-1449
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• 2020

In this article we make a local classification of n-dimensional Riemannian manifolds (M, g) with harmonic curvature and less than four Ricci eigenvalues which admit a smooth non constant solution f to the following equation $$(1)\hspace{20}{\nabla}df=f(r-{\frac{R}{n-1}}g)+x{\cdot} r+y(R)g,$$ where ∇ is the Levi-Civita connection of g, r is the Ricci tensor of g, x is a constant and y(R) a function of the scalar curvature R. Indeed, we showed that, in a neighborhood V of each point in some open dense subset of M, either (i) or (ii) below holds; (i) (V, g, f + x) is a static space and isometric to a domain in the Riemannian product of an Einstein manifold N and a static space (W, gW, f + x), where gW is a warped product metric of an interval and an Einstein manifold. (ii) (V, g) is isometric to a domain in the warped product of an interval and an Einstein manifold. For the proof we use eigenvalue analysis based on the Codazzi tensor properties of the Ricci tensor.

• Communications of the Korean Mathematical Society
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• v.37 no.1
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• pp.137-161
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• 2022

In this article, we study the existence and multiplicity of homoclinic solutions for the following fourth-order differential equation (1) u⁽⁴⁾(x) + ωu''(x) + a(x)u(x) = f(x, u(x)), ∀x ∈ ℝ where a(x) is not required to be either positive or coercive, and F(x, u) = ∫^u₀ f(x, v)dv is of subquadratic or superquadratic growth as |u| → ∞, or satisfies only local conditions near the origin (i.e., it can be subquadratic, superquadratic or asymptotically quadratic as |u| → ∞). To the best of our knowledge, there is no result published concerning the existence and multiplicity of homoclinic solutions for (1) with our conditions. The proof is based on variational methods and critical point theory.

• Nuclear Engineering and Technology
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• v.14 no.4
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• pp.186-195
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• 1982

The steam line break accident for Kori Unit 1 is analyzed by a code SYSRAN which calculates nuclear power and heat flux using the point kinetics equation and the lumped-parameter model and calculates system transient using the mass and energy balance equation with the assumption of uniform reactor coolant system pressure. The 1.4 f $t^2$ steam line break accident is analyzed at EOL (End of Life), hot shutdown condition in which case the accident would be most severe. The steam discharge rate is assumed to follow the Moody critical flow model. The results reveal the peak heat flux of 38% of nominal full power value at 60 second after the accident initiates, which is higher than the FSAR result of 26%. Trends for the transient are in good agreement with FSAR results. A sensitivity study shows that this accident is most sensitive to the moderator density coefficient and the lower plenum mixing factor. The DNBR calculation under the assumption of $F_{{\Delta}H}$=3.66, which is used in the FSAR with all the control and the shutdown assemblies inserted except one B bank assembly and of Fz=1.55 shows that minimum DNBR reaches 1.62 at 60 second, indicating that the fuel failure is not anticipated to occur. The point kinetics equation, the lumped-parameter model and the system transient model which uses the mass and energy balance equation are verified to be effective to follow the system transient phenomena of the nuclear power plants.lear power plants.

• Applied Chemistry for Engineering
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• v.17 no.6
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• pp.625-632
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• 2006

Dependence of the critical micelle concentration (CMC) on temperature is examined from a statistical-mechanical point of view. A simple and primitive model examined in this article yields ln CMC= A+BT+C/T+D ln T with T being temperature and A, B, C, D being constants depending on the properties of the surfactant molecules which comprise the micelles. The resulting equation combines Muller's and Lim's equations, which have already been proven to fit well measured CMC data with temperature. The statistical-mechanical model on micellization discussed in this article provides a theoretical basis on these equations.

• Journal of Korean Association for Spatial Structures
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• v.18 no.3
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• pp.83-91
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• 2018

In this study, we investigated the dynamic stability of the system and the semi-analytical solution of the shallow arch. The governing equation for the primary symmetric mode of the arch under external load was derived and expressed simply by using parameters. The semi-analytical solution of the equation was obtained using the Taylor series and the stability of the system for the constant load was analyzed. As a result, we can classify equilibrium points by root of equilibrium equation, and classified stable, asymptotical stable and unstable resigns of equilibrium path. We observed stable points and attractors that appeared differently depending on the shape parameter h, and we can see the points where dynamic buckling occurs. Dynamic buckling of arches with initial condition did not occur in low shape parameter, and sensitive range of critical boundary was observed in low damping constants.

• The Journal of the Acoustical Society of Korea
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• v.37 no.1
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• pp.1-11
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• 2018

Sound propagation in shallow water changes from spherical spreading to cylindrical spreading, depending on boundary conditions, and this point is defined as a transition point of the sound propagation condition. Theoretically, the transition point can be estimated using the transmission loss as a function of source-receiver range. In this paper, the transmission loss curve in a Pekeris waveguide is predicted using a parabolic-equation based acoustic propagation model and using this transmission loss curve, the range from the source of the transition point is estimated, which is compared to the critical distance calculated using the sound speed ratio of water to sediment. In addition, the effects of the sound speed profile and source depth change on the transition point are investigated. Finally, the transition point is estimated using the transmission loss data measured during the period of the SAVEX15 (Shallow Water Acoustic Variability EXperiment 2015) conducted 65 km southwest of Jeju Island in May 2015, and it is compared to the ocean environmental parameters to understand the properties of sound propagation in the experimental area.