• Water Engineering Research
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• v.1 no.2
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• pp.119-127
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• 2000

In the process of crossflow microfiltration, a deposit of cake layer tends to form on the membrane, which usually controls the performance of filtration. It is found, however, that there exist a condition under which no deposit of cake layer is made. This condition is called the sub-critical flux condition, and the critical flux here means a flux below which a decline of flux with time due to the deposit of cake layer does not occur. In order to study the characteristics of the critical flux, a numerical model is developed to predict the critical flux condition, and is verified with experimental results. For development of the model, the concept of effective particle diameter is introduced to find a representative size of various particles in relation to diffusive properties of particles. The model is found to be in good match with the experimental results. The findings from the use of the model include that the critical flux condition is determined by the effective particle diameter and the ratio of initial permeate flux to crossflow velocity.

• Korean Journal of Mathematics
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• v.17 no.4
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• pp.461-471
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• 2009

Let ${\Omega}$ be a bounded subset of $R^n$ with smooth boundary and H be a Sobolev space $W_0^{1,2}({\Omega})$. Let $I{\in}C^{1,1}$ be a strongly definite functional defined on a Hilbert space H. We investigate the conditions on which the functional I satisfies the Palais-Smale condition. Palais-Smale condition is important for determining the critical points for I by applying the critical point theory.

• Journal of the Korean Mathematical Society
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• v.51 no.1
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• pp.55-65
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• 2014

A graph G is called a fractional (g, f, n)-critical graph if any n vertices are removed from G, then the resulting graph admits a fractional (g, f)-factor. In this paper, we determine the new toughness condition for fractional (g, f, n)-critical graphs. It is proved that G is fractional (g, f, n)-critical if $t(G){\geq}\frac{b^2-1+bn}{a}$. This bound is sharp in some sense. Furthermore, the best toughness condition for fractional (a, b, n)-critical graphs is given.

• Journal of the Korean Society of Industry Convergence
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• v.2 no.2
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• pp.73-81
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• 1999

Shake mixing has been widely used in cell culture. The mixing performance for shake mixing, however, has not been reported quantitatively. The critical circulating frequency and the power consumption for complete suspension of particles, based on the definition of Zwietering, were measured in a shaking vessel containing a solid-liquid system. The critical suspension frequency was correlated by the equation from Baldi's particle suspension model modified with the physical properties of the particles. Critical suspension frequency was correlated as following ; $$N_{JS}={\frac{0.58\;d{_p}^{0.06}(g{\Delta}{\rho}/{\rho}_L)^{0.004}X^{0.03}}{D^{0.35}d^{0.17}{\upsilon}^{0.04}}}$$ The power consumption at the critical suspension condition in the shaking vessel was less than that in an agitated vessel with impeller.

• Journal of Industrial Technology
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• v.30 no.B
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• pp.17-23
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• 2010

Since the propagation of a short fatigue crack is directly related to the large crack which causes the fracture of bulk specimen, the detailed study on the propagation of the short crack is essential to prevent the fatigue fracture. However, a number of recent studies have demonstrated that the short crack can grow at a low applied stress level which are predicted from the threshold condition of large crack. In present study, the threshold condition for the propagation of short fatigue crack is examined with respect to the micro-structure and cyclic loading history. Specimens employed in this study were decarburized eutectoid steels which have various decarburized ferrite volume fraction. Rotating bending fatigue test was carried out on these specimens with the special emphasis on the "critical non-propagating crack length" It is found that the reduction of the endurance limit of their particular micro-structures can be due to the increase of the length of critical non-propagating crack, and the quantitative relationship between the threshold stress ${\sigma}_{wo}$ and the critical non-propagating crack length $L_c$ can be written as ${\sigma}_{wo}{^m}{\cdot}L_c=C$ where m,C is constant. Further experiments were carried out on cyclic loading history on the length of critical non-propagating crack. It shown that the length of critical non-propagating crack is closely related to cyclic loading history.

• Journal of the Korean Geotechnical Society
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• v.19 no.1
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• pp.61-75
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• 2003

Comprehensive review on the determination of critical state parameters in sandy soils from standard triaxial testing was performed to facilitate the application of critical state soil mechanics to the shear behavior of sandy soils. First, semantic differences in literature were clarified, inferring that critical state should be considered as the ultimate state at large deformation. Second, the characteristics of critical state parameters were discussed, and also the uniqueness of critical state line and the sensitivity of quasi-steady state condition were verified in relation to initial state, fabric, loading condition, and drainage condition. Third, as an example, the critical state soil mechanics was applied to evaluate the post-liquefaction shear strength, i.e. the reliable ultimate shear strength in liquified soils, in terms of critical state parameters.

• 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.

• Journal of The Korean Society of Agricultural Engineers
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• v.63 no.5
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• pp.27-38
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• 2021

The physical condition assessment criteria of fill dam safety inspection are now weakly regulated and inappropriate for small agricultural reservoirs since these criteria have fundamental backgrounds suitable for large-scale dams. This study proposes the degree (critical values) of defects for the quantitative condition assessment of the embankment in order to prepare the condition assessment criteria for a small reservoir with a storage capacity of less than one (1) million cubic meters. The critical values of defects were calculated by applying the method that considers the size ratios based on the dimensional data of reservoirs, and the method of statistical analysis on the measured values of the defect degree which extracted from comprehensive annual reports on reservoir safety inspection. In comparison with the current criteria, the newly proposed critical values for each condition assessment item of the reservoir embankment are presented in paragraphs 4 and 6 of the conclusion. In addition, this study presents a method of displaying geometric figures to clarify the rating classification for condition assessment items with the two defect indicators.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.12 no.4
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• pp.239-247
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• 2008

Let $I{\in}C^{1,1}$ be a strongly indefinite functional defined on a Hilbert space H. We investigate the number of the critical points of I when I satisfies two pairs of Torus-Sphere variational linking inequalities and when I satisfies m ($m{\geq}2$) pairs of Torus-Sphere variational linking inequalities. We show that I has at least four critical points when I satisfies two pairs of Torus-Sphere variational linking inequality with $(P.S.)^*_c$ condition. Moreover we show that I has at least 2m critical points when I satisfies m ($m{\geq}2$) pairs of Torus-Sphere variational linking inequalities with $(P.S.)^*_c$ condition. We prove these results by Theorem 2.2 (Theorem 1.1 in [1]) and the critical point theory on the manifold with boundary.

• Journal of Mechanical Science and Technology
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• v.19 no.11
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• pp.2077-2081
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• 2005

A symmetry breaking nonlinear fluid flow in a two-dimensional wall-driven square cavity taking symmetric boundary condition after some transients has been investigated numerically. It has been shown that the symmetry breaking critical Reynolds number is dependent on the time history of the boundary condition. The cavity has at least three stable steady state solutions for Re=300-375, and two stable solutions if Re>400. Also, it has also been showed that a particular solution among several possible solutions can be obtained by a controlled boundary condition.