• Water Engineering Research
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• 제1권2호
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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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• 제17권4호
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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.

• 대한수학회지
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• 제51권1호
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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.

• 한국산업융합학회 논문집
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• 제2권2호
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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.

• 산업기술연구
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• 제30권B호
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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.

• 한국지반공학회논문집
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• 제19권1호
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• pp.61-75
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• 2003

한계상태 토질역학을 사질토의 전단거동에 대한 적용을 용이하게 하기 위해서, 표준삼축 시험으로부터 사질토에서의 한계상태정수 결정에 관하여 종합적인 고찰을 실시하였다. 첫째로, 문헌에 있는 어휘론적인 차이점들을 명확히 함으로써, 한계상태는 대변형에서의 궁극적인 최종상태를 나타냄을 추론하였다. 둘째로, 한계상태정수의 특성들에 관하여 검토하였고, 초기상태, 구주 하중조건 및 배수조건에 따른 한계상태선의 유일성과 유사한계상태조건의 민감성을 검증하였다. 셋째로, 한계상태정수로부터 액상화후 전단강도 즉 액상화된 흙에서의 신뢰할 수 있는 궁극적인 전단강도를 산정하기 위하여 한계상태 토질역학을 예제로서 적용하였다.

• 대한수학회보
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• 제37권3호
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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.

• 한국농공학회논문집
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• 제63권5호
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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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• 제12권4호
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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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• 제19권11호
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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.