• Bulletin of the Korean Mathematical Society
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• v.32 no.2
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• pp.171-177
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• 1995

Let P be a finite poset and let $\mid$P$\mid$ be the number of vertices in pp. A subposet of P is a subset of P with the induced order. A chain C in P is a subposet of P which is a linear order. The length of the chain C is $\mid$C$\mid$ - 1. A linear extension of a poset P is a linear order $L = x_1, x_2, \ldots, x_n$ of the elements of P such that $x_i < x_j$ is P implies i < j. Let L(P) be the set of all linear extensions of pp. E. Szpilrajn [5] showed that L(P) is not empty.

• Journal of Mechanical Science and Technology
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• v.19 no.2
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• pp.664-673
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• 2005

The heat transfer characteristics of rarefied flows in a micro-actuator are studied numerically. The effect of Knudsen number (Kn) on the heat transfer of the micro-actuator flows is also examined. The Kn based on gas density and characteristic dimension is varied from near-continuum to highly rarefied conditions. Direct simulation Monte Carlo calculations have been performed to estimate the performance of the micro-actuator. The results show that the magnitude of the temperature jump at the wall increases with Kn. Also, the heat transfer to the isothermal wall is found to increase significantly with Kn.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.24 no.1
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• pp.103-119
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• 2020

In this work, the hydromagnetic and thermal characteristics of natural convection flow in a vertical parallel plate micro-porous-channel with suction/injection is analytically studied in the presence of Hall current by taking the temperature jump and the velocity slip at the wall into account. The governing equations, exhibiting the physics of the flow formation are displayed and the exact analytical solutions have been obtained for momentum and energy equations under relevant boundary conditions. The impact of distinct admissible parameters such as Hartmann number, Hall current parameter, permeability parameter, suction/injection parameter, fluid wall interaction parameter, Knudsen number and wall-ambient temperature ratio on the flow formation is discussed with the aid of line graphs. In particular, as rarefaction parameter on the micro-porous-channel surfaces increases, the fluid velocity increases and the volume flow rate decreases for injection/suction.

• Journal of the Korean Society of Industry Convergence
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• v.7 no.1
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• pp.5-11
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• 2004

벽면에 충돌하는 액체 분무의 충돌 거동과 액적 비산에 관하여 실험을 통하여 조사하였다. 액체 분무는 홀노즐에 의해 직경 40mm의 충돌판에 분사하게 된다. 액체 분무는 반경방향으로 퍼져나가 5개의 영역으로 분류되어 나타내게 된다. 난류 혹은 층류 분무의 경우, 충돌판에 충돌한 후 두꺼운 액막을 형성하게 되며, 이러한 상태에서 충돌하는 분무의 비산량은 매우 적으며 충돌 거리에 영향을 받지 않는다. 한편, 파동이 있는 분무의 충돌은 수력도약(Hydraulic jump)과 함께 반경방향으로 엷은 액막을 형성하게 되며 비산율도 증가하게 된다. 액체분무의 초속도가 증가하면 비산율도 증가하게 된다. 분열이 일어난 후에 충돌하는 파동 분무의 비산율은 분열이 일어나기 전에 비해 약 2~3배 정도 크게 나타난다. 비산율은 웨버수(Weber number)를 이용하여 요약할 수가 있다.

• Proceedings of the Korean Society of Propulsion Engineers Conference
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• 2012.05a
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• pp.309-317
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• 2012

Recent years have witnessed the use of micro shock tube in various engineering applications like micro combustion, micro propulsion, particle delivery systems etc. The flow characteristics occurring in the micro shock tube shows a considerable deviation from that of well established conventional macro shock tube due to very low Reynolds number and high Knudsen number effects. Also the diaphragm rupture process, which is considered to be instantaneous process in many of the conventional shock tubes, will be crucial for micro shock tubes in determining the near diaphragm flow field and shock formation. In the present study, an axi-symmetric CFD method has been applied to simulate the micro shock tube, with Maxwell's slip velocity and temperature jump boundary conditions. The effects of finite diaphragm rupture process on the flow field and the shock formation was investigated, in detail. The results show that the shock strength attenuates rapidly as it propagates through micro shock tubes.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.31 no.8
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• pp.702-710
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• 2007

Direct numerical simulation (DNS) is performed to investigate suppressed wake transition and occurrence of lock-on in the wake of a circular cylinder disturbed by sinusoidal perturbation at the Reynolds number of 220 (A-mode instability regime). The sinusoidal perturbation, of which the frequency is near twice the natural shedding frequency, is superimposed on the free stream velocity. It is shown that the wake transition behind the circular cylinder can be suppressed due to the perturbation of the free stream velocity. This change causes a jump in the Strouhal number from the value corresponding to A-mode instability regime to the value corresponding to retarded wake transition regime (extrapolated from laminar shedding regime) in the Strouhal-Reynolds number relationship. As a result, vortex shedding frequency is locked on the perturbation frequency depending not on the natural shedding frequency but on the modified shedding frequency.

• Journal of the Korean Mathematical Society
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• v.54 no.2
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• pp.461-477
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• 2017

A dual substructuring method with a penalty term was introduced in the previous works by the authors, which is a variant of the FETI-DP method. The proposed method imposes the continuity not only by using Lagrange multipliers but also by adding a penalty term which consists of a positive penalty parameter ${\eta}$ and a measure of the jump across the interface. Due to the penalty term, the proposed iterative method has a better convergence property than the standard FETI-DP method in the sense that the condition number of the resulting dual problem is bounded by a constant independent of the subdomain size and the mesh size. In this paper, a further study for a dual iterative substructuring method with a penalty term is discussed in terms of its convergence analysis. We provide an improved estimate of the condition number which shows the relationship between the condition number and ${\eta}$ as well as a close spectral connection of the proposed method with the FETI-DP method. As a result, a choice of a moderately small penalty parameter is guaranteed.

• Journal of the Korean School Mathematics Society
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• v.17 no.2
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• pp.235-249
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• 2014

In this paper, teaching contents in area between Korea and Japan's first grade math textbooks are compared. Based on the results of this comparison, implications for improving our grade 1 math textbooks are obtained as follows. Firstly, when describing the configuration of two-digit numbers, it needs to be considered that, after the mathematical description of a concrete material representing two-digit numbers, then it should be processed mathematically. Secondly, with respect to the composition and decomposition of numbers, use of the expression of 'some number and some number' needs to be considered. Thirdly, when reading addition expression and subtraction expression with an equal sign, the way of reading them with terms 'sum' and 'difference' respectively needs to be reconsidered. Fourthly, use of the distinct expression for the supplementing situation and the merging situation respectively and use of the distinct expression for the removing situation and the comparing situation respectively need to be considered. Fifthly, the jump in representing the expression of subtraction of two numbers as the expression of the subtraction or mixed operation of three numbers to explain (some number)-(some number) with borrowing need to be resolved.

• Atmosphere
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• v.16 no.2
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• pp.67-83
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• 2006

The statistical analysis for the springtime windstorm in Korea shows that Yeongdong region has the highest occurrence frequency during recent 10 years. The objective of this study is to find possible mechanisms for the downslope windstorm formation in the Yeongdong region by using a mesoscale numerical model, WRF. Dynamical process, wave breaking (hereafter WB), is qualitatively investigated as the candidate mechanism for a windstorm event occurred in 5 April, 2005. WB is developed in upper troposphere downstream, since stable air is lifted by the Taebaek mountain. This process can cause and maintain the severe downslope windstorm by drawing the upper flow down to the surface. And the intensified downslope wind leads the hydraulic jump (hereafter HJ) in downstream region. Froude numbers at Chuncheon (upslope side), Seorak Mountain (crest), Yangyang (lee side), and the East Sea (distant downstream position) are estimated by about 0.4, 1.0, 1.6, and 0.6, respectively. This result implies that the accelerated and supercritical (Fr>1) flow adjusts to the ambient subcritical (Fr<1) conditions in the turbulent HJ. In addition, we find the formation of upstream inversion near top level of the mountain cause the intensification of HJ. Experiments to examine the orographic effect on the mechanisms suggest that the magnitudes of WB and HJ are larger in the experiment of higher topography, but there is no significant difference of windstorm magnitude among the experiments. Another important result from these sensitivity experiments is that the intensity of downslope windstorm strongly depends on the magnitude of upper (2~4 km) wind in upstream side.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.47 no.1
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• pp.9-16
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• 2019

In the present study, to investigate flows around space launch vehicles at mid-high altitudes efficiently, a three-dimensional unstructured mesh Navier-Stokes solver employing a Maxwell slip boundary condition was developed. Validation of the present flow solver was made for a blunted cone-tip configuration by comparing the results with those of the DSMC simulation and experiment. It was found that the present flow solver works well by capturing the velocity slip and the temperature jump on the solid surface more efficiently than the DSMC simulation. Flow simulations of space launch vehicles were conducted by using the flow solver. Mach number of 6 at the mid-high altitude around 86km was considered, and the flow phenomena at the mid-high altitude was discussed.